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Europe, Measured

ESS-03 / The social contract / Published research

When the economy loses legitimacy

The lower end is steeper: 1.99 democratic-satisfaction points for an economic-score step from 2 to 5, versus 1.56 for 5 to 8. The bend remains after accounting for countries.

A bend in a model is not a proven tipping point. These are perceptions of how democracy works, not a measure of allegiance to democracy.

Inspect the assumption

The observation

Lower economic satisfaction is associated with lower democratic satisfaction. The steps are not all equivalent.

The test

Hold the survey wave in view. Compare a single slope with a fixed flexible curve, then inspect the same respondents under further adjustment.

The boundary

The model does not identify what would happen if policy changed the economy, or where a sharp democratic tipping point lies.

An unfavorable view of the economy and disappointment with democratic performance can appear in the same interview. How closely do those judgments line up, and does the relationship look the same among people who are deeply dissatisfied and those who are relatively content?

In the pinned Round 11 European Social Survey, equal differences in economic satisfaction correspond to unequal differences in satisfaction with democracy. The fitted democratic-satisfaction difference is 1.99 points between economic ratings of 2 and 5, compared with 1.56 between 5 and 8. That is a bend in the association, not an identified point at which democracy loses legitimacy.

The comparison uses 47,836 paired responses across 30 countries in ESS Round 11, edition 4.2, conventionally labeled 2023/24. The whole source release spans March 11, 2023, to December 1, 2024. These are survey-period judgments, not a reading of public opinion in 2026.

The useful question is whether a straight line conceals something consequential, and whether the bend survives more demanding comparisons. We begin with the answers people actually gave, then ask what a model adds, which assumptions it needs, and where it stops being informative. Keep one country and round in view while examining those assumptions. France in Round 11 provides a concrete example; the headline remains the registered multi-country result.

The model desk

Keep one comparison. Change the assumption.

The estimates are already calculated and reviewed. These controls select evidence; they do not refit a model or move a threshold.

Preparing the reviewed comparison...

The comparison you are carrying

France / Round 11

2023/24 / Flexible curve within countries

Economic satisfaction score
50-10 response scale
Observed democratic mean
5.10France95%: 4.78 to 5.42
Selected fitted mean
5.17France95%: 5.05 to 5.29

1,697 paired responses in the observed scope; 284 at score 5. Model sample: 47,836 respondents across 30 countries.

Country-adjusted models assume a shared curve with different country intercepts. Selecting a country does not estimate a separate national slope. Different question constructs, not an objective democracy score or a causal effect.

Start with the answers, before trusting the curve

The two questions share a scale, but not a subject. One asks about the present state of the country's economy; the other asks about the way democracy works. Both run from 0, "Extremely dissatisfied," to 10, "Extremely satisfied." Dissatisfaction with democratic performance is not necessarily rejection of democracy as a regime, and neither response is an objective measure of institutional quality.

The mean compresses those answers into one number. The distribution layer restores the eleven actual categories, using the same paired-response population for both questions. The paired-response matrix asks a different question: which answers occur together? Its joint view shows a pair's share of all paired respondents; its conditional view changes the denominator to respondents at one economic score. Those percentages are not interchangeable, and a confidence interval around a mean is not the spread of people's answers.

Across the 30 included Round 11 countries, 31.0% of paired respondents give democratic performance a rating at or below 3 under the original ESS analysis weights (95% interval: 30.1% to 31.9%). That is a declared part of the response distribution, not a diagnosis of opposition to democracy. The weighted share and the unweighted count answer different questions.

The people behind the mean / exploratory extension

Look behind the average.

A confidence interval around a mean is not the distribution of respondents. Here, each probability refers to actual answer categories and an explicit survey population.

France / Round 11 / 2023/24

Paired responses
1,697Unweighted respondents with both valid answers
Paired share of the eligible design
95.0%Survey-weighted response coverage, not a country population total
Complete adjustment records
1,676The complete-case domain is smaller than, or equal to, the paired domain

Distribution laboratory / marginal distributions

Two paired-response distributions on their original 0–10 scales

France / ESS Round 11 (2023/24). Weighted category shares use the same 1,697 matched paired responses; they are discrete response probabilities, not smoothed densities.

  • Economic satisfactionGold comparison columns; square interval caps.
  • Democratic satisfactionBlue primary columns; round interval mark.
Weighted economic and democratic satisfaction distributionsTwo weighted discrete distributions across the original response scores zero to ten. Bars begin at zero. Whiskers are survey-design 95% pointwise intervals. Missing estimates have no bar, and sample-boundary estimates have no population interval.Weighted share of matched paired responses0.0%5.0%10.0%15.0%20.0%012345678910Response score: 0 extremely dissatisfied · 10 extremely satisfied

Use Left/Right to move across scores and Up/Down to switch questions; Home/End moves to the ends of the current series. Enter/Space or a tap pins; Escape dismisses and restores focus. Pointer movement only inspects. Only an explicit Follow action changes the selected evidence.

Unavailable or suppressed estimates are labelled NA rather than plotted at zero. A sample estimate of 0% or 100% is retained as a boundary observation, but it has no manufactured population interval. Domain n governs precision; sparse event support is reported separately.

Exact weighted marginal estimates, intervals and support
France; ESS Round 11 (2023/24). Probability estimates and pointwise 95% intervals retain their supplied numeric precision. n is the matched-pair domain; events are observed category responses.
ScoreEconomic estimateEconomic 95% intervalEconomic n / eventsEconomic statusDemocratic estimateDemocratic 95% intervalDemocratic n / eventsDemocratic status
00.1237819033 (12.378%)[0.1074421355, 0.142210693]1,697 / 197Estimated. Domain n = 1,697; event n = 197. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1098183603 (10.982%)[0.09433834846, 0.1274809452]1,697 / 181Estimated. Domain n = 1,697; event n = 181. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
10.05308789126 (5.309%)[0.04260179013, 0.06597719558]1,697 / 87Estimated. Domain n = 1,697; event n = 87. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.04564193074 (4.564%)[0.03625620835, 0.05731286331]1,697 / 82Estimated. Domain n = 1,697; event n = 82. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
20.1198181526 (11.982%)[0.1038326512, 0.1378860331]1,697 / 213Estimated. Domain n = 1,697; event n = 213. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.09846198929 (9.846%)[0.0845091991, 0.1144304956]1,697 / 168Estimated. Domain n = 1,697; event n = 168. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
30.1740776077 (17.408%)[0.1567501986, 0.1928822932]1,697 / 301Estimated. Domain n = 1,697; event n = 301. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1465745434 (14.657%)[0.1291239164, 0.1659341985]1,697 / 241Estimated. Domain n = 1,697; event n = 241. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
40.1604273978 (16.043%)[0.1431115342, 0.1793997613]1,697 / 277Estimated. Domain n = 1,697; event n = 277. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1169758834 (11.698%)[0.1019462863, 0.133890895]1,697 / 198Estimated. Domain n = 1,697; event n = 198. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
50.1713445645 (17.134%)[0.1525788856, 0.1918955977]1,697 / 284Estimated. Domain n = 1,697; event n = 284. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1699719709 (16.997%)[0.1507988742, 0.1910344148]1,697 / 288Estimated. Domain n = 1,697; event n = 288. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
60.09724588856 (9.725%)[0.08286395071, 0.1138142031]1,697 / 171Estimated. Domain n = 1,697; event n = 171. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1027814875 (10.278%)[0.08930975192, 0.1180219835]1,697 / 181Estimated. Domain n = 1,697; event n = 181. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
70.07142327517 (7.142%)[0.05984600008, 0.08503761021]1,697 / 120Estimated. Domain n = 1,697; event n = 120. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1165410799 (11.654%)[0.102460045, 0.1322720781]1,697 / 204Estimated. Domain n = 1,697; event n = 204. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
80.02152172488 (2.152%)[0.01491315407, 0.03096673908]1,697 / 35Estimated. Domain n = 1,697; event n = 35. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.06274553676 (6.275%)[0.05090743407, 0.07711282577]1,697 / 107Estimated. Domain n = 1,697; event n = 107. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
90.003502736343 (0.350%)[0.001620578217, 0.00755431427]1,697 / 7Estimated. Domain n = 1,697; event n = 7. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01764435517 (1.764%)[0.01190867402, 0.02606967753]1,697 / 27Estimated. Domain n = 1,697; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
100.003768857978 (0.377%)[0.001443497946, 0.009803411148]1,697 / 5Estimated. Domain n = 1,697; event n = 5. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01284286268 (1.284%)[0.00810017737, 0.02030556247]1,697 / 20Estimated. Domain n = 1,697; event n = 20. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.

Source: European Social Survey, ESS Round 11 (2023/24). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Marginal and joint denominators use all matched pairs; conditional denominators use paired responses at the same economic score. Sources, design and limitations.

Distribution laboratory / paired response matrix

Where paired responses sit across both 0–10 scales

France / ESS Round 11 (2023/24). Joint percentages use all 1,697 matched pairs; conditional percentages use only respondents at the same economic-satisfaction score.

Percentage denominator

Conditional view: each column is a democratic-response distribution within one economic-satisfaction score.

0%51.4%Separate explicit scale for the selected denominator; unavailable cells are hatched.
Economic and democratic satisfaction response matrixAn eleven by eleven table of paired discrete responses. Economic satisfaction runs left to right and democratic satisfaction bottom to top. Cell intensity represents the percentage within the selected economic-score column. Unavailable cells are hatched and never encoded as zero.Economic satisfaction scoreDemocratic satisfaction score001122334455667788991010

Use the arrow keys to move across economic and democratic scores; Home/End moves to the ends of the current democratic row. Enter/Space or a tap pins; Escape dismisses and restores focus. Pointer movement only inspects. Only an explicit Follow action changes the selected evidence.

The matrix describes paired responses, not transitions, flows or causal effects. Joint and conditional percentages use visibly different denominators. Domain precision and sparse event support remain separate; boundary cells do not receive zero-width population intervals. Color locates the responses; the visible interval ledger below carries their precision without requiring hover.

