| component | status | note |
|---|---|---|
| Study 1 take-up | Available | Invitation randomization files and the status-code export can be joined directly. |
| Study 2 treatment assignment | Available | c_0001 is present for all analyzed respondents. |
| Fair monthly fee (EUR) | Available | Constructed from v_65, v_67, and the bracketed current-fee item v_180. |
| Donation amount (EUR) | Available | Recovered from v_168. |
| Lottery participation / opt-out | Available | The codebook identifies explicit opt-out responses in both v_168 and v_116. |
| Prior-belief gap within T3 | Available | v_56 is the pre-treatment parent-share estimate, and the archived T3 treatment text states parents pay about EUR 70 of EUR 993 total costs. |
| Income moderation | Available | v_95 is the five-category household income item. |
| Treatment-by-letter interaction | Partial | Estimable only for respondents with a non-missing invitation code in c_0002. |
| Ideology moderation | Available | v_37 is the codebook-labelled 11-point left-right self-placement item. |
| Education moderation | Available | v_76 is the highest-school-degree item; v_77 contains open-text 'other' entries when v_76 = 9. |
POLITSOLID Preregistration Reanalysis
Scope
This report re-analyzes the Unipark data against the preregistration in prereg.md. The goal is to estimate the preregistered outcomes as closely as the current export permits.
This version incorporates the 2026-04-16 codebook, so variable mappings now follow the documented questionnaire items where those labels are available.
For the within-survey experiment, I retain the arm codes T0 to T3 used in the existing project files, but the substantive mapping is now identified: T0 = control with no additional information screen, T1 = generic information about Duisburg kindergartens and fees, T2 = empathy-story vignette about a child benefiting from the solidarity system, and T3 = fiscal information about taxpayer contributions and the gap between total costs and parental payments.
Summary
- The invitation letter does not shift take-up in the latest export
- The within-survey treatments produce small, imprecise movements in the fair-fee proxy and donation outcome, with no confirmatory contrast surviving Holm correction.
- Even with the moderator items, we do not see patterns that change the overall conclusion.
Preregistration coverage
| analysis_variable | export_variable | status | evidence |
|---|---|---|---|
| Ideology | v_37 | Identified | The codebook labels v_37 as the 11-point left-right self-placement item. |
| Current kindergarten fee | v_180 | Identified | The codebook labels v_180 as the current monthly fee bracket; bracket midpoints are used when a EUR-scale covariate is needed. |
| Education | v_76 | Identified | The codebook labels v_76 as highest school degree, with v_77 as the open-text 'other' follow-up. |
| Income | v_95 | Identified | The codebook labels v_95 as five-category household income after taxes and deductions. |
| Prior belief about parent share | v_56 | Identified | The codebook labels v_56 as the respondent's estimate of the percentage of costs paid by parents. |
| Donation amount | v_168 | Identified | The codebook labels v_168 as the 0-100 EUR donation split item. |
| Lottery participation / opt-out | v_168 + v_116 | Identified with derived rule | The codebook shows explicit opt-out codes in both the donation item and the follow-up contact item. |
| Substantive T1-T3 labels | c_0001 | Identified | T1 = generic kindergarten-fee information, T2 = empathy story vignette, and T3 = fiscal information about taxpayer contributions and the parent-cost gap. |
| True T3 financing split | Archived treatment text | Identified | The treatment archive states total costs of about EUR 993 per month, with parents paying EUR 70 on average and taxpayers EUR 923. |
Data preparation
| sample | n |
|---|---|
| Study 1 randomized invitation rows | 13161 |
| Study 2 non-test respondents with valid completion/consent | 2298 |
| Study 2 respondents with non-missing invitation code | 733 |
| Study 2 observed fair monthly fee proxy | 1989 |
| Study 2 non-missing donation response in v_168 | 2198 |
| Study 2 explicit lottery opt-out in v_168 or v_116 | 258 |
| Study 2 confirmed lottery participation (v_168 and v_116) | 2040 |
| Study 2 observed donation amount among confirmed participants | 2040 |
| Study 2 observed financing satisfaction | 2080 |
| Study 2 observed prior-belief item (v_56) | 2003 |
| Study 2 T3 fair-fee belief-gap sample | 456 |
| Study 2 T3 donation belief-gap sample | 516 |
| Study 2 ideology item observed | 1852 |
| Study 2 education item observed | 2137 |
| Study 2 income item observed | 2042 |
Core models
Study 1: Invitation letter take-up
| letter_treatment | n | take_up_n | take_up_rate |
|---|---|---|---|
| Efficiency letter | 6581 | 1157 | 0.176 |
| Empathy letter | 6580 | 1141 | 0.173 |
The preregistered take-up estimand is the difference in proportions between the empathy and efficiency letters, supplemented by a logistic regression. In the current export, the estimated take-up difference is -0.24 pp with a 95% CI of [-1.06 pp, 1.54 pp] and p = 0.716. The corresponding odds ratio from the logistic model is 0.983.
