What each mark represents
The empirical displays on this site reproduce published summary statistics. A point may represent an adjusted mean or a correlation, while a bar segment represents a response percentage. None of these marks represents an individual participant. The separate methods demonstration uses generated points and is explicitly labeled as synthetic.
Correlation and causation
A positive correlation means that higher values on one measure tend to accompany higher values on another in the analyzed sample. It does not establish that changing the first variable will change the second. Shared causes, reverse direction, measurement choices, and the sample itself can all matter. A bivariate correlation also differs from a regression coefficient adjusted for other variables.
Standard deviations and confidence intervals
A standard deviation describes variation in observed scores. A confidence interval describes uncertainty in an estimate under a statistical model. The antisemitism correlation chart uses the published 95% confidence intervals. The optional profile chart instead shows one standard deviation around a mean. The Study 4 mean chart shows adjusted means without error bars because exact uncertainty intervals are not supplied numerically in its source figure.
Comparing waves
A change in mean level, a within-wave correlation, and an association between individual changes answer different questions. The Study 4 views separate mean scores from within-wave correlations. Comparing two displayed correlations does not test whether their difference is statistically significant, and a line joining two group means does not depict any one person’s trajectory.