Interval ledger / economic score 5 / conditional share within this economic score
Democratic scoreWeighted estimate95% intervalDomain n / eventsSupport
04.914%95% CI 2.2% to 10.6%284 / 12Estimated
11.191%95% CI 0.4% to 3.2%284 / 4Estimated / sparse events
24.219%95% CI 2.1% to 8.1%284 / 10Estimated
310.813%95% CI 7.6% to 15.2%284 / 31Estimated
410.744%95% CI 7.4% to 15.3%284 / 32Estimated
525.803%95% CI 20.0% to 32.6%284 / 71Estimated
616.212%95% CI 12.1% to 21.4%284 / 49Estimated
714.057%95% CI 10.2% to 19.1%284 / 42Estimated
89.613%95% CI 6.3% to 14.4%284 / 27Estimated
91.114%95% CI 0.2% to 5.8%284 / 3Estimated / sparse events
101.319%95% CI 0.4% to 4.2%284 / 3Estimated / sparse events
Exact 121 paired-response cells, both denominators and intervals
France; ESS Round 11 (2023/24). Every ordered response pair is retained. Joint n is all matched pairs; conditional n is the economic-score domain. Numeric probabilities retain their supplied precision.
Economic scoreDemocratic scoreJoint estimateJoint 95% intervalJoint n / eventsJoint statusConditional estimateConditional 95% intervalConditional n / eventsConditional status
000.06360964673 (6.361%)[0.05133474973, 0.07857654217]1,697 / 101Estimated. Domain n = 1,697; event n = 101. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.5138848656 (51.388%)[0.4375933079, 0.5895348415]197 / 101Estimated. Domain n = 197; event n = 101. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
010.0111810962 (1.118%)[0.006982125149, 0.01785986386]1,697 / 18Estimated. Domain n = 1,697; event n = 18. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.09032900535 (9.033%)[0.05529243365, 0.1441785397]197 / 18Estimated. Domain n = 197; event n = 18. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
020.007509838321 (0.751%)[0.004302385203, 0.01307706168]1,697 / 13Estimated. Domain n = 1,697; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.06066992122 (6.067%)[0.03449862539, 0.1045454328]197 / 13Estimated. Domain n = 197; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
030.01002359149 (1.002%)[0.005829184388, 0.01718392992]1,697 / 15Estimated. Domain n = 1,697; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.08097784267 (8.098%)[0.04740901449, 0.1349484684]197 / 15Estimated. Domain n = 197; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
040.00726282013 (0.726%)[0.003875058342, 0.01357197262]1,697 / 11Estimated. Domain n = 1,697; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.0586743291 (5.867%)[0.03020509012, 0.1109080121]197 / 11Estimated. Domain n = 197; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
050.01367083162 (1.367%)[0.008528597169, 0.02184521335]1,697 / 22Estimated. Domain n = 1,697; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.110442894 (11.044%)[0.06958419749, 0.1708866881]197 / 22Estimated. Domain n = 197; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
060.003076207411 (0.308%)[0.001236612389, 0.007631489336]1,697 / 5Estimated. Domain n = 1,697; event n = 5. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.0248518348 (2.485%)[0.009345401895, 0.06441447492]197 / 5Estimated. Domain n = 197; event n = 5. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
070.005748647952 (0.575%)[0.002805787011, 0.0117417958]1,697 / 9Estimated. Domain n = 1,697; event n = 9. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.04644174794 (4.644%)[0.02262964828, 0.09292784157]197 / 9Estimated. Domain n = 197; event n = 9. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
080.0004576795006 (0.046%)[0.00006371513822, 0.003279620442]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.003697466984 (0.370%)[0.0005031163773, 0.02663274091]197 / 1Estimated. Domain n = 197; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
090.000792190027 (0.079%)[0.0001107765565, 0.005641493882]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.006399885654 (0.640%)[0.0008755814741, 0.04520180347]197 / 1Estimated. Domain n = 197; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
0100.0004493538927 (0.045%)[0.00006277002257, 0.003209163903]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.003630206685 (0.363%)[0.0005036666663, 0.02566653337]197 / 1Estimated. Domain n = 197; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
100.008798034551 (0.880%)[0.005316385548, 0.01452648267]1,697 / 15Estimated. Domain n = 1,697; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1657258245 (16.573%)[0.09834561477, 0.2656684866]87 / 15Estimated. Domain n = 87; event n = 15. Low domain precision: the estimation domain contains 50-99 responses. Event support is not sparse under the reviewed rule.
110.01194726795 (1.195%)[0.007756179376, 0.01836112425]1,697 / 22Estimated. Domain n = 1,697; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2250469489 (22.505%)[0.1478742817, 0.3270374032]87 / 22Estimated. Domain n = 87; event n = 22. Low domain precision: the estimation domain contains 50-99 responses. Event support is not sparse under the reviewed rule.
120.0120715892 (1.207%)[0.007464934227, 0.01946528616]1,697 / 18Estimated. Domain n = 1,697; event n = 18. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2273887494 (22.739%)[0.1441236669, 0.3396676458]87 / 18Estimated. Domain n = 87; event n = 18. Low domain precision: the estimation domain contains 50-99 responses. Event support is not sparse under the reviewed rule.
130.0090560038 (0.906%)[0.005212723562, 0.01568820258]1,697 / 15Estimated. Domain n = 1,697; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1705851106 (17.059%)[0.09737917675, 0.2816519464]87 / 15Estimated. Domain n = 87; event n = 15. Low domain precision: the estimation domain contains 50-99 responses. Event support is not sparse under the reviewed rule.
140.005886963194 (0.589%)[0.003123624273, 0.01106777059]1,697 / 9Estimated. Domain n = 1,697; event n = 9. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.1108908841 (11.089%)[0.05956462764, 0.1971717665]87 / 9Estimated. Domain n = 87; event n = 9. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events.
150.002055007565 (0.206%)[0.0004597132977, 0.009135683987]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.03870953462 (3.871%)[0.00843029094, 0.160175429]87 / 3Estimated. Domain n = 87; event n = 3. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events.
160.0005832332356 (0.058%)[0.00008183533059, 0.004143920948]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.010986182 (1.099%)[0.001456073791, 0.07801804626]87 / 1Estimated. Domain n = 87; event n = 1. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events.
170.002085332046 (0.209%)[0.0006369986858, 0.006804295801]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.0392807474 (3.928%)[0.01176200856, 0.12315931]87 / 3Estimated. Domain n = 87; event n = 3. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events.
180.0006044597142 (0.060%)[0.00008425421818, 0.004322652162]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01138601854 (1.139%)[0.001500013818, 0.08113269106]87 / 1Estimated. Domain n = 87; event n = 1. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events.
190 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.0 (0.000%)Unavailable87 / 0Sample boundary. Domain n = 87; event n = 0. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.
1100 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.0 (0.000%)Unavailable87 / 0Sample boundary. Domain n = 87; event n = 0. Low domain precision: the estimation domain contains 50-99 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.
200.01422265795 (1.422%)[0.009617976133, 0.02098515581]1,697 / 27Estimated. Domain n = 1,697; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1187020301 (11.870%)[0.0803418704, 0.1719531509]213 / 27Estimated. Domain n = 213; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
210.007490645768 (0.749%)[0.004222651967, 0.01325414049]1,697 / 13Estimated. Domain n = 1,697; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.06251678571 (6.252%)[0.03549073151, 0.1078224124]213 / 13Estimated. Domain n = 213; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
220.0254486303 (2.545%)[0.01856159385, 0.03480040261]1,697 / 47Estimated. Domain n = 1,697; event n = 47. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2123937797 (21.239%)[0.159193601, 0.2775048833]213 / 47Estimated. Domain n = 213; event n = 47. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
230.03061612934 (3.062%)[0.02369466391, 0.03947767458]1,697 / 54Estimated. Domain n = 1,697; event n = 54. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2555216274 (25.552%)[0.201415438, 0.3183679374]213 / 54Estimated. Domain n = 213; event n = 54. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
240.01453572858 (1.454%)[0.009157294829, 0.0229997977]1,697 / 23Estimated. Domain n = 1,697; event n = 23. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1213149115 (12.131%)[0.07698180598, 0.1860332906]213 / 23Estimated. Domain n = 213; event n = 23. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
250.01236601088 (1.237%)[0.007944282598, 0.01920120553]1,697 / 22Estimated. Domain n = 1,697; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1032064893 (10.321%)[0.06667181259, 0.1564063917]213 / 22Estimated. Domain n = 213; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
260.00439763733 (0.440%)[0.001944651519, 0.009914086524]1,697 / 8Estimated. Domain n = 1,697; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.03670259669 (3.670%)[0.01650889681, 0.07959809862]213 / 8Estimated. Domain n = 213; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
270.006554261489 (0.655%)[0.003476020063, 0.01232477123]1,697 / 11Estimated. Domain n = 1,697; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.0547017405 (5.470%)[0.02924058258, 0.100048228]213 / 11Estimated. Domain n = 213; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
280.001968808563 (0.197%)[0.0007187817283, 0.005381039505]1,697 / 4Estimated. Domain n = 1,697; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01643163846 (1.643%)[0.005888725109, 0.04499576659]213 / 4Estimated. Domain n = 213; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
290.0008310119216 (0.083%)[0.000205519273, 0.003353789617]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.006935609537 (0.694%)[0.001720948444, 0.0275157359]213 / 2Estimated. Domain n = 213; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
2100.001386630452 (0.139%)[0.0003463951357, 0.005533432974]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01157279112 (1.157%)[0.002835269631, 0.04599494099]213 / 2Estimated. Domain n = 213; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
300.007176669897 (0.718%)[0.003891647009, 0.01319791098]1,697 / 13Estimated. Domain n = 1,697; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.04122684125 (4.123%)[0.02271023156, 0.07370225624]301 / 13Estimated. Domain n = 301; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
310.007270331445 (0.727%)[0.003969730655, 0.0132786052]1,697 / 13Estimated. Domain n = 1,697; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.04176488603 (4.176%)[0.02295156354, 0.07481853173]301 / 13Estimated. Domain n = 301; event n = 13. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
320.02668205027 (2.668%)[0.01976712194, 0.03592729674]1,697 / 47Estimated. Domain n = 1,697; event n = 47. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1532767518 (15.328%)[0.1147240921, 0.2018312258]301 / 47Estimated. Domain n = 301; event n = 47. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
330.04515786141 (4.516%)[0.03528843045, 0.057622692]1,697 / 75Estimated. Domain n = 1,697; event n = 75. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2594122358 (25.941%)[0.2057469663, 0.3214106835]301 / 75Estimated. Domain n = 301; event n = 75. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
340.02440679829 (2.441%)[0.01772789817, 0.03351608514]1,697 / 40Estimated. Domain n = 1,697; event n = 40. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1402064207 (14.021%)[0.1028800452, 0.1882338473]301 / 40Estimated. Domain n = 301; event n = 40. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
350.02746397086 (2.746%)[0.02101656569, 0.03581692978]1,697 / 50Estimated. Domain n = 1,697; event n = 50. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1577685449 (15.777%)[0.1209542992, 0.2031976484]301 / 50Estimated. Domain n = 301; event n = 50. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
360.01419282894 (1.419%)[0.009397217401, 0.02138292195]1,697 / 25Estimated. Domain n = 1,697; event n = 25. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.08153161758 (8.153%)[0.05401798142, 0.1212627132]301 / 25Estimated. Domain n = 301; event n = 25. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
370.0131311359 (1.313%)[0.008636677646, 0.01991748398]1,697 / 22Estimated. Domain n = 1,697; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.07543265371 (7.543%)[0.04926117837, 0.1138435675]301 / 22Estimated. Domain n = 301; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
380.005774631769 (0.577%)[0.003154712841, 0.01054731386]1,697 / 11Estimated. Domain n = 1,697; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.03317274315 (3.317%)[0.01770745785, 0.06130211658]301 / 11Estimated. Domain n = 301; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
390.000880786964 (0.088%)[0.0002118562821, 0.003654129182]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.005059737296 (0.506%)[0.001205236248, 0.02098246312]301 / 2Estimated. Domain n = 301; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
3100.001940541949 (0.194%)[0.0006047908418, 0.006208129087]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01114756789 (1.115%)[0.003484642855, 0.0350686789]301 / 3Estimated. Domain n = 301; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
400.004281330028 (0.428%)[0.001978422559, 0.009240031237]1,697 / 7Estimated. Domain n = 1,697; event n = 7. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.02668702533 (2.669%)[0.01229201121, 0.05696755299]277 / 7Estimated. Domain n = 277; event n = 7. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
410.004807976345 (0.481%)[0.002581316824, 0.00893815364]1,697 / 10Estimated. Domain n = 1,697; event n = 10. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.02996979575 (2.997%)[0.01586139104, 0.05591437011]277 / 10Estimated. Domain n = 277; event n = 10. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
420.01456374589 (1.456%)[0.00945505733, 0.02237038615]1,697 / 24Estimated. Domain n = 1,697; event n = 24. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.09078091458 (9.078%)[0.05964450662, 0.1358238164]277 / 24Estimated. Domain n = 277; event n = 24. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
430.01923283052 (1.923%)[0.01321215348, 0.02791945917]1,697 / 31Estimated. Domain n = 1,697; event n = 31. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1198849498 (11.988%)[0.08267733966, 0.1707209303]277 / 31Estimated. Domain n = 277; event n = 31. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
440.03273926647 (3.274%)[0.02557656196, 0.04182179033]1,697 / 59Estimated. Domain n = 1,697; event n = 59. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2040752822 (20.408%)[0.1616752296, 0.2542229064]277 / 59Estimated. Domain n = 277; event n = 59. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
450.04216947766 (4.217%)[0.03327200819, 0.05331505353]1,697 / 74Estimated. Domain n = 1,697; event n = 74. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.262857082 (26.286%)[0.2123032775, 0.3205500157]277 / 74Estimated. Domain n = 277; event n = 74. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
460.01870405267 (1.870%)[0.01304505298, 0.02675141059]1,697 / 32Estimated. Domain n = 1,697; event n = 32. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1165888928 (11.659%)[0.08197955352, 0.1632116248]277 / 32Estimated. Domain n = 277; event n = 32. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
470.01719953425 (1.720%)[0.01202857838, 0.02453821714]1,697 / 29Estimated. Domain n = 1,697; event n = 29. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.107210704 (10.721%)[0.07500675753, 0.1509844316]277 / 29Estimated. Domain n = 277; event n = 29. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
480.005375236517 (0.538%)[0.002676885043, 0.01076422088]1,697 / 9Estimated. Domain n = 1,697; event n = 9. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.03350572652 (3.351%)[0.01651886893, 0.06677467014]277 / 9Estimated. Domain n = 277; event n = 9. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
490.001353947417 (0.135%)[0.0002921421583, 0.006250806835]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.008439627122 (0.844%)[0.0018004389, 0.03861401556]277 / 2Estimated. Domain n = 277; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
4100 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.0 (0.000%)Unavailable277 / 0Sample boundary. Domain n = 277; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.
500.008419582837 (0.842%)[0.004348183768, 0.01624103009]1,697 / 12Estimated. Domain n = 1,697; event n = 12. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.04913831298 (4.914%)[0.02203966415, 0.1059462708]284 / 12Estimated. Domain n = 284; event n = 12. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
510.00204072411 (0.204%)[0.0007547043971, 0.005506052256]1,697 / 4Estimated. Domain n = 1,697; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01191006039 (1.191%)[0.004377762812, 0.03198593139]284 / 4Estimated. Domain n = 284; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
520.007229312107 (0.723%)[0.0037049035, 0.01405911637]1,697 / 10Estimated. Domain n = 1,697; event n = 10. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.04219166291 (4.219%)[0.0214961222, 0.08115937207]284 / 10Estimated. Domain n = 284; event n = 10. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
530.01852762015 (1.853%)[0.01293844619, 0.02646647696]1,697 / 31Estimated. Domain n = 1,697; event n = 31. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1081307726 (10.813%)[0.07573280928, 0.1521074669]284 / 31Estimated. Domain n = 284; event n = 31. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
540.01840994953 (1.841%)[0.0127420178, 0.02653134808]1,697 / 32Estimated. Domain n = 1,697; event n = 32. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1074440242 (10.744%)[0.0743175081, 0.152897529]284 / 32Estimated. Domain n = 284; event n = 32. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
550.04421287715 (4.421%)[0.03331442365, 0.05846102704]1,697 / 71Estimated. Domain n = 1,697; event n = 71. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2580348976 (25.803%)[0.2001825516, 0.3257960827]284 / 71Estimated. Domain n = 284; event n = 71. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
560.02777913442 (2.778%)[0.02064307214, 0.03728812467]1,697 / 49Estimated. Domain n = 1,697; event n = 49. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1621243983 (16.212%)[0.1208034629, 0.2141367594]284 / 49Estimated. Domain n = 284; event n = 49. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
570.02408573706 (2.409%)[0.0174334806, 0.03319061263]1,697 / 42Estimated. Domain n = 1,697; event n = 42. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1405690174 (14.057%)[0.1016277082, 0.1912550832]284 / 42Estimated. Domain n = 284; event n = 42. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
580.01647173596 (1.647%)[0.01051082559, 0.02572531431]1,697 / 27Estimated. Domain n = 1,697; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.0961322351 (9.613%)[0.06287047892, 0.1442818998]284 / 27Estimated. Domain n = 284; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
590.001908525769 (0.191%)[0.0005383962041, 0.00674188919]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01113852532 (1.114%)[0.00206162909, 0.05786184255]284 / 3Estimated. Domain n = 284; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
5100.0022593654 (0.226%)[0.0007014133851, 0.00725266439]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01318609322 (1.319%)[0.004054069416, 0.04202062434]284 / 3Estimated. Domain n = 284; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
600.002171017121 (0.217%)[0.0007859514403, 0.005982341282]1,697 / 4Estimated. Domain n = 1,697; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.02232502734 (2.233%)[0.008038230609, 0.06045694043]171 / 4Estimated. Domain n = 171; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
610 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.0 (0.000%)Unavailable171 / 0Sample boundary. Domain n = 171; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.
620.002547681407 (0.255%)[0.0009507664137, 0.006808508696]1,697 / 4Estimated. Domain n = 1,697; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.02619834571 (2.620%)[0.009602668107, 0.0694636511]171 / 4Estimated. Domain n = 171; event n = 4. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
630.009973707116 (0.997%)[0.005487112219, 0.0180621865]1,697 / 15Estimated. Domain n = 1,697; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1025617357 (10.256%)[0.05738512962, 0.1766390578]171 / 15Estimated. Domain n = 171; event n = 15. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
640.008832680892 (0.883%)[0.005220848289, 0.01490577318]1,697 / 16Estimated. Domain n = 1,697; event n = 16. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.09082832213 (9.083%)[0.05314121595, 0.1509808888]171 / 16Estimated. Domain n = 171; event n = 16. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
650.01460501088 (1.461%)[0.009906444335, 0.02148372354]1,697 / 27Estimated. Domain n = 1,697; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1501864099 (15.019%)[0.1034887888, 0.2129503965]171 / 27Estimated. Domain n = 171; event n = 27. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
660.01711851808 (1.712%)[0.01163620127, 0.02511814813]1,697 / 30Estimated. Domain n = 1,697; event n = 30. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.176033335 (17.603%)[0.1207428409, 0.2494591371]171 / 30Estimated. Domain n = 171; event n = 30. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
670.02426645865 (2.427%)[0.01737691442, 0.03379360649]1,697 / 45Estimated. Domain n = 1,697; event n = 45. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2495371168 (24.954%)[0.1842460206, 0.3286440619]171 / 45Estimated. Domain n = 171; event n = 45. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
680.01217880586 (1.218%)[0.007742520795, 0.01910803004]1,697 / 21Estimated. Domain n = 1,697; event n = 21. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1252372316 (12.524%)[0.08016763906, 0.1903998165]171 / 21Estimated. Domain n = 171; event n = 21. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
690.00494117502 (0.494%)[0.002429468488, 0.01002351816]1,697 / 8Estimated. Domain n = 1,697; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.05081114578 (5.081%)[0.0251112511, 0.1001123624]171 / 8Estimated. Domain n = 171; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
6100.0006108335263 (0.061%)[0.00008570028093, 0.004339784303]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.006281330093 (0.628%)[0.0008667119877, 0.04403199057]171 / 1Estimated. Domain n = 171; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
700 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.0 (0.000%)Unavailable120 / 0Sample boundary. Domain n = 120; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.
710.0009038889161 (0.090%)[0.0002216572574, 0.003678213899]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01265538319 (1.266%)[0.003046886755, 0.05101421433]120 / 2Estimated. Domain n = 120; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
720.0008299062227 (0.083%)[0.0002057137487, 0.003341741028]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01161954868 (1.162%)[0.002548849612, 0.05130999518]120 / 2Estimated. Domain n = 120; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
730.002083815093 (0.208%)[0.000670685319, 0.006455167591]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.0291755746 (2.918%)[0.009225706846, 0.08841569511]120 / 3Estimated. Domain n = 120; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
740.004901676284 (0.490%)[0.002243061254, 0.01067772359]1,697 / 8Estimated. Domain n = 1,697; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.06862855661 (6.863%)[0.03011262661, 0.1488481986]120 / 8Estimated. Domain n = 120; event n = 8. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
750.01145645088 (1.146%)[0.006561548896, 0.01992968405]1,697 / 16Estimated. Domain n = 1,697; event n = 16. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1604022058 (16.040%)[0.0932675013, 0.2619029563]120 / 16Estimated. Domain n = 120; event n = 16. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
760.01551125205 (1.551%)[0.01074693037, 0.02233999224]1,697 / 29Estimated. Domain n = 1,697; event n = 29. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2171736315 (21.717%)[0.1506034049, 0.3026836045]120 / 29Estimated. Domain n = 120; event n = 29. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
770.01657789909 (1.658%)[0.0113239937, 0.02420972826]1,697 / 30Estimated. Domain n = 1,697; event n = 30. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.2321077975 (23.211%)[0.1622815758, 0.3204845674]120 / 30Estimated. Domain n = 120; event n = 30. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
780.01316760324 (1.317%)[0.008472497437, 0.02041098174]1,697 / 22Estimated. Domain n = 1,697; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.0.1843601153 (18.436%)[0.1187303131, 0.2749493045]120 / 22Estimated. Domain n = 120; event n = 22. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.
790.005078983171 (0.508%)[0.002235559127, 0.01149730511]1,697 / 6Estimated. Domain n = 1,697; event n = 6. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.07111103711 (7.111%)[0.03111126857, 0.15434598]120 / 6Estimated. Domain n = 120; event n = 6. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
7100.0009118002233 (0.091%)[0.0002258936217, 0.003672752416]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.0.01276614971 (1.277%)[0.003110691458, 0.05086263575]120 / 2Estimated. Domain n = 120; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.
800.0006908981655 (0.069%)[0.00009698270393, 0.004904073066]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 1Suppressed. Domain n = 35; event n = 1. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
810 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable35 / 0Suppressed. Domain n = 35; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
820.001579235579 (0.158%)[0.0004664936296, 0.005332076639]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 3Suppressed. Domain n = 35; event n = 3. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
830.001902984454 (0.190%)[0.0003882218981, 0.00927321243]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 2Suppressed. Domain n = 35; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
840 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable35 / 0Suppressed. Domain n = 35; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
850.001142214762 (0.114%)[0.0002744398185, 0.004740870173]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 2Suppressed. Domain n = 35; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
860.001418623399 (0.142%)[0.0003270428414, 0.006131258705]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 2Suppressed. Domain n = 35; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
870.005573830551 (0.557%)[0.002778516099, 0.01114991605]1,697 / 10Estimated. Domain n = 1,697; event n = 10. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.UnavailableUnavailable35 / 10Suppressed. Domain n = 35; event n = 10. The estimation domain contains fewer than 50 responses. Event support is not sparse under the reviewed rule. The estimation domain has fewer than 50 respondents.
880.006746575635 (0.675%)[0.003694919469, 0.01228752884]1,697 / 11Estimated. Domain n = 1,697; event n = 11. Domain support: at least 100 responses. Event support is not sparse under the reviewed rule.UnavailableUnavailable35 / 11Suppressed. Domain n = 35; event n = 11. The estimation domain contains fewer than 50 responses. Event support is not sparse under the reviewed rule. The estimation domain has fewer than 50 respondents.
890.001402891521 (0.140%)[0.0003092136782, 0.006340335307]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 2Suppressed. Domain n = 35; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
8100.001064470816 (0.106%)[0.0002488319328, 0.004541523381]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable35 / 2Suppressed. Domain n = 35; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
900 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
910 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
920 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
930 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
940 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
950.0008301186147 (0.083%)[0.0001153968892, 0.005945217331]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable7 / 1Suppressed. Domain n = 7; event n = 1. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
960 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
970.0009350104079 (0.094%)[0.000232456721, 0.003752920782]1,697 / 2Estimated. Domain n = 1,697; event n = 2. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable7 / 2Suppressed. Domain n = 7; event n = 2. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
980 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable7 / 0Suppressed. Domain n = 7; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
990.0004548433582 (0.045%)[0.00006358670659, 0.003245734795]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable7 / 1Suppressed. Domain n = 7; event n = 1. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
9100.001282763963 (0.128%)[0.0004081153785, 0.004024360601]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable7 / 3Suppressed. Domain n = 7; event n = 3. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1000.0004485230249 (0.045%)[0.00006233670378, 0.003219495203]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable5 / 1Suppressed. Domain n = 5; event n = 1. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1010 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1020 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1030 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1040 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1050 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1060 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1070.0003832324987 (0.038%)[0.00005354537479, 0.002737297218]1,697 / 1Estimated. Domain n = 1,697; event n = 1. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable5 / 1Suppressed. Domain n = 5; event n = 1. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1080 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
1090 (0.000%)Unavailable1,697 / 0Sample boundary. Domain n = 1,697; event n = 0. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events. Observed sample boundary; no population interval is estimable.UnavailableUnavailable5 / 0Suppressed. Domain n = 5; event n = 0. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.
10100.002937102455 (0.294%)[0.0009137197578, 0.009399003704]1,697 / 3Estimated. Domain n = 1,697; event n = 3. Domain support: at least 100 responses. Sparse event support: fewer than 10 events or non-events.UnavailableUnavailable5 / 3Suppressed. Domain n = 5; event n = 3. The estimation domain contains fewer than 50 responses. Sparse event support: fewer than 10 events or non-events. The estimation domain has fewer than 50 respondents.