Study 2: Descriptive arm means
| outcome | survey_treatment | n | mean | sd |
|---|---|---|---|---|
| Donation amount with explicit opt-outs -> 0 (EUR) | T0 | 550 | 27.709 | 34.98 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T1 | 557 | 26.822 | 35.27 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T2 | 591 | 27.056 | 34.37 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T3 | 600 | 27.183 | 35.20 |
| Fair monthly fee proxy (EUR) | T0 | 475 | 86.495 | 97.79 |
| Fair monthly fee proxy (EUR) | T1 | 482 | 83.855 | 102.89 |
| Fair monthly fee proxy (EUR) | T2 | 508 | 90.526 | 104.67 |
| Fair monthly fee proxy (EUR) | T3 | 524 | 80.239 | 99.49 |
| Fairness perception item (-5 to +5) | T0 | 527 | 0.935 | 2.22 |
| Fairness perception item (-5 to +5) | T1 | 536 | 0.713 | 2.03 |
| Fairness perception item (-5 to +5) | T2 | 562 | 0.546 | 2.03 |
| Fairness perception item (-5 to +5) | T3 | 573 | 0.981 | 2.13 |
| Financing satisfaction (1-11) | T0 | 497 | 6.000 | 3.02 |
| Financing satisfaction (1-11) | T1 | 514 | 6.023 | 3.04 |
| Financing satisfaction (1-11) | T2 | 538 | 6.290 | 2.84 |
| Financing satisfaction (1-11) | T3 | 531 | 5.768 | 2.95 |
| Observed donation amount among confirmed participants (EUR) | T0 | 496 | 30.726 | 35.55 |
| Observed donation amount among confirmed participants (EUR) | T1 | 488 | 30.615 | 36.11 |
| Observed donation amount among confirmed participants (EUR) | T2 | 520 | 30.750 | 35.06 |
| Observed donation amount among confirmed participants (EUR) | T3 | 536 | 30.429 | 35.90 |
Study 2: Confirmatory preregistered tests
The preregistration defines two primary Study 2 outcomes at the analysis stage used here: the fair-fee outcome and donation amount. For each outcome separately, the confirmatory family is T1 vs T0, T2 vs T0, and T3 vs T0, adjusted with the Holm procedure. As a supplement, I also report the false-discovery-rate q-values across all six confirmatory tests.
| outcome | contrast | estimate | conf_low | conf_high | p_value | holm_p | fdr_q |
|---|---|---|---|---|---|---|---|
| Fair monthly fee proxy (EUR) | T1 vs T0 | 1.648 | -9.03 | 12.33 | 0.762 | 0.762 | 0.799 |
| Fair monthly fee proxy (EUR) | T2 vs T0 | 6.942 | -3.61 | 17.50 | 0.197 | 0.592 | 0.700 |
| Fair monthly fee proxy (EUR) | T3 vs T0 | -6.369 | -16.85 | 4.11 | 0.233 | 0.592 | 0.700 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T1 vs T0 | -0.887 | -5.01 | 3.23 | 0.673 | 1.000 | 0.799 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T2 vs T0 | -0.653 | -4.71 | 3.41 | 0.752 | 1.000 | 0.799 |
| Donation amount with explicit opt-outs -> 0 (EUR) | T3 vs T0 | -0.526 | -4.57 | 3.52 | 0.799 | 1.000 | 0.799 |
Secondary and exploratory contrasts
| outcome | contrast_type | contrast | estimate | conf_low | conf_high | p_value |
|---|---|---|---|---|---|---|
| Fair monthly fee proxy (EUR) | Secondary | T2 vs T1 | 5.294 | -5.191 | 15.779 | 0.322 |
| Fair monthly fee proxy (EUR) | Secondary | T3 vs T1 | -8.017 | -18.431 | 2.396 | 0.131 |
| Fair monthly fee proxy (EUR) | Exploratory | T2 vs T3 | 13.311 | 3.024 | 23.598 | 0.011 |
| Donation amount with explicit opt-outs -> 0 (EUR) | Secondary | T2 vs T1 | 0.234 | -3.814 | 4.281 | 0.910 |
| Donation amount with explicit opt-outs -> 0 (EUR) | Secondary | T3 vs T1 | 0.361 | -3.672 | 4.394 | 0.861 |
| Donation amount with explicit opt-outs -> 0 (EUR) | Exploratory | T2 vs T3 | -0.127 | -4.100 | 3.845 | 0.950 |
