Psychologists report effect sizes in randomized controlled trials to facilitate interpretation and inform clinical or policy guidance. Since commonly used effect size measures (e.g., standardized mean difference) are not sensitive to heterogeneous treatment effects, methodologists have suggested the use of an alternative effect size δ, a between-subjects causal parameter describing the probability that the outcome of a random participant in the treatment group is better than the outcome of another random participant in the control group. Although this effect size is useful, researchers could mistakenly use δ to describe its within-subject analogue, ψ, the probability that an individual will do better under the treatment than the control. Hand’s paradox describes the situation where ψ and δ are on opposing sides of 0.5: δ may imply most are helped whereas the (unknown) underlying ψ indicates that most are harmed by the treatment. The current study used Monte Carlo simulations to investigate plausible situations under which Hand’s paradox does and does not occur, tracked the magnitude of the discrepancy between ψ and δ, and explored whether the size of the discrepancy could be reduced with a relevant covariate. The findings suggested that although the paradox should not occur under bivariate normal data conditions in the population, there could be sample cases with the paradox. The magnitude of the discrepancy between ψ and δ depended on both the size of the average treatment effect and the underlying correlation between the potential outcomes, ρ. Smaller effects led to larger discrepancies when ρ < 0 and ρ = 1, whereas larger effects led to larger discrepancies when 0 < ρ < 1. It was useful to consider a relevant covariate when calculating ψ and δ. Although ψ and δ were still discrepant within covariate levels, results indicated that conditioning upon relevant covariates is still useful in describing heterogeneous treatment effects.

Decision trees is a machine learning technique that searches the predictor space for the variable and observed value that leads to the best prediction when the data are split into two nodes based on the variable and splitting value. Conditional Inference Trees (CTREEs) is a non-parametric class of decision trees that uses statistical theory in order to select variables for splitting. Missing data can be problematic in decision trees because of an inability to place an observation with a missing value into a node based on the chosen splitting variable. Moreover, missing data can alter the selection process because of its inability to place observations with missing values. Simple missing data approaches (e.g., deletion, majority rule, and surrogate split) have been implemented in decision tree algorithms; however, more sophisticated missing data techniques have not been thoroughly examined. In addition to these approaches, this dissertation proposed a modified multiple imputation approach to handling missing data in CTREEs. A simulation was conducted to compare this approach with simple missing data approaches as well as single imputation and a multiple imputation with prediction averaging. Results revealed that simple approaches (i.e., majority rule, treat missing as its own category, and listwise deletion) were effective in handling missing data in CTREEs. The modified multiple imputation approach did not perform very well against simple approaches in most conditions, but this approach did seem best suited for small sample sizes and extreme missingness situations.

Collider effects pose a major problem in psychological research. Colliders are third variables that bias the relationship between an independent and dependent variable when (1) the composition of a research sample is restricted by the scores on a collider variable or (2) researchers adjust for a collider variable in their statistical analyses. Both cases interfere with the accuracy and generalizability of statistical results. Despite their importance, collider effects remain relatively unknown in the social sciences. This research introduces both the conceptual and the mathematical foundation for collider effects and demonstrates how to calculate a collider effect and test it for statistical significance. Simulation studies examined the efficiency and accuracy of the collider estimation methods and tested the viability of Thorndike’s Case III equation as a potential solution to correcting for collider bias in cases of biased sample selection.

Relations between two aspects of the parent-child relationship, parent warmth and modeling of emotion expression, and youth internalizing and externalizing problems and maladaptive grief were examined in a longitudinal sample of parentally bereaved youth. Youth expressive suppression was tested as a mediator of these relations and youth age was examined as a moderator. Parentally bereaved youth (N=244) aged 8 to 16 and their parents were assessed at three timepoints. Across 14 months, parent modeling of maladaptive emotion expression was significantly associated with increased parent report of both internalizing and externalizing problems, and youth report of parental warmth was significantly associated with decreased youth report of externalizing problems. There was no support for youth expressive suppression mediating these relations and the pattern of relations did not differ significantly by youth age. Implications for intervention programs targeting parents and youth are discussed.