Source: European Social Survey, ESS Round 11 (2023/24). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Marginal and joint denominators use all matched pairs; conditional denominators use paired responses at the same economic score. Sources, design and limitations.

For France, the observed, survey-weighted democratic-satisfaction mean at economic score 2 is 3.17, with a 95% interval from 2.85 to 3.49, based on 213 paired responses. At score 5, it is 5.10, with an interval from 4.78 to 5.42, based on 284 responses. At score 8 there are only 35 responses, so the public observed mean is suppressed. The gap marks insufficient support for displaying that mean; it is not a zero.

The distributions show how much variation a single curve must summarize. Now the model has to earn its place: does a simple straight line describe the association adequately, or does its convenience hide a meaningful difference?

A straight-line model makes a stronger claim than a general positive association. It requires every additional economic-rating point to correspond to the same fitted difference in democratic satisfaction. Two equal three-score intervals must therefore yield equal differences. Its upper-minus-lower contrast is exactly zero by construction, not because the survey has discovered zero curvature with perfect certainty.

Evidence 01

One slope hides the bend in the satisfaction curve

France / Round 11 / 2023/24. Observed score means, the country-linear reference, and your selected model. The primary claim refers to Round 11.

Observed, fitted and uncertain layers stay separate.

Readout perspective; the curve stays visible
  • Observed means / FranceHollow circles; diamonds flag low precision
  • One slope within countriesFrance / model n = 47,836
  • Flexible curve within countriesFrance / model n = 47,836
France: observed and fitted satisfaction at eleven scoresEconomic satisfaction at the eleven response scores, 0 to 10, against democratic-satisfaction means. Observed hollow marks and whiskers are separate from fitted lines and 95% pointwise bands. The displayed outcome axis is 0 to 10; intervals are not clipped to the response scale. Paired response counts have zero-baseline bars. Hatched bars indicate suppressed observed means below 50 responses; asterisks flag 50-99. Straight segments connect actual score predictions; no threshold is estimated.Democratic satisfaction0246810012345678910Economic satisfaction (0-10)Paired n / zero-based bars019787*21330127728417112035x7x5x
France: observed and fitted satisfaction at eleven scoresEconomic satisfaction at the eleven response scores, 0 to 10, against democratic-satisfaction means. Observed hollow marks and whiskers are separate from fitted lines and 95% pointwise bands. The displayed outcome axis is 0 to 10; intervals are not clipped to the response scale. Paired response counts have zero-baseline bars. Hatched bars indicate suppressed observed means below 50 responses; asterisks flag 50-99. Straight segments connect actual score predictions; no threshold is estimated.Democratic satisfaction0246810012345678910Economic satisfaction (0-10)Paired n / zero-based bars019787*21330127728417112035x7x5x

Both response scales run from 0 to 10. Shading shows 95% pointwise intervals, not a simultaneous confidence band.