| Observed donation amount among confirmed participants (EUR) | Confirmatory | T1 vs T0 | -0.111 | -4.569 | 4.347 | 0.961 |
| Observed donation amount among confirmed participants (EUR) | Confirmatory | T2 vs T0 | 0.024 | -4.364 | 4.413 | 0.991 |
| Observed donation amount among confirmed participants (EUR) | Confirmatory | T3 vs T0 | -0.297 | -4.653 | 4.060 | 0.894 |
| Observed donation amount among confirmed participants (EUR) | Secondary | T2 vs T1 | 0.135 | -4.271 | 4.542 | 0.952 |
| Observed donation amount among confirmed participants (EUR) | Secondary | T3 vs T1 | -0.186 | -4.560 | 4.189 | 0.934 |
| Observed donation amount among confirmed participants (EUR) | Exploratory | T2 vs T3 | 0.321 | -3.983 | 4.625 | 0.884 |
| Financing satisfaction (1-11) | Confirmatory | T1 vs T0 | 0.023 | -0.342 | 0.389 | 0.900 |
| Financing satisfaction (1-11) | Confirmatory | T2 vs T0 | 0.290 | -0.071 | 0.651 | 0.116 |
| Financing satisfaction (1-11) | Confirmatory | T3 vs T0 | -0.232 | -0.594 | 0.131 | 0.210 |
| Financing satisfaction (1-11) | Secondary | T2 vs T1 | 0.267 | -0.091 | 0.625 | 0.144 |
| Financing satisfaction (1-11) | Secondary | T3 vs T1 | -0.255 | -0.614 | 0.104 | 0.164 |
| Financing satisfaction (1-11) | Exploratory | T2 vs T3 | 0.522 | 0.166 | 0.877 | 0.004 |
Invitation-letter interactions
| letter_treatment | T0 | T1 | T2 | T3 |
|---|---|---|---|---|
| Efficiency letter | 95 | 103 | 94 | 87 |
| Empathy letter | 77 | 92 | 92 | 93 |
| outcome | term | Estimate | Pr(>|t|) |
|---|---|---|---|
| Fair monthly fee proxy (EUR) | survey_treatmentT1:letter_treatmentEmpathy letter | -23.35 | 0.234 |
| Fair monthly fee proxy (EUR) | survey_treatmentT2:letter_treatmentEmpathy letter | -23.57 | 0.234 |
| Fair monthly fee proxy (EUR) | survey_treatmentT3:letter_treatmentEmpathy letter | -36.66 | 0.066 |
| Donation amount with explicit opt-outs -> 0 (EUR) | survey_treatmentT1:letter_treatmentEmpathy letter | -3.60 | 0.625 |
| Donation amount with explicit opt-outs -> 0 (EUR) | survey_treatmentT2:letter_treatmentEmpathy letter | -4.25 | 0.568 |
| Donation amount with explicit opt-outs -> 0 (EUR) | survey_treatmentT3:letter_treatmentEmpathy letter | -12.91 | 0.086 |
These interaction models are the best available approximation to the preregistered cumulative-empathy hypothesis. They should be treated cautiously because the linkage back to invitation assignment depends on the respondent-level invitation code in c_0002, which is not complete.
Prior-belief gap within T3
I define the preregistered belief gap as the absolute difference between each respondent’s estimate in v_56 and 7.05%. Because only T3 reveals that split, the models below are restricted to respondents assigned to T3.
| quantity | value |
|---|---|
| True parent share shown in T3 (%) | 7.05 |
| T3 respondents with non-missing belief item | 516 |
| Mean estimated parent share in T3 (%) | 41.94 |
| Mean absolute belief gap in T3 (%) | 35.36 |
| SD absolute belief gap in T3 (%) | 23.72 |
| Fair-fee slope per 10 pp larger gap (EUR) | -2.568 |
| Fair-fee slope p-value | 0.137 |
| Donation slope per 10 pp larger gap (EUR) | -1.676 |
| Donation slope p-value | 0.010 |
In this implementation, positive coefficients mean that respondents whose prior beliefs were further from the true split ended up with higher fair-fee or donation outcomes inside the contribution arm. This remains exploratory rather than causal, because the moderator varies only within T3.
