Wave 2 interim analysis: input and output democracy
What we check
The preregistration asks which kind of democracy people prefer. Good input means good political processes, such as fair elections. Good output means good government results, such as public services.
The second choice offers good political processes and good government results for people like the respondent, but poor processes and results for others. We call this the self-focused option, or the own-group option. The other scenario applies equally to everyone.
We expect fewer people to choose the self-focused option when the other option is the one they preferred in the first choice.
gap <-with(choice_summary, ego_percent[comparison_with_preferred ==1] - ego_percent[comparison_with_preferred ==0])
The difference is -30.8 percentage points: preferred alternative minus rejected alternative. Its sign is as expected. This is a simple unadjusted comparison. The adjusted comparison below also accounts for country, the first choice and the alternative shown.
Size and direction of the choice difference
We expect a negative difference: fewer self-focused choices when the alternative was preferred. This bar shows the observed difference in percentage points. The adjusted comparison below provides a second check.
The answer records the scenario number on screen. The scenario texts can swap positions. We use the position variables to identify the text each person chose.
In the first choice, State A has good output and poor input. State B has good input and poor output. In the second choice, the original first text applies equally to everyone. The original second text is self-focused. Text_inptotpt2 = 2 selects State A as the alternative.
The questionnaire and the saved Run 4 screen check support this coding.
In the graph, each dot shows the percentage choosing the own-group option. “Previously preferred” and “Previously rejected” describe the alternative shown alongside it, based on the respondent’s first choice. They do not describe whether the own-group option itself was preferred or rejected.
Comparison after accounting for other variables
This simple linear model accounts for country, the first choice and the universal alternative shown. Its coefficient is in percentage points. We expect a negative sign. The registered final analysis uses logistic regression.
Code
fit <-lm(ego_choice ~ comparison_with_preferred + universal_A + absolute_preference + country, data = w2)adjusted_difference <-100*unname(coef(fit)["comparison_with_preferred"])tibble(records_used =nobs(fit), difference_pp = adjusted_difference) %>%kable(digits =2, col.names =c("Records used", "Preferred minus rejected (percentage points)"))
Records used
Preferred minus rejected (percentage points)
2188
-26.07
Do Wave 1 answers point in the expected direction?
We use Wave 1 answers for the personal characteristics. We match records by country and serial number. These matches still need confirmation from the survey provider. Germany has no matches.
The tables show the number of matches and any differences in age or gender.
Code
link_check %>%kable()
matched
gender_mismatch
age_mismatch
1823
2
3
Code
panel %>%count(country) %>%kable()
country
n
Croatia
200
France
356
Italy
301
Poland
215
Spain
405
Sweden
346
The check finds 2 gender differences and 3 age gaps larger than one year among the possible matches. These pairs are retained for this overview and need review.
Each model uses one predictor and accounts for country. We do not put all predictors in one model. The estimate shows the change in the percentage choosing an option for a one-unit increase in the predictor.
Each model uses records with the answers it needs. The sample size can therefore differ between rows. “Expected” means that the estimate has the predicted sign. It does not mean that we have confirmed the prediction.
Green means the sign matches the expected sign. Orange means the opposite. Each estimate uses a one-unit change on that predictor’s scale. The scales differ, so bar lengths do not rank the predictors by importance. These are the same separate models as in the table.
We expect more output choices in Poland, Croatia and East Germany. We expect fewer in Sweden. The country table allows a first look at Poland, Croatia and Sweden. We do not calculate the registered eight-category country contrasts in this simple overview. Germany has no Wave 1 matches, so the models of individual Wave 1 predictors exclude it.
We do not use weights or fill in missing answers. The updated figures and tables include confidence intervals. We leave the full models and the extra Wave 2 predictors for the main analysis.
Data source and assignment check
We use only w2_data/POLITSOLID_W2_Interim_261007.dta, with 2188 records. Collection is still ongoing. We do not read or add either soft-launch file.
All eight combinations occur in this export. Their presence alone does not prove that randomization worked in every respect. We keep the analysis unweighted and do not fill in missing answers ; confidence intervals and unadjusted p-values are reported below. Panel matches still need provider confirmation.
How to read the confidence intervals
The bars show 95% confidence intervals. If an interval crosses zero, the estimate is not statistically distinguishable from zero at the unadjusted two-sided 5% level. A green estimate can still have an interval crossing zero. The colour records the predicted sign, not statistical significance.
The current export has no Wave 2 weights. Regression intervals use HC2 standard errors. Each panel model uses one change score per person. The graphs of proportions use Wilson intervals. The paired country-change graph uses the variation in each person’s change. The histogram shows counts, so it does not need a confidence interval.
All results remain preliminary. Many comparisons are shown, and their p-values are not corrected for multiple testing. These simple baseline models do not implement every part of the final preregistered analysis.
Choice difference: age and gender robustness
The all-respondent experiment models use Wave 2 age and gender. The individual Wave 1 predictor models use Wave 1 demographics and still exclude unmatched German records. The log-age predictor model adds gender only, to avoid entering age twice.
The primary regression intervals use HC2. An additional CSV repeats uncertainty calculations using observed administrative regions as clusters. These regions are not documented survey sampling units. This sensitivity checks possible within-region dependence without replacing the primary models.