Counts are unweighted paired responses at each score. x / hatched: below 50, observed mean and interval suppressed. * / diamond: 50-99, low precision. Fitted values are not observed means for those sparse cells.

Inspect response scores with the arrow keys or Home/End. Enter/Space or a tap pins; Escape dismisses. Moving the pointer only inspects. Only an explicit Follow action changes the selected evidence.

The country-linear and country-flexible fits use exactly the same paired sample in each wave. Other model choices change declared sample or adjustment conditions. Straight segments join eleven actual score predictions; fixed spline knots are 0, 3, 7 and 10. No outcome-selected knot or sharp threshold is estimated.

Exact response-score means, intervals and support
Round 11 / 2023/24. Democratic-satisfaction rating points. Full published precision; pointwise 95% intervals. Observed cell n and fitted model n are different denominators. Suppressed or unavailable is never zero.
Economic score / seriesScopeEstimateSE95% lower95% uppernSupport / sample
0 / observed meanFrance1.839198180.17885363731.4846792432.193717117197At least 100 paired responses.
0 / One slope within countriesFrance1.959070910.067610018081.8265506292.09159119147,836Fitted model sample; not a score-cell count.
0 / Flexible curve within countriesFrance1.7620644290.082008685141.6013217711.92280708747,836Fitted model sample; not a score-cell count.
1 / observed meanFrance2.2606614610.19886589411.8605948852.66072803787Low precision: 50-99 paired responses.
1 / One slope within countriesFrance2.5809832510.06354163112.4564372892.70552921447,836Fitted model sample; not a score-cell count.
1 / Flexible curve within countriesFrance2.4736218990.066179034082.3439064452.60333735347,836Fitted model sample; not a score-cell count.
2 / observed meanFrance3.1678905880.1628420142.8453614613.490419716213At least 100 paired responses.
2 / One slope within countriesFrance3.2028955920.060651877413.0840137453.32177743947,836Fitted model sample; not a score-cell count.
2 / Flexible curve within countriesFrance3.1779293740.062007677143.0563900663.29946868247,836Fitted model sample; not a score-cell count.
3 / observed meanFrance3.9158370450.12638808543.6662564984.165417593301At least 100 paired responses.
3 / One slope within countriesFrance3.8248079330.05911386133.7089407043.94067516347,836Fitted model sample; not a score-cell count.
3 / Flexible curve within countriesFrance3.8677368580.062832522873.7445807963.99089292147,836Fitted model sample; not a score-cell count.
4 / observed meanFrance4.4957837540.12109347064.2563140564.735253451277At least 100 paired responses.
4 / One slope within countriesFrance4.4467202740.059033329374.3310108934.56242965647,836Fitted model sample; not a score-cell count.
4 / Flexible curve within countriesFrance4.5348014210.061417530984.414418844.65518400247,836Fitted model sample; not a score-cell count.
5 / observed meanFrance5.0985313410.16192040054.7784645495.418598133284At least 100 paired responses.
5 / One slope within countriesFrance5.0686326150.060416110184.9502128885.18705234247,836Fitted model sample; not a score-cell count.
5 / Flexible curve within countriesFrance5.1669083890.061204145055.0469440595.28687271947,836Fitted model sample; not a score-cell count.
6 / observed meanFrance5.799298530.17350627385.4548450266.143752034171At least 100 paired responses.
6 / One slope within countriesFrance5.6905449560.063166175885.5667349125.81435500147,836Fitted model sample; not a score-cell count.
6 / Flexible curve within countriesFrance5.7508501530.06479134735.623854665.87784564647,836Fitted model sample; not a score-cell count.
7 / observed meanFrance6.3702845850.16707446086.0375269576.703042212120At least 100 paired responses.
7 / One slope within countriesFrance6.3124572970.067115662816.1809059876.44400860847,836Fitted model sample; not a score-cell count.
7 / Flexible curve within countriesFrance6.2734191040.069463661336.1372655546.40957265347,836Fitted model sample; not a score-cell count.
8 / observed meanFranceUnavailableUnavailableUnavailableUnavailable35Suppressed: fewer than 50 paired responses.
8 / One slope within countriesFrance6.9343696380.07206764626.79311217.07562717647,836Fitted model sample; not a score-cell count.
8 / Flexible curve within countriesFrance6.7277522570.079047622466.5728134856.88269102947,836Fitted model sample; not a score-cell count.
9 / observed meanFranceUnavailableUnavailableUnavailableUnavailable7Suppressed: fewer than 50 paired responses.
9 / One slope within countriesFrance7.5562819790.077831009747.4037278537.70883610647,836Fitted model sample; not a score-cell count.
9 / Flexible curve within countriesFrance7.132365130.10548596686.9256053867.33912487347,836Fitted model sample; not a score-cell count.
10 / observed meanFranceUnavailableUnavailableUnavailableUnavailable5Suppressed: fewer than 50 paired responses.
10 / One slope within countriesFrance8.178194320.084239382358.0130793438.34330929847,836Fitted model sample; not a score-cell count.
10 / Flexible curve within countriesFrance7.5121178610.14738911557.2232250677.80101065647,836Fitted model sample; not a score-cell count.

Source: European Social Survey. ESS11, edition 4.2 (10.21338/ess11e04_2). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Sources, design and limitations.

The bend remains with country-specific starting levels

The first challenge is geography. A pooled curve can reflect country composition as well as associations within countries. The pooled spline gives an upper-minus-lower contrast of -0.46 points, with a 95% interval from -0.58 to -0.33. Allowing each country its own intercept retains a negative contrast. This model permits different starting levels, but assumes a common slope and curvature across countries; it does not estimate a separate national relationship.

The prespecified comparison makes the curvature readable. In the country-adjusted model, the fitted difference from economic scores 2 to 5 is 1.99 democratic-satisfaction points, with a 95% interval from 1.92 to 2.06. From 5 to 8, it is 1.56 points, with an interval from 1.46 to 1.66. Upper minus lower is -0.43 points, with an interval from -0.55 to -0.30. Each comparison spans three rating scores, not three years or an improvement in one person's circumstances.

For France, the fitted democratic-satisfaction levels at economic scores 2, 5 and 8 are 3.18, 5.17 and 6.73. The last number is a model prediction despite the suppressed observed mean. Selecting France retains its intercept, not a France-only gradient. Fitted levels standardize the remaining nuisance predictors at their analysis-weighted means.

Evidence 02

The lower three-score step is associated with a larger difference

Round 11 / 2023/24 / Flexible curve within countries. The Round 11 country-flexible result is 1.989 versus 1.561 points; the selected specification is shown below.

Model n = 47,836 / 30 included countries. Differences are in democratic-satisfaction rating points; all three panels share one scale.

Lower step: 2 to 5

m(5) - m(2)

+1.989rating pointsLower step: 2 to 5: +1.989 points; 95% CI 1.920 to 2.058Rating-point differences on the shared -1.00 to 3.00 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-1.00.01.02.03.0

Estimate 1.988979015
95% CI [1.919857298, 2.058100732]

Upper step: 5 to 8

m(8) - m(5)

+1.561rating pointsUpper step: 5 to 8: +1.561 points; 95% CI 1.458 to 1.664Rating-point differences on the shared -1.00 to 3.00 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-1.00.01.02.03.0

Estimate 1.560843868
95% CI [1.45771918, 1.663968557]

Upper minus lower

[m(8) - m(5)] - [m(5) - m(2)]

-0.428rating pointsUpper minus lower: -0.428 points; 95% CI -0.552 to -0.304Rating-point differences on the shared -1.00 to 3.00 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-1.00.01.02.03.0

Estimate -0.4281351466
95% CI [-0.5518883813, -0.3043819119]

Inspect the three contrasts with the arrow keys or Home/End. Enter/Space or a tap pins; Escape dismisses. Moving the pointer only inspects. Only an explicit Follow action changes the selected evidence.

One contrast, with its own uncertainty

C = m(8) - 2m(5) + m(2). Its interval retains the covariance between both steps. Overlap between their separate intervals is not a test of their difference.

The whole-shape test is separate: F(2, 22652) = 24.157, p = 3.310e-11.

Exact step contrasts and covariance-aware difference
Round 11 / 2023/24; Flexible curve within countries. Rating-point differences, full published precision, survey-design 95% pointwise intervals. These are associations, not individual changes.
ContrastEstimateSE95% lower95% upperModel nInterpretation
Lower step: 2 to 5 / m(5) - m(2)1.9889790150.035264945741.9198572982.05810073247,836Estimated from the full model covariance.
Upper step: 5 to 8 / m(8) - m(5)1.5608438680.052612792281.457719181.66396855747,836Estimated from the full model covariance.
Upper minus lower / [m(8) - m(5)] - [m(5) - m(2)]-0.42813514660.0631371919-0.5518883813-0.304381911947,836Estimated from the full model covariance.

Source: European Social Survey. ESS11, edition 4.2 (10.21338/ess11e04_2). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Sources, design and limitations.

The flexible model uses a smooth restricted cubic spline, with knots fixed at 0, 3, 7 and 10 before examining results. The joint test of its two nonlinear terms also rejects the straight-line restriction in Round 11 (p = 3.31e-11). But the knots are modeling choices, not discovered political fault lines. The smooth model tests neither a sharp threshold's location nor its nonexistence.

Adjustment must keep the respondents fixed

Country-specific starting levels address one source of difference, but people in the same country can face very different circumstances. Household financial difficulty is also a different question from satisfaction with the national economy. The further-adjusted model adds financial-difficulty categories, age and age squared, the source's binary gender coding, recorded education years and self-reported unemployment as main activity. That last measure is not an ILO unemployment rate.

Adding these fields reduces the Round 11 sample from 47,836 to 46,091 respondents. A fair comparison therefore first refits the country spline on those same complete cases. Its contrast is -0.43 points, with a 95% interval from -0.55 to -0.30. With the additional covariates, the contrast is -0.38, with an interval from -0.51 to -0.25. The negative equal-step contrast remains under this specification.

Evidence 03

Compare adjustment on the same complete-case sample

France / Round 11 / 2023/24. These are always the complete-case country baseline and the additionally adjusted model, regardless of the model selected elsewhere.

  • Same complete-case sampleFrance / model n = 46,091
  • Financial and demographic adjustmentFrance / model n = 46,091
Country baseline

Flexible country curve, restricted to the same complete cases as the adjusted model.

Additional adjustment

Age, age squared, source gender coding, fractional years of education, financial-strain categories and main-activity unemployment.

France: complete-case baseline and adjusted fitted curvesEconomic satisfaction at the eleven response scores, 0 to 10, against democratic-satisfaction means. Two fitted curves and their 95% pointwise bands; no observed means are shown. The displayed outcome axis is 0 to 10; intervals are not clipped to the response scale. Both curves use the same complete-case sample. Straight segments connect actual score predictions; no threshold is estimated.Democratic satisfaction0246810012345678910Economic satisfaction (0-10)
France: complete-case baseline and adjusted fitted curvesEconomic satisfaction at the eleven response scores, 0 to 10, against democratic-satisfaction means. Two fitted curves and their 95% pointwise bands; no observed means are shown. The displayed outcome axis is 0 to 10; intervals are not clipped to the response scale. Both curves use the same complete-case sample. Straight segments connect actual score predictions; no threshold is estimated.Democratic satisfaction0246810012345678910Economic satisfaction (0-10)

Both response scales run from 0 to 10. Shading shows 95% pointwise intervals, not a simultaneous confidence band.

Inspect response scores with the arrow keys or Home/End. Enter/Space or a tap pins; Escape dismisses. Moving the pointer only inspects. Only an explicit Follow action changes the selected evidence.

Common score axes and pointwise bands, not an "explained share." The models are correlated; no independent difference test or causal decomposition is implied. Country effects remain different intercepts on one shared curve.