Moderator analyses
The codebook directly identifies three moderator items strong enough to estimate exploratory interaction models. v_37 is the 11-point left-right self-placement item, v_76 is the highest-school-degree item with a category-9 open-text follow-up in v_77, and v_95 is the five-category household-income item. I analyze them as ordered moderators in the models below.
| moderator | outcome | term | Estimate | Pr(>|t|) |
|---|---|---|---|---|
| Ideology | Fair monthly fee proxy (EUR) | T1 x ideology | -4.437 | 0.501 |
| Ideology | Fair monthly fee proxy (EUR) | T2 x ideology | -3.650 | 0.564 |
| Ideology | Fair monthly fee proxy (EUR) | T3 x ideology | -10.550 | 0.093 |
| Ideology | Donation amount with explicit opt-outs -> 0 (EUR) | T1 x ideology | -0.614 | 0.801 |
| Ideology | Donation amount with explicit opt-outs -> 0 (EUR) | T2 x ideology | -2.022 | 0.382 |
| Ideology | Donation amount with explicit opt-outs -> 0 (EUR) | T3 x ideology | -3.048 | 0.195 |
| Education | Fair monthly fee proxy (EUR) | T1 x education | -2.019 | 0.735 |
| Education | Fair monthly fee proxy (EUR) | T2 x education | -2.429 | 0.672 |
| Education | Fair monthly fee proxy (EUR) | T3 x education | -1.261 | 0.828 |
| Education | Donation amount with explicit opt-outs -> 0 (EUR) | T1 x education | -1.484 | 0.506 |
| Education | Donation amount with explicit opt-outs -> 0 (EUR) | T2 x education | -3.206 | 0.132 |
| Education | Donation amount with explicit opt-outs -> 0 (EUR) | T3 x education | -2.494 | 0.252 |
| Income | Fair monthly fee proxy (EUR) | T1 x income | -8.142 | 0.172 |
| Income | Fair monthly fee proxy (EUR) | T2 x income | 1.726 | 0.772 |
| Income | Fair monthly fee proxy (EUR) | T3 x income | -5.343 | 0.365 |
| Income | Donation amount with explicit opt-outs -> 0 (EUR) | T1 x income | -2.793 | 0.206 |
| Income | Donation amount with explicit opt-outs -> 0 (EUR) | T2 x income | -1.851 | 0.391 |
| Income | Donation amount with explicit opt-outs -> 0 (EUR) | T3 x income | -3.371 | 0.126 |
For ideology, lower values on v_37 correspond to more left-leaning self-placement, so negative treatment-by-ideology coefficients would be directionally consistent with the preregistered expectation of stronger treatment effects among more left-leaning respondents. In the current data, those interaction terms do not show a clear, robust pattern. For education, the interaction models are estimable using the ordered school-degree item v_76, but directional interpretation remains limited by the unresolved mapping from arm numbers to the substantive T1/T2/T3 treatment texts. For income, v_95 provides a five-category household-income item with strong enough coverage to estimate the same exploratory interaction models.
Hypothesis-by-hypothesis assessment
| hypothesis | estimable | verdict | summary |
|---|---|---|---|
| Study 1 H1: empathy invitation increases take-up | Yes | Not supported | Difference = -0.24 pp, 95% CI [-1.06 pp, 1.54 pp], p = 0.716; OR = 0.983 [0.899, 1.076]. |
| Study 2 H1a: T2/T3 increase fair monthly fee | Yes, with fee proxy | Not supported | T2 vs T0: 6.942 EUR, Holm p = 0.592; T3 vs T0: -6.369 EUR, Holm p = 0.592. |
| Study 2 H1b: T2/T3 increase donation | Yes, with codebook-supported opt-out coding | Not supported | T2 vs T0: -0.653 EUR, Holm p = 1.000; T3 vs T0: -0.526 EUR, Holm p = 1.000. |
| Study 2 H2: information effects are stronger after empathy invitation | Partially | No clear interaction evidence | Interaction rows estimated on n = 733 for donation and n = 619 for fair fee; no preregistered moderator coding beyond invitation letter was recoverable. |
| Study 2 H3: ideology moderates treatment effects | Yes, with identified ideology item | Directionally consistent only | Using the codebook-labelled left-right self-placement item v_37, T2 and T3 interaction estimates are -3.650 and -10.550 for fair fee, and -2.022 and -3.048 for donation. Negative coefficients would imply stronger effects among more left-leaning respondents. |
| Study 2 H4: education moderates treatment effects | Yes, with identified education item | No clear interaction evidence | Using the codebook-labelled highest-school-degree item v_76 on categories 1:8, fair-fee interactions are imprecise, while donation interactions for T2 and T3 are -3.206 and -2.494 with p-values 0.132 and 0.252; substantive T2/T3 interpretation still depends on unresolved arm-label mapping. |
| Study 2 H5: income moderates treatment effects | Yes, with identified income item | No clear interaction evidence | Using the codebook-labelled household-income item v_95, fair-fee income interactions range from -8.142 to 1.726 and donation income interactions range from -3.371 to -1.851; none of these interactions are clearly decisive in the current file unless their p-values indicate otherwise. |
| Study 2 H6: T2 moves donation more; T3 moves fair fee more | Yes, exploratory | Not supported | Fair-fee T2 vs T3 = 13.311 EUR, p = 0.011; donation T2 vs T3 = -0.127 EUR, p = 0.950. |