Fatima Gallardo Ibarra • 2024 McNair Summer Research Symposium • July 8, 2024

Fatima Gallardo Ibarra

Class of 2024

Major: Psychology

Mentor: Rick Sperling, PhD

St. Mary’s University

The Emergence of Optimal F: Applying Optimal t Logic to ANOVAs

Practitioners often deal with missingness when using with-subject designs. While there are

useful approaches for dealing with missingness, such as imputation, most are too sophisticated

for practitioners to apply. Those that are more manageable, such as deletion methods, have

deleterious effects on the interpretability of results.

In attempts to reduce the loss of statistical power through preservation of data, research on the

use of between-subjects test in within-subjects scenarios have been examined (Avila et. al.,

2021). Rather than using a paired samples t-test on pretest/posttest data, an independent sample t-

test is used for its potential to increase statistical power form the preservation of data. This

method was applied in a previous study in the development of Optima t, where R code is used to

identify and perform the t-test with the highest statistical power based on specified parameters

(Cuevas et al., 2023).

This study examined whether the logic of Optimal t can be applied to within-subjects scenarios

that have three or more measurement points. We considered specified sample sizes (25, 50, 75),

correlation (0,0.15, 0.3), missingness (0, 0.15, 0.3), and differences in means (0 sd, 0.25 sd, 0.5

sd). Results were encouraging as this new method, which we refer to as Optimal F, showed

promising outcomes with respect to both Type I and Type II error rates. Recommendations for

future research are discussed.

Keywords: t-test, ANOVA, analysis of variance, within-subject design, missing data,

missingness