Exact response-score means, intervals and support
Round 11 / 2023/24. Democratic-satisfaction rating points. Full published precision; pointwise 95% intervals. Observed cell n and fitted model n are different denominators. Suppressed or unavailable is never zero.
Economic score / seriesScopeEstimateSE95% lower95% uppernSupport / sample
0 / Same complete-case sampleFrance1.7613719660.08282994691.5990193741.92372455846,091Fitted model sample; not a score-cell count.
0 / Financial and demographic adjustmentFrance1.8113312360.08198308141.6506385581.97202391546,091Fitted model sample; not a score-cell count.
1 / Same complete-case sampleFrance2.4753719680.066220610352.3455748582.60516907846,091Fitted model sample; not a score-cell count.
1 / Financial and demographic adjustmentFrance2.506422580.065308149392.3784139552.63443120446,091Fitted model sample; not a score-cell count.
2 / Same complete-case sampleFrance3.1816458550.061867246283.0603816483.30291006146,091Fitted model sample; not a score-cell count.
2 / Financial and demographic adjustmentFrance3.1939143970.060908598953.0745292053.31329958946,091Fitted model sample; not a score-cell count.
3 / Same complete-case sampleFrance3.872467510.062823225443.7493295173.99560550446,091Fitted model sample; not a score-cell count.
3 / Financial and demographic adjustmentFrance3.8662071650.061971845463.7447379343.98767639646,091Fitted model sample; not a score-cell count.
4 / Same complete-case sampleFrance4.5393161270.061387485674.4189922854.65963996846,091Fitted model sample; not a score-cell count.
4 / Financial and demographic adjustmentFrance4.5153045350.060781449954.3961685644.63444050646,091Fitted model sample; not a score-cell count.
5 / Same complete-case sampleFrance5.1704921230.061168442375.0505976225.29038662446,091Fitted model sample; not a score-cell count.
5 / Financial and demographic adjustmentFrance5.1316228770.06075628245.0125362365.25070951746,091Fitted model sample; not a score-cell count.
6 / Same complete-case sampleFrance5.7535012270.064979769015.6261362555.880866246,091Fitted model sample; not a score-cell count.
6 / Financial and demographic adjustmentFrance5.7051817360.064593265435.5785743355.83178913646,091Fitted model sample; not a score-cell count.
7 / Same complete-case sampleFrance6.2758491660.069953478386.1387353696.41296296346,091Fitted model sample; not a score-cell count.
7 / Financial and demographic adjustmentFrance6.2260006590.069711022776.089362096.36263922946,091Fitted model sample; not a score-cell count.
8 / Same complete-case sampleFrance6.7311882370.079812105966.5747508286.88762564646,091Fitted model sample; not a score-cell count.
8 / Financial and demographic adjustmentFrance6.6892470680.080252318366.5319468096.84654732846,091Fitted model sample; not a score-cell count.
9 / Same complete-case sampleFrance7.1377570150.10669655996.9286241637.34688986746,091Fitted model sample; not a score-cell count.
9 / Financial and demographic adjustmentFrance7.1106798850.10803625026.898921147.3224386346,091Fitted model sample; not a score-cell count.
10 / Same complete-case sampleFrance7.5199406470.14924179857.2274160997.81246519646,091Fitted model sample; not a score-cell count.
10 / Financial and demographic adjustmentFrance7.5112059050.15125494217.2147354467.80767636446,091Fitted model sample; not a score-cell count.

Source: European Social Survey. ESS11, edition 4.2 (10.21338/ess11e04_2). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Sources, design and limitations.

The two estimates come from overlapping fitted models, not independent experiments. Their separate intervals do not test the difference between them, and the change cannot be read as a percentage of the relationship "explained" by household circumstances. Matching respondents removes one ambiguity, sample composition, while leaving the interpretation of adjustment unresolved.

A probability asks what the mean cannot

The average curve answers one question well, but it cannot tell us how much probability sits among the most dissatisfied responses. A lower mean can arise through different changes in the answer distribution. The exploratory probability layer estimates the chance of a democratic-performance rating at or below each cutoff from 0 to 9. It uses ten separately fitted, survey-weighted binary models on the same 46,091 complete Round 11 records, with the original country, economic-score and additional adjustment terms.

The selected reference population matters. Fitted probabilities average predictions over its actual weighted covariate distribution; they are not predictions for an invented person with average characteristics. The uncertainty conditions on that fixed empirical reference. Every displayed target must pass an ordering check across all cutoffs and all eleven economic scores. If separate models cross, the whole target CDF is unavailable rather than sorted into a more convenient picture. The cutoff does not define rejection of democracy.

For the complete-case all-country reference, the adjusted chance of a democratic-performance rating at or below 3 is 53.2% at economic score 2 (95% interval: 51.6% to 54.8%), 16.5% at score 5 (15.6% to 17.6%) and 7.0% at score 8 (6.1% to 7.9%). The first three-score comparison is therefore a 36.7-percentage-point decline; the second is a 9.6-point decline. Upper minus lower is positive here, 27.1 percentage points (24.7 to 29.4), because the second change is less negative. These are standardized associations, not movements observed in the same people.

Probability laboratory / pinned ESS Round 11 (2023/24)

Adjusted probabilities across registered scores and cutoffs

Ten complete-case adjusted binomial/logit threshold models, always Round 11. The models share one n = 46,091 fit sample across 30 countries; the displayed empirical reference n is a separate target quantity.

Probability view
Full adjusted model family10 models · n = 46,091One cutoff model for each threshold 0–9; 30-country complete-case fit.
Fixed empirical referenceFrance · n = 1,6761 country; prediction standardization, not a separate refit.
Adjusted Round 11 low democratic-rating probabilityEleven registered economic-score predictions for the probability that democratic satisfaction is at or below cutoff 3. Straight segments connect actual score predictions; the band and whiskers are pointwise 95% intervals. The probability axis always runs from zero to 100 percent. This is an adjusted association, not a forecast or causal effect.0%25%50%75%100%012345678910Adjusted cumulative probabilityEconomic satisfaction score

Use Arrow keys or Previous/Next to inspect registered values; Home/End moves to the first or last point. Enter/Space or a tap pins. Escape dismisses and restores focus. Pointer movement only inspects. Only an explicit Follow action changes the linked score or cutoff.

Registered cutoff 3 contrasts

Percentage-point differences use the full fitted covariance. Signed intervals are not clipped to 0–100.

Lower step: score 2 → 5-40.62 ppSE +1.07 pp · 95% CI -42.73 pp to -38.52 pp
Upper step: score 5 → 8-11.57 ppSE +0.81 pp · 95% CI -13.16 pp to -9.97 pp
Upper minus lower+29.06 ppSE +1.35 pp · 95% CI +26.40 pp to +31.71 pp

Eleven actual registered score predictions are connected by straight segments at cutoff 3; no smoothing or KDE is applied. Pointwise interval bounds are never sorted or repaired across cutoffs. A low democratic-satisfaction rating is not a measure of rejecting democracy, and these adjusted associations are not causal.

Exact 110 standardized score-by-cutoff predictions
ESS Round 11 (2023/24); target FR; empirical reference n = 1,676; full adjusted fit n = 46,091 across 30 countries. Probabilities retain supplied precision; intervals are pointwise and are not reordered across cutoffs.
CutoffEconomic scoreEstimatePercentageSE95% lower95% upper
000.476644072347.664%0.026131404040.42584659960.5279293776
010.237203384123.720%0.017446297690.20471750210.2730742505
020.104654034910.465%0.0097853761870.086967025220.125443942
030.051152940235.115%0.005394729590.04155532150.0628219324
040.031830715863.183%0.003574773840.025522531350.03963462564
050.024230787322.423%0.0031420568860.018778600080.03121560538
060.020563619412.056%0.0030026968610.015433329160.02735192485
070.017635594161.764%0.0026512749260.013125273590.02365866815
080.01413248351.413%0.0027935710240.0095838309370.02079467813
090.010662017971.066%0.0036469853990.0054426926520.02078188308
0100.0077996429360.780%0.0042148287450.0026957721350.02235005243
100.573106540457.311%0.023184725030.52717105390.6178146829
110.359049024935.905%0.019392283180.32198583310.3978749395
120.196243278319.624%0.01376224340.17065963970.224623406
130.104358150110.436%0.008576776440.08870324420.1224048243
140.059629709765.963%0.0053597252440.0499510780.07104345816
150.038049185483.805%0.0040022680190.030935940820.04671915919
160.027380704572.738%0.0033970623670.021453474120.03488714463
170.022241308482.224%0.002996150030.017067554890.02893723046
180.020220955072.022%0.0030286748780.015064367230.02709410595
190.01990431561.990%0.0041122407530.013256930430.02978427024
1100.020387771852.039%0.0061516109730.011251448720.03666778155
200.690355460269.036%0.01893712090.65206797820.7261988109
210.544359589654.436%0.018567521420.50779350240.5804535889
220.388550110838.855%0.017454414350.35493576070.4232590934
230.249539152924.954%0.0140917630.22294875990.2781656302
240.146763064214.676%0.0095182047310.12907051990.1664174276
250.085320201718.532%0.0065566429930.073315602830.09908025558
260.053949569555.395%0.0049614250880.045011481580.06454257122
270.040550216824.055%0.0041089263320.033219779320.04941554449
280.038226784933.823%0.0042423063630.030726795760.04746776723
290.042695275164.270%0.0062550557180.031984392080.05678260215
2100.051829941545.183%0.010773314040.034348161840.07749517797
300.79757108379.757%0.014673060360.76728550570.8248151672
310.714958832171.496%0.014839110630.68500498170.7431323915
320.607131038560.713%0.016157259980.57505248090.6383111186
330.471141499947.114%0.016923853780.43814503380.50439211
340.321794232632.179%0.014685324280.29371071770.3512276558
350.200912728120.091%0.011629627370.17908155920.2246768681
360.127457223412.746%0.0091997270540.11048732890.1466039709
370.093095304329.310%0.007614345380.07920585750.1091317188
380.085254011718.525%0.0079399876630.070924600260.1021601587
390.093034111089.303%0.011826363330.072301736090.1189491905
3100.110552362411.055%0.019947540640.077077379390.1561065874
400.841738114784.174%0.012343328930.81601869970.8644593168
410.798101874379.810%0.011842820330.77389126070.8203220131
420.735219734573.522%0.012998060850.70897206040.7599018335
430.635311225163.531%0.015389154770.60465055660.6649118177
440.487075125848.708%0.016354670860.45511564340.519140642
450.32929983632.930%0.014953376840.30068045520.3592439095
460.212971235221.297%0.01241201450.18965509220.2383108675
470.151741920415.174%0.010420373870.13242522970.1733134255
480.133445385613.345%0.01126494420.11286799860.1571099201
490.139414587513.941%0.0167189380.10975008970.1755163498
4100.158521740115.852%0.026802916770.11273431940.2183297748
500.917072872391.707%0.0084574046090.89891700410.9322136133
510.897412528489.741%0.0075565352950.88162587150.9113056435
520.86729096286.729%0.0080661009450.85066830870.8823192602
530.813281713481.328%0.010500731760.79182111930.8329965936
540.715253299871.525%0.013574299110.68791686380.7410964317
550.574064301857.406%0.015911465050.54262228490.6049186121
560.425656942942.566%0.016705449930.39328379930.4586802838
570.315011148931.501%0.015793936810.28490455450.3467564738
580.256570074625.657%0.016092299510.22631485410.2893572896
590.230612452423.061%0.02073688040.19248610380.2737307018
5100.218800076121.880%0.02869032490.1677477780.2801593438
600.941596623594.160%0.0069752285510.92632681410.9538591935
610.931475142393.148%0.0059283654750.91890223340.9422213865
620.91574319491.574%0.0060687416510.90306023780.9269011139
630.886562877288.656%0.0077995097290.87035402220.9009758005
640.830326605783.033%0.010479949320.80878584190.8498911231
650.737007641573.701%0.013828290120.70902125480.7632012778
660.611242042461.124%0.017434304640.57657469690.644819517
670.480514460348.051%0.019220128040.44302302890.5182266292
680.374902892437.490%0.020104642260.33639703190.4150595567
690.295656030429.566%0.024239932480.25044769270.3452659338
6100.233820908723.382%0.029976787410.18022299670.2975726599
700.976746215197.675%0.0039190617520.96769062750.9833075073
710.971753050297.175%0.003527727410.96395268090.9779041693
720.964619901196.462%0.0037573822040.95646959590.9712900099
730.952902085195.290%0.004900054470.94231155010.9616275653
740.932094092193.209%0.0067146364620.91769067660.9441304829
750.895995981189.600%0.0094614156930.87593625450.9131339227
760.836264033483.626%0.014019334480.80690220180.8619251801
770.744913279874.491%0.02017144590.70341046260.7824050122
780.621171074362.117%0.026224429150.56858643050.671054322
790.476753161647.675%0.032825166510.41314706620.5411223375
7100.33488079233.488%0.038268863040.26445176830.4135215994
800.988998679198.900%0.0030248573310.98117847680.99359087
810.989005115298.901%0.0023907804820.98318165880.9928268746
820.988387257998.839%0.0022227332760.98311660110.9920258677
830.986304629998.630%0.002532025210.98034348170.9904755298
840.981243973598.124%0.0032881705230.97358652240.9867117757
850.970821679597.082%0.0048141204690.95975165850.9789138637
860.950446592495.045%0.0080527679280.93205853060.9640499579
870.912114059691.211%0.014223690020.87994785050.9362858405
880.844649983884.465%0.023866509840.79195180620.8859225953
890.736726450373.673%0.037880298010.65615886820.8040533024
8100.58828861358.829%0.0553844060.47718853780.691064233
900.990248132899.025%0.0034700962550.98047148880.9951544418
910.992525238699.253%0.0021074913310.98702820010.9957029475
920.993845054699.385%0.0016490487570.98960443310.9963621756
930.994145397699.415%0.0016244551880.98992526620.9966038537
940.993193346499.319%0.0018057767770.98856371980.9959564768
950.990402607599.040%0.0023067320540.98464669370.9940137634
960.98399380298.399%0.0036443916680.97503753780.989770368
970.969303259696.930%0.0070206437890.95211743340.9804474858
980.934910141393.491%0.014688240580.89949045020.9584248146
990.857552303785.755%0.031014320680.78540788260.9082748552
9100.708202663670.820%0.059323643680.58029674690.809898363
Exact 30 covariance-aware probability contrasts
ESS Round 11 (2023/24); ten complete-case adjusted binomial/logit threshold models. Estimates, standard errors and intervals are percentage points and may extend beyond the nominal probability range.
CutoffContrastEstimate, ppSE, pp95% lower, pp95% upper, pp
0lower-step-8.0423247590.8075272680000001-9.625135717-6.459513801
0upper-step-1.0098303830.330102976-1.6568557259999999-0.3628050394
0upper-minus-lower7.0324943760.87972148300000015.3081776158.756811138
1lower-step-15.8194092799999991.136496874-18.04702409-13.591794460000001
1upper-step-1.78282304099999990.3042917088-2.3792564620000003-1.18638962
1upper-minus-lower14.0365862400000021.082379682999999911.9150449716.1581275
2lower-step-30.3229909099999981.3549478849999999-32.97878527-27.66719656
2upper-step-4.7093416780.4685101259-5.627654892000001-3.791028463
2upper-minus-lower25.613649231.27113079623.1221423428.105156129999997
3lower-step-40.6218310400000041.074049285-42.72704413-38.516617939999996
3upper-step-11.565871640.8149117686-13.163156749999999-9.968586536
3upper-minus-lower29.05595941.35270382226.4045635731.70735523
4lower-step-40.591989840.8852760566-42.327193969999996-38.85678572
4upper-step-19.585445041.1222705689999999-21.78517529-17.3857148
4upper-minus-lower21.00654481.648911437999999817.7745609524.23852866
5lower-step-29.322666021.045614953-31.372145800000002-27.27318624
5upper-step-31.749422721.2182453180000001-34.13727031-29.361575130000002
5upper-minus-lower-2.42675671.8624011230000002-6.0771955439999991.223682144
6lower-step-17.873555250.9504643974999999-19.73653316-16.01057734
6upper-step-36.210474911.341600215-38.84010688-33.58084294
6upper-minus-lower-18.336919661.60142821-21.475833010000002-15.19800631
7lower-step-6.8623920020000010.6567090683-8.149588547-5.575195455999999
7upper-step-27.4824906799999981.942820201-31.29055665-23.67442472
7upper-minus-lower-20.620098681.646168286-23.84670576-17.3934916
8lower-step-1.7565578350.3175856861-2.379048398-1.134067271
8upper-step-12.617169571.986443774-16.51074084-8.723598298
8upper-minus-lower-10.860611741.750093224-14.2909191-7.430304373
9lower-step-0.344244711499999970.13358036880000002-0.606071748-0.08241767492
9upper-step-5.5492466161.286991815-8.071842235-3.026650997
9upper-minus-lower-5.20500190399999951.200125479-7.557333319-2.85267049

