Fig. 2: Standardized effect size ITT estimates of the impact of the BFY high-cash gift with adjusted and unadjusted confidence intervals.

All presented estimates come from the two-sided intent-to-treat regression analysis pooling measures across ages found in Tables 4–6, clustering the standard errors at the individual level and controlling for baseline covariates, child age at interview, and phone interview status. Standardized treatment effects are represented by the square markers, and the whiskers (lines) represent unadjusted and adjusted 95% confidence interval (CI) estimates. Effect sizes are standardized by the standard deviation of the low-cash gift group and adjusted for multiple hypothesis testing with Westfall and Young⁷² step-down resampling methods. Based on the adjusted p-value, degrees of freedom, and estimated effect size, the corresponding t-statistic and the standard error estimates were calculated to approximate the adjusted standard error and CI. Confidence intervals adjusted for multiple comparisons are represented by thin lines, and unadjusted confidence intervals are represented by thick lines. Filled square marker indicates that the estimate is statistically significant at the 0.05 level using the unadjusted p-value. Hypothesized direction of cash-gift treatment effects (preregistered) are presented in the “Hypoth.” column with “+” indicating a directional increase in outcome and “-” indicating decrease in outcome. Blue shows impact estimates that were in the expected direction; red shows those that were not in the expected direction. Standardized estimates for spanking disciplinary strategy, a dichotomous outcome, come from a linear probability model. Raw linear probability model coefficients are presented in Table 4. Applying a logistic regression model and converting the resulting log of odds ratio into Cohen’s d by a factor of the square root of 3 divided by pi estimates the effect sizes to be −0.14 for spanking disciplinary strategy (unadjusted p = 0.15).