Source: European Social Survey, ESS Round 11 (2023/24). ESS analysis weights; ten complete-case adjusted binomial/logit threshold models with fixed empirical-reference standardization and survey-design pointwise 95% intervals. Sources, design and limitations.

The ordering gate passes for 20 of the 32 reference populations, including France, the all-country reference and the fixed recent-country reference. Twelve national reference surfaces are withheld because separate cutoff fits cross somewhere on the registered grid. That is a limitation of the fitted distribution, not an absence of survey answers. The observed distributions remain available; rejected model surfaces are not selectively repaired.

The common curve is a restriction, not a European law

The shared curve is useful precisely because it summarizes many interviews, but that convenience is also an assumption. The original country-adjusted curve permits different intercepts, while retaining a common slope and curvature. The exploratory interaction models relax that restriction explicitly. One estimates country-specific shapes within a joint Round 11 fit. The other estimates shapes by reported household financial difficulty on the same complete-case sample, with the remaining covariates retained.

Each profile carries the same registered two-step comparison. The formal joint tests concern the common-shape restrictions; the individual intervals remain pointwise. A country's position is not a significant-country ranking, and a profile's respondent support is not the full model sample. Differences in conditional associations do not establish that financial circumstances caused a change in democratic attitudes.

The country common-shape test gives F(87, 22565) = 6.31, with p below 0.001. The financial-strain test gives F(9, 22114) = 2.67, p = 0.0042. These exploratory tests reject their respective shared-shape restrictions, but they do not establish that curvature rises monotonically with hardship. The four financial-profile curvature estimates are -0.30, -0.47, -0.05 and -0.42 rating points, in the source's order from living comfortably to finding income very difficult. The last two intervals include zero. A more elaborate model exposes that uncertainty rather than turning it into a tidy social gradient.

Model laboratory / pinned ESS Round 11 (2023/24)

Does a common curve hide different shapes?

This figure always remains at Round 11 even when another wave is explored elsewhere. It displays the registered upper-minus-lower curvature contrast with survey-design pointwise 95% intervals; no profile is ranked by estimate or statistical significance.

Heterogeneity profile

Country labels are alphabetical; estimates are not significance-ranked.

Joint shape testF(87, 22565) = 6.311535379p = 3.421076207e-67
Interaction-model samplen = 47,83630 profiles; profile support counts partition this model sample.

The F test evaluates all registered country-by-spline shape interactions jointly. It is the formal common-shape evidence; individual interval overlap is not that test.

Shared-curve reference: -0.428; 95% CI -0.552 to -0.304. This comes from another fitted model and is a visual reference, not an independent test of any profile difference.

Round 11 heterogeneity in the upper-minus-lower curvature contrastAlphabetically ordered profile estimates from one joint Gaussian interaction model. Points show upper-minus-lower differences in democratic-rating points and whiskers show survey-design pointwise 95% intervals. Profile support and the model sample are different quantities. Intervals extend beyond response-scale bounds when supplied by the fitted model.-3.00-2.00-1.000.00+1.00+2.00Austriasupport n 2,292-0.320Belgiumsupport n 1,555-0.219Bulgariasupport n 2,156-0.403Croatiasupport n 1,489-0.038Cyprussupport n 660-1.135Estoniasupport n 1,222-0.580Finlandsupport n 1,529-0.281Francesupport n 1,697-0.173Germanysupport n 2,389-0.618Greecesupport n 2,699-0.701Hungarysupport n 2,040-0.434Icelandsupport n 814-0.525Irelandsupport n 1,920-0.546Israelsupport n 847-0.615Italysupport n 2,733-0.046Latviasupport n 1,141-0.614Lithuaniasupport n 1,282-0.583Montenegrosupport n 1,565+0.275Netherlandssupport n 1,642-0.614Norwaysupport n 1,323-0.878Polandsupport n 1,327-0.320Portugalsupport n 1,303-0.453Serbiasupport n 1,363-0.028Slovakiasupport n 1,389-0.905Sloveniasupport n 1,172-0.371Spainsupport n 1,796-0.095Swedensupport n 1,198-0.882Switzerlandsupport n 1,320-0.730Ukrainesupport n 2,405-0.560United Kingdomsupport n 1,568-0.301[m(8) − m(5)] − [m(5) − m(2)] · democratic-rating points

Use Arrow keys or Previous/Next to inspect profiles; Home/End moves to the first or last registered profile. Enter/Space or a tap pins. Escape dismisses and restores focus. Pointer movement only inspects. Only Follow changes the selected country.

Exact profile contrasts, intervals and respondent support
ESS Round 11 (2023/24); country-by-spline Gaussian interaction model. Profiles are alphabetic or ordinal, never significance-ranked. All intervals are survey-design pointwise 95% intervals in democratic-rating points.
ProfileProfile support nModel nLower stepLower 95% intervalUpper stepUpper 95% intervalUpper minus lowerDifference 95% interval
Austria AT2,29247,8362.288711351[2.031414092, 2.546008611]1.968345336[1.729319194, 2.207371478]-0.3203660153[-0.6726326364, 0.03190060572]
Belgium BE1,55547,8361.688755376[1.371195191, 2.006315562]1.469849086[1.119060823, 1.820637349]-0.2189062903[-0.7675755102, 0.3297629295]
Bulgaria BG2,15647,8361.881976506[1.662119784, 2.101833228]1.4791716[0.8789825792, 2.07936062]-0.4028049065[-1.097217583, 0.2916077696]
Croatia HR1,48947,8361.845317198[1.613848964, 2.076785432]1.807098519[1.39968177, 2.214515269]-0.03821867846[-0.5663519927, 0.4899146358]
Cyprus CY66047,8361.817365647[1.396507873, 2.238223422]0.6826819205[-0.3727307203, 1.738094561]-1.134683727[-2.402777803, 0.1334103502]
Estonia EE1,22247,8362.089037324[1.848366345, 2.329708303]1.50938022[1.126126858, 1.892633583]-0.5796571035[-1.094503057, -0.06481115002]
Finland FI1,52947,8361.414568931[1.108669335, 1.720468527]1.133942409[0.9166347253, 1.351250094]-0.2806265218[-0.6872687608, 0.1260157171]
France FR1,69747,8361.944947008[1.702833079, 2.187060938]1.771507523[1.171410367, 2.371604678]-0.1734394857[-0.9230900921, 0.5762111207]
Germany DE2,38947,8362.207137745[1.966629552, 2.447645938]1.588737314[1.228917865, 1.948556763]-0.6184004309[-1.030982162, -0.2058186995]
Greece GR2,69947,8362.287150645[2.107456032, 2.466845258]1.585908059[1.086218861, 2.085597257]-0.7012425861[-1.293083531, -0.1094016408]
Hungary HU2,04047,8362.644161168[2.469612827, 2.818709508]2.210000146[1.972260905, 2.447739388]-0.4341610213[-0.7615327055, -0.1067893371]
Iceland IS81447,8361.439211184[1.093694221, 1.784728146]0.9145414992[0.4723998248, 1.356683174]-0.5246696846[-1.111264137, 0.06192476789]
Ireland IE1,92047,8361.938828122[1.679432897, 2.198223347]1.393033887[1.161953799, 1.624113974]-0.5457942353[-0.9125307793, -0.1790576913]
Israel IL84747,8362.023040149[1.723301065, 2.322779233]1.408364572[1.002583263, 1.814145881]-0.614675577[-1.1815884, -0.04776275444]
Italy IT2,73347,8361.877306529[1.664659288, 2.08995377]1.831414812[1.551198891, 2.111630732]-0.04589171727[-0.4311733065, 0.339389872]
Latvia LV1,14147,8362.086409883[1.763300506, 2.40951926]1.472847141[0.8285992337, 2.117095049]-0.613562742[-1.447901777, 0.220776293]
Lithuania LT1,28247,8361.752562782[1.483915393, 2.021210171]1.169229198[0.8842953651, 1.454163031]-0.5833335837[-0.9893354753, -0.177331692]
Montenegro ME1,56547,8361.268436433[0.941094628, 1.595778237]1.543048493[1.055457812, 2.030639174]0.2746120601[-0.3811784028, 0.930402523]
Netherlands NL1,64247,8361.914471744[1.620739368, 2.208204119]1.30084932[1.074819345, 1.526879296]-0.6136224236[-1.012435317, -0.2148095298]
Norway NO1,32347,8361.801731275[1.39727812, 2.20618443]0.9233295595[0.6663308206, 1.180328298]-0.8784017154[-1.425527798, -0.331275633]
Poland PL1,32747,8361.835824807[1.509803271, 2.161846343]1.515605442[1.20517729, 1.826033594]-0.3202193649[-0.8119954322, 0.1715567024]
Portugal PT1,30347,8361.696293478[1.441352003, 1.951234953]1.243757775[0.7995673995, 1.68794815]-0.4525357037[-0.9985631706, 0.09349176329]
Serbia RS1,36347,8362.428021801[2.170112857, 2.685930745]2.39991879[2.073902527, 2.725935054]-0.02810301041[-0.4431792931, 0.3869732723]
Slovakia SK1,38947,8362.069159733[1.730380543, 2.407938924]1.163852182[0.5135156101, 1.814188754]-0.9053075516[-1.78629724, -0.02431786326]
Slovenia SI1,17247,8361.969654944[1.705201979, 2.234107908]1.598484821[1.268766479, 1.928203163]-0.3711701228[-0.8390158079, 0.09667556218]
Spain ES1,79647,8361.902329716[1.715403272, 2.089256161]1.807628587[1.558797083, 2.056460091]-0.09470112914[-0.4193668928, 0.2299646345]
Sweden SE1,19847,8361.386142201[1.023399665, 1.748884737]0.5042374912[0.1012499658, 0.9072250166]-0.8819047097[-1.481226084, -0.2825833355]
Switzerland CH1,32047,8362.032875637[1.416405334, 2.649345939]1.302632002[1.062982568, 1.542281437]-0.7302436342[-1.442584452, -0.01790281638]
Ukraine UA2,40547,8361.882178766[1.638139437, 2.126218095]1.322383865[0.7688405571, 1.875927172]-0.5597949014[-1.213103385, 0.09351358225]
United Kingdom GB1,56847,8361.924513793[1.677307367, 2.171720218]1.623691199[1.305260318, 1.942122081]-0.3008225932[-0.7272360597, 0.1255908733]

The displayed profiles are estimated jointly in Gaussian survey regressions with profile-by-spline interactions. They are not separate profile regressions, transitions, causal effects or the earlier shared country-slope model.

Source: European Social Survey, ESS Round 11 (2023/24). ESS analysis weights; Gaussian survey regressions and survey-design pointwise 95% intervals. Sources, design and limitations.

Earlier rounds test recurrence, not a European trajectory

A pattern in one survey wave might be peculiar to that period. Earlier rounds let us ask whether the chosen contrast recurs, although their changing coverage limits the comparison. Across the eleven separately fitted rounds, every country-spline contrast has a negative point estimate. The uncertainty is not uniform: the intervals include zero in Rounds 1, 3 and 4. Nor is this contrast interchangeable with the joint test of the entire nonlinear function. In Rounds 1 and 4, that joint test rejects a straight line even though the interval for this particular contrast crosses zero. Counting vaguely defined "significant waves" would obscure which question was tested.

Evidence 04

Separate waves are checks, not a single European trajectory

Eleven country-flexible finite contrasts and three recent fixed-country checks. Each row is a survey wave, not an equally spaced calendar year.

C = [m(8) - m(5)] - [m(5) - m(2)], in democratic-satisfaction points. Blue circles use each wave's included countries; gold squares use the same 19 recent countries. No individual or fixed-Europe trajectory is drawn.

Round 1 2002/03

7 countries / n = 11,457

Round 1: C -0.280, 95% CI -0.575 to 0.015; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.280 95% CI -0.575 to 0.015

Fixed set: not specified

Round 2 2004/05

10 countries / n = 17,801

Round 2: C -0.351, 95% CI -0.565 to -0.138; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.351 95% CI -0.565 to -0.138

Fixed set: not specified

Round 3 2006/07

8 countries / n = 14,215

Round 3: C -0.161, 95% CI -0.391 to 0.069; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.161 95% CI -0.391 to 0.069

Fixed set: not specified

Round 4 2008/09

7 countries / n = 13,669

Round 4: C -0.113, 95% CI -0.344 to 0.117; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.113 95% CI -0.344 to 0.117

Fixed set: not specified

Round 5 2010/11

20 countries / n = 35,889

Round 5: C -0.428, 95% CI -0.589 to -0.266; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 95% CI -0.589 to -0.266

Fixed set: not specified

Round 6 2012/13

27 countries / n = 48,027

Round 6: C -0.456, 95% CI -0.577 to -0.334; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.456 95% CI -0.577 to -0.334

Fixed set: not specified

Round 7 2014/15

21 countries / n = 38,597

Round 7: C -0.297, 95% CI -0.409 to -0.185; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.297 95% CI -0.409 to -0.185

Fixed set: not specified

Round 8 2016/17

23 countries / n = 42,395

Round 8: C -0.395, 95% CI -0.520 to -0.270; fixed-country estimate absentRating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.395 95% CI -0.520 to -0.270

Fixed set: not specified

Round 9 2018/19

29 countries / n = 47,005

Fixed 19 / n = 30,624

Round 9: C -0.352, 95% CI -0.457 to -0.247; fixed-country C -0.330Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.352 95% CI -0.457 to -0.247

Fixed -0.330 95% CI -0.467 to -0.193

Round 10 2020-22

22 countries / n = 36,264

Fixed 19 / n = 29,753

Round 10: C -0.333, 95% CI -0.481 to -0.186; fixed-country C -0.292Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.333 95% CI -0.481 to -0.186

Fixed -0.292 95% CI -0.450 to -0.134

Round 11 2023/24

30 countries / n = 47,836

Fixed 19 / n = 29,719

Declared primary wave
Round 11: C -0.428, 95% CI -0.552 to -0.304; fixed-country C -0.425Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 95% CI -0.552 to -0.304

Fixed -0.425 95% CI -0.576 to -0.274

Inspect waves with the arrow keys or Home/End. Enter/Space or a tap pins; Escape dismisses. Moving the pointer only inspects. Only an explicit Follow action changes the selected evidence.

The early waves qualify the claim

The finite-contrast intervals in Rounds 1, 3 and 4 cross zero. The latest whole-shape test supports a bend; that does not make the same finite comparison conclusive in every wave.

Reading these rows needs no further download. Following another wave commits that selection and may load the verified evidence.

Exact wave contrasts, country coverage and samples
Country-flexible model in every wave; fixed-country model only in Rounds 9-11. C is in democratic-satisfaction rating points. Full published precision and 95% pointwise intervals; model-wide, not country-specific estimates.
Wave / modelCountriesModel nEstimateSE95% lower95% upperWhole-shape FWhole-shape p
Round 1 / 2002/03 / Included countries711,457-0.28004927160.1503521674-0.57481217230.014713629073.9665973480.01900299916
Round 2 / 2004/05 / Included countries1017,801-0.35137820470.1090055031-0.5650860272-0.13767038215.5147923390.004055679858
Round 3 / 2006/07 / Included countries814,215-0.16096066960.1173668763-0.39106856320.069147224031.1713458320.3100610254
Round 4 / 2008/09 / Included countries713,669-0.11346109890.1173520194-0.3435316960.11660949824.9466898560.007147456771
Round 5 / 2010/11 / Included countries2035,889-0.42776734780.08242709705-0.589337439-0.266197256614.110350837.568225178e-7
Round 6 / 2012/13 / Included countries2748,027-0.45569813680.06187337927-0.5769755677-0.334420705939.222670351.003176132e-17
Round 7 / 2014/15 / Included countries2138,597-0.29701459480.05710760643-0.4089512492-0.185077940413.734681040.000001096016252
Round 8 / 2016/17 / Included countries2342,395-0.39459264070.06373969702-0.5195285663-0.269656715220.433936751.366878448e-9
Round 9 / 2018/19 / Included countries2947,005-0.35209766750.05357055138-0.4571000047-0.247095330425.675291887.291634361e-12
Round 9 / 2018/19 / Fixed 19 countries1930,624-0.33002409120.06980420943-0.4668505482-0.193197634111.390035880.00001142070531
Round 10 / 2020-22 / Included countries2236,264-0.33326449220.07521167416-0.4806888414-0.18584014299.8257124710.00005440088821
Round 10 / 2020-22 / Fixed 19 countries1929,753-0.29157702170.08061221766-0.4495879057-0.13356613776.5678993620.001409134603
Round 11 / 2023/24 / Included countries3047,836-0.42813514660.0631371919-0.5518883813-0.304381911924.15735143.309545234e-11
Round 11 / 2023/24 / Fixed 19 countries1929,719-0.4245371820.07705204221-0.5755685641-0.273505799820.022990612.068626646e-9

Source: European Social Survey. ESS1, edition 6.7; ESS2, edition 3.6; ESS3, edition 3.7; ESS4, edition 4.6; ESS5, edition 3.6; ESS6, edition 2.7; ESS7, edition 2.3; ESS8, edition 2.3; ESS9, edition 3.3; ESS10, edition 3.3; ESS11, edition 4.2. ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Sources, design and limitations.

Coverage also changes, from seven eligible countries in some early rounds to 30 in Round 11. Only Finland and France have reviewed usable designs in all eleven rounds. Those two countries cannot stand in for a fixed Europe, and the successive surveys are neither an individual panel nor an annual path.

A narrower check holds the 19 countries shared by Rounds 9 to 11 fixed. Their contrasts are -0.33 points in Round 9 (95% interval: -0.47 to -0.19) and -0.29 in Round 10 (-0.45 to -0.13). In Round 11, the contrast is -0.42 (-0.58 to -0.27), based on 29,719 paired responses. This supports recurrence within that recent country set; it does not establish a historical trend in the strength of the association.

A surviving result still needs a boundary

The final checks ask how much depends on the way the comparison was assembled. Restricting Round 11 to face-to-face interviews leaves 45,991 paired responses. The contrast is -0.43 points, with a 95% interval from -0.55 to -0.30, close to the primary estimate. Together with the complete-case and fixed-country checks, this shows that the reported bend survives several declared restrictions. It does not show that interview mode, missingness or country coverage is irrelevant.

Evidence 05

Six declared checks retain the same qualitative bend

Round 11 / 2023/24. Each row shows the same finite contrast C under one prespecified set of conditions. Country selection does not change these model-wide contrasts.

Read conditions before comparing the estimates. Sample, country coverage and covariates can change together. The intervals do not establish independent differences between specifications. All interval marks share one rating-point scale.

Pooled responses

Paired answers / Included countries

30 countries / n = 47,836

Country interceptsNo
Additional covariatesNone
Interview modeAs available
Pooled responses: C -0.456, 95% CI -0.581 to -0.330Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.456 / 95% CI -0.581 to -0.330

Flexible curve within countries

Paired answers / Included countries

30 countries / n = 47,836

Country interceptsYes
Additional covariatesNone
Interview modeAs available
Flexible curve within countries: C -0.428, 95% CI -0.552 to -0.304Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 / 95% CI -0.552 to -0.304

Same complete-case sample

Complete cases / Included countries

30 countries / n = 46,091

Country interceptsYes
Additional covariatesNone
Interview modeAs available
Same complete-case sample: C -0.428, 95% CI -0.553 to -0.303Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 / 95% CI -0.553 to -0.303

Financial and demographic adjustment

Complete cases / Included countries

30 countries / n = 46,091

Country interceptsYes
Additional covariatesDemographic + financial
Interview modeAs available
Financial and demographic adjustment: C -0.380, 95% CI -0.508 to -0.253Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.380 / 95% CI -0.508 to -0.253

Face-to-face interviews

Paired answers / Included countries

30 countries / n = 45,991

Country interceptsYes
Additional covariatesNone
Interview modeFace-to-face only
Face-to-face interviews: C -0.427, 95% CI -0.553 to -0.301Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.427 / 95% CI -0.553 to -0.301

The same 19 recent countries

Paired answers / Fixed 19 / R9-11

19 countries / n = 29,719

Country interceptsYes
Additional covariatesNone
Interview modeAs available
The same 19 recent countries: C -0.425, 95% CI -0.576 to -0.274Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.425 / 95% CI -0.576 to -0.274

Inspect model conditions with the arrow keys or Home/End. Enter/Space or a tap pins; Escape dismisses. Moving the pointer only inspects. Only an explicit Follow action changes the selected evidence.

Conventional interval baseline / the same six specifications

The same estimates, intervals and common scale, without the condition columns. No alternative calculation or reordering.

Pooled responses

n = 47,836 / 30 countries

Pooled responses: -0.456, 95% CI -0.581 to -0.330Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.456 / 95% CI -0.581 to -0.330

Flexible curve within countries

n = 47,836 / 30 countries

Flexible curve within countries: -0.428, 95% CI -0.552 to -0.304Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 / 95% CI -0.552 to -0.304

Same complete-case sample

n = 46,091 / 30 countries

Same complete-case sample: -0.428, 95% CI -0.553 to -0.303Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.428 / 95% CI -0.553 to -0.303

Financial and demographic adjustment

n = 46,091 / 30 countries

Financial and demographic adjustment: -0.380, 95% CI -0.508 to -0.253Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.380 / 95% CI -0.508 to -0.253

Face-to-face interviews

n = 45,991 / 30 countries

Face-to-face interviews: -0.427, 95% CI -0.553 to -0.301Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.427 / 95% CI -0.553 to -0.301

The same 19 recent countries

n = 29,719 / 19 countries

The same 19 recent countries: -0.425, 95% CI -0.576 to -0.274Rating-point differences on the shared -0.80 to 0.20 scale. Whiskers are 95% pointwise confidence intervals. Missing estimates have no mark.-0.8-0.6-0.4-0.20.00.2

-0.425 / 95% CI -0.576 to -0.274

What the adjustment includes

Age, age squared, source gender, fractional education, financial-strain categories and main-activity unemployment. The complete-case baseline and adjusted fit share their respondents; other rows change sample or country conditions.

Following a model preserves the selected country. If that country is outside the model, the curve is explicitly unavailable rather than replaced by a pooled fit.

Exact six-model contrasts, conditions and samples
Round 11 / 2023/24. C = [m(8)-m(5)]-[m(5)-m(2)], democratic-satisfaction points. Full published precision and 95% pointwise intervals. Correlated specifications; no independent difference tests.
Model / conditionsCountriesModel nEstimateSE95% lower95% upperAvailability
Pooled responsesPaired answers; Included countries; country intercepts: No; covariates: None; mode: As available.3047,836-0.45562695570.06390234369-0.5808799319-0.3303739794Available
Flexible curve within countriesPaired answers; Included countries; country intercepts: Yes; covariates: None; mode: As available.3047,836-0.42813514660.0631371919-0.5518883813-0.3043819119Available
Same complete-case sampleComplete cases; Included countries; country intercepts: Yes; covariates: None; mode: As available.3046,091-0.42815015490.06384749444-0.5532957889-0.303004521Available
Financial and demographic adjustmentComplete cases; Included countries; country intercepts: Yes; covariates: Demographic + financial; mode: As available.3046,091-0.38008428780.06505700235-0.5076006458-0.2525679297Available
Face-to-face interviewsPaired answers; Included countries; country intercepts: Yes; covariates: None; mode: Face-to-face only.3045,991-0.42696290480.06433576312-0.5530659533-0.3008598564Available
The same 19 recent countriesPaired answers; Fixed 19 / R9-11; country intercepts: Yes; covariates: None; mode: As available.1929,719-0.4245371820.07705204221-0.5755685641-0.2735057998Available

Source: European Social Survey. ESS11, edition 4.2 (10.21338/ess11e04_2). ESS analysis weights; survey-design 95% pointwise intervals, not simultaneous bands. Sources, design and limitations.

The observed evidence deserves the same discipline as the models. Of 2,398 raw-score aggregates across the study, 640 are suppressed below 50 responses and another 303 are flagged for low precision at 50 to 99. An attractive fitted curve must not turn sparse observations into apparently precise local knowledge. France's suppressed high-score means remain suppressed even when a smooth model passes through that part of the scale.

Both answers are ordinal ratings on bounded scales. Equal numerical steps need not represent equal differences in underlying satisfaction, while a ceiling of 10 could compress differences toward the satisfied end. A common-response style could also contribute to the association between the answers. These are possible explanations for part of the association or its shape, not mechanisms established by this analysis.

Country intercepts and additional covariates also leave reverse causality and omitted influences unresolved. Respondents may use the rating scale differently across settings; the study does not establish measurement equivalence. Design-aware confidence intervals quantify sampling uncertainty under the model and survey conventions, not these broader uncertainties.

What the association permits us to say

For an analyst interpreting democratic dissatisfaction, a constant economic gradient discards information in the primary comparison. The association is steeper over the prespecified low-to-middle interval than over the equally wide middle-to-high interval, and that contrast persists under the declared adjustments.

The practical implication is to preserve the shape and its uncertainty when describing the evidence. A policy claim about what improving the economy would do requires a design that identifies causality. A claim about where democratic legitimacy collapses requires both a different political measure and a test designed to locate such a break. These satisfaction answers establish neither.

The audit stays with the argument

Sources, design and failure boundaries

Questions and analytical scope

The study asks whether economic dissatisfaction is nonlinearly associated with satisfaction with the way democracy works. The original English questions in the Round 11 source questionnaire, PDF page 12 are:

  • B28: "On the whole how satisfied are you with the present state of the economy in [country]?"
  • B30: "And on the whole, how satisfied are you with the way democracy works in [country]?"

Both use 0, "Extremely dissatisfied," to 10, "Extremely satisfied." Refusal, don't know and no answer codes are missing, not ratings. The outcome concerns reported democratic performance, not regime support or objective democracy.

Eleven pinned rounds contain 518,597 source records. Reviewed sampling designs yield 372,349 eligible records across 204 country-round cells, including 353,155 paired satisfaction responses and 339,587 complete adjustment records. Round 11 is primary: 47,836 paired responses across 30 countries. Its 2023/24 label accompanies a whole-source fieldwork range of March 11, 2023, to December 1, 2024; it does not measure 2026 opinion.

Weights, domains and covariates

Estimation uses the original ESS analysis weight, anweight, or the documented historical product pspwght * pweight where it is absent. Country weights are not renormalized to equal shares. Country, score, paired-response, complete-case and mode restrictions are domains of the eligible full survey designs. Excluded domain observations contribute zero linearized scores without deleting their sampling units from the variance design.

Adjustment adds age and age squared, source-coded binary gender, recorded education years, household financial-difficulty categories and self-reported unemployment as main activity. Activity codes 3 and 4 include unemployed respondents looking and not looking for work; this is not an ILO unemployment rate. Missing activity remains missing. Fractional education values, including 11.5 and 14.5 years in Round 2, are retained.

Covariate missingness is matched explicitly: the country-spline baseline and adjusted spline use the same 46,091 complete Round 11 records. This separates sample exclusion from added adjustment without making either comparison causal.

The prespecified mean model

A survey-weighted Gaussian identity-link model estimates the mean coded democratic-satisfaction response. Both scales are ordinal and bounded; their numeric coding does not establish equal spacing in underlying satisfaction. Ceiling effects and common-response style are possible contributors to the association or its shape, not mechanisms identified by these models.

The restricted, or natural, cubic basis retains a linear term and two nonlinear terms, with knots fixed at 0, 3, 7 and 10 before inspecting outcomes. Predictions are evaluated only at the eleven observed integer scores.

The primary model combines country-specific intercepts with a common slope and curvature. Selecting a country retains its intercept; it does not refit a country-only gradient. All fitted levels standardize nuisance predictors at their analysis-weighted means.

Writing the fitted mean as m(x), the registered contrast is C = [m(8) - m(5)] - [m(5) - m(2)], in democratic-satisfaction rating points. Negative C means a smaller fitted difference over 5 to 8 than over 2 to 5. The linear model forces C to zero. A joint Wald F test examines both nonlinear coefficients and is distinct from this one finite contrast. These tests concern smooth curvature; they do not test the location or nonexistence of a sharp threshold.

Variance and disclosure

Uncertainty uses full-design Taylor linearization, with strata and primary sampling units nested within country-round designs. Genuine-singleton and single-contributing-PSU domain adjustments follow the conventions independently checked against R survey 4.5. No independent-respondent covariance replaces the complex design.

Let D be occupied analysis-domain PSUs minus represented strata. Model residual degrees of freedom are D + 1 - model rank; nonpositive values are rejected, never floored to one. Observed-mean intervals use design degrees of freedom. Fitted means and finite contrasts use the full coefficient covariance and pointwise 95% t intervals, not simultaneous coverage. Separate model intervals do not test between-model differences.

Observed means below 50 responses are suppressed; displayed means with 50 to 99 are flagged for low precision. There are 640 suppressed and 303 flagged aggregates among 2,398 raw-score cells. Gaussian means and intervals are not clipped to 0-10. Negative lower limits in some early UK score cells express imprecision, not negative observed ratings.

Historical checks and verification

The eligible country counts in Rounds 1 to 11 are 7, 10, 8, 7, 20, 27, 21, 23, 29, 22 and 30. Only Finland and France span all eleven. The fixed recent comparison covers Rounds 9 to 11 in Belgium, Bulgaria, Switzerland, Estonia, Finland, France, the United Kingdom, Croatia, Hungary, Ireland, Iceland, Italy, Lithuania, Montenegro, the Netherlands, Norway, Portugal, Slovenia and Slovakia. These are repeated cross-sections, not individual trajectories.

Earlier waves, pooled and complete-case models, further adjustment, face-to-face interviews and the recent fixed-country sample are secondary checks. These checks do not rule out confounding, reverse causality or nonresponse bias. Original wording and source labels were checked, but national translations were not independently retranslated and measurement invariance is unestablished.

Two independently executed research runs produced byte-identical aggregate evidence. Reference checks against separately executed R survey 4.5 passed for all 69 fitted models, including coefficients and entire covariance matrices, 12,562 predictions and 320 raw-score mean references, at absolute tolerance 1e-9 and relative tolerance 1e-7. Derived floating-point outputs are serialized to ten significant digits; respondent inputs and counts are not rounded. Public evidence is aggregate-only.

Frozen ESS sources

The pinned releases are R1, edition 6.7, R2, 3.6, R3, 3.7, R4, 4.6, R5, 3.6, R6, 2.7, R7, 2.3, R8, 2.3, R9, 3.3, R10, 3.3 and R11, 4.2. The frozen source licenses specify ESS not-for-profit use terms for Rounds 1 to 7 and CC BY-NC-SA 4.0 for Rounds 8 to 11. The ESS Round 11 data record provides the primary release documentation.

Distribution extension: a separate exploratory question

Version 1.1.0 extends the unchanged 1.0.0 mean-model analysis. The extension was registered after the original mean results had been examined, so its new questions remain secondary and exploratory. They are not an independent confirmation of the original finding.

The extension reuses the same eleven source editions, question mappings, analysis weights and reviewed designs. It contains 204 national country-round scopes, eleven corresponding all-country scopes and the three recent fixed 19-country scopes. Holding those countries fixed does not also fix demographics or their population-weight shares. These are still repeated cross-sections.

Discrete probability mass and its denominator

Marginals and joint cells use respondents with both valid satisfaction answers. Conditional cells use the paired respondents at one economic score. The two marginals, complete 121-cell joint table and empirical cumulative probabilities are derived coherently, not fitted as unrelated visual summaries.

Probabilities use the original ESS analysis weights. Displayed respondent and event counts are unweighted support counts, not estimated population totals. The paired-response share is relative to the eligible design; the complete-case share is relative to the paired sample. Those response-coverage measures do not describe countries excluded because no reviewed sampling design was available.

Every variance retains the full relevant design, including zero contributions from observations outside a declared domain. Conditional-score variances use that score's own domain-singleton configuration; they are not a shortcut from the broader paired covariance. Interior probability intervals are pointwise 95% logit-transformed t intervals using positive domain-specific survey degrees of freedom. Standard errors are reported on the probability scale.

Domains with fewer than 50 respondents are suppressed, and 50-99 are flagged for low precision. Fewer than ten events or non-events receives a separate sparse-support warning. At an observed sample probability of zero or one, the point and counts remain visible but no zero-width population interval is invented. Missing, empty, suppressed and sample-boundary cases are distinct. These display rules are not a claim that response style or item nonresponse has been eliminated.

Ten cutoff models and a coherent target

Each binary outcome indicates whether the democratic-satisfaction response is at or below a cutoff from 0 through 9. The models use the same 46,091 complete Round 11 records, country intercepts, the three original fixed spline columns and the original additional covariates. There is no new outcome-selected breakpoint and no country or financial-strain interaction in this cutoff family.

For a selected reference population, economic satisfaction and its basis columns are set to each registered score while the other observed covariates remain fixed. Inverse-link predictions are averaged using that reference population's normalized original analysis weights. Averaging probabilities is not equivalent to evaluating the inverse link at mean covariates.

The references are the complete respondents of each included country, all 30 countries, and the existing recent 19-country set. The latter is a target population for the same 30-country fit, not a model refitted only to 19 countries. Reference sample size and full model sample size are reported separately.

Prediction variance uses the weighted average response-scale gradient and the full corrected coefficient covariance. Pointwise probability intervals use the model's residual survey degrees of freedom and a logit transformation. This uncertainty conditions on the specified empirical reference composition. The two economic-score changes and their difference use differences of the standardized gradients and the same covariance, not independent-model errors. Their signed uncertainty intervals are not clipped.

A target is displayed as a fitted CDF only if all ten unrounded cutoff probabilities are interior and ordered at all eleven economic scores. Any crossing withholds the complete target surface and its contrasts. No sorting, clipping, isotonic projection or selective omission repairs it. Separate pointwise interval endpoints need not be ordered, and they are not a simultaneous band. Cross-cutoff covariance is not available for constructing category-mass intervals by subtraction. A response at or below a chosen cutoff remains a performance rating, not a measure of opposition to democracy.

Two explicit tests of common shape

The country interaction model retains 47,836 paired Round 11 records and allows each of the 30 countries its own three economic-score basis coefficients. The joint common-shape test covers 87 interaction coefficients. National curvature comparisons come from this one full model and its covariance.

The financial-strain interaction model uses the same 46,091 complete records as the original adjusted model. It adds nine strain-by-basis interactions to country intercepts, strain main effects and the five demographic and main-activity control terms. All four profiles use the same fixed weighted covariate reference. Their support counts remain distinct from the complete model sample.

Both are Gaussian coded-rating models, so their coefficients and contrasts remain in democratic-satisfaction rating points. They do not become probabilities merely because they appear beside the cutoff analysis. Their pointwise intervals do not establish a ranking or an independent difference from the original shared-curve model.

Independent acceptance and preserved source identity

New estimates require pinned R survey 4.5 checks of all published empirical probabilities, full coefficient covariances, predictions, gradients, contrasts, sample identities and design degrees of freedom. The acceptance gate also checks rejected raw CDF targets privately. Two separately executed guarded research runs must produce identical aggregate bytes before import.

The derived outputs retain ten significant digits; respondent inputs are not rounded. Original v1 scientific files, code owners and accepted results remain unchanged. Only validated aggregates and receipts are distributed. Neither these research checks nor the native preview authorizes publication or deployment.

Pinned original releases. Source-wide fieldwork ranges are not individual interview histories.
RoundEditionObserved fieldworkSource
16.72002-01-14 to 2003-12-1510.21338/ess1e06_7
23.62004-04-03 to 2006-12-2910.21338/ess2e03_6
33.72006-01-02 to 2007-12-1910.21338/ess3e03_7
44.62008-01-01 to 2010-03-1210.21338/ess4e04_6
53.62010-01-21 to 2012-02-0510.21338/ess5e03_6
62.72012-01-31 to 2013-12-1610.21338/ess6e02_7
72.32014-08-21 to 2015-12-0210.21338/ess7e02_3
82.32016-08-22 to 2017-12-2810.21338/ess8e02_3
93.32018-08-31 to 2020-01-3110.21338/ess9e03_3
103.32020-09-18 to 2022-09-0210.21338/ess10e03_3
114.22023-03-11 to 2024-12-0110.21338/ess11e04_2
Distribution and interaction-model downloads / 1.1.0

The extension has its own accepted aggregate fingerprint, 0adfca2086c8d353. Original mean-model downloads remain at version 1.0.0.

Original questions and questionnaire pages

Economic satisfaction: On the whole how satisfied are you with the present state of the economy in [country]?

Democratic satisfaction: And on the whole, how satisfied are you with the way democracy works in [country]?

Both are coded 0, extremely dissatisfied, to 10, extremely satisfied. A common numerical range does not make the two questions the same construct.

Analysis 1.0.0 / evidence fingerprint cb9015dccf7ff3b9. Two separately executed research runs match; original respondent records are not public. Published native edition; scientific execution and website release are reviewed separately.