Longitudinal Hypothesis Testing Research

Two waves (baseline and follow-up) are the logical minimum for testing change, but two-wave designs cannot distinguish linear from nonlinear trajectories and are sensitive to regression to the mean. Three or more waves are generally recommended, with four or more required if you want to model curvilinear or phase-specific change.

Repeated-measures ANOVA requires complete data across all waves and assumes compound symmetry of the covariance structure. Linear mixed-effects (multilevel) models are more flexible: they handle missing waves under the MAR assumption, allow different covariance structures, accommodate time-varying covariates, and support unequally spaced measurement occasions. For most real longitudinal data sets, mixed-effects models are the better default.

First, test whether dropout is random (MCAR) or related to observed variables (MAR) using attrition analysis at baseline. Under MAR, full-information maximum likelihood (FIML) estimation or multiple imputation retains all available data and produces unbiased estimates. If dropout is informative (MNAR), sensitivity analyses using pattern-mixture or selection models are needed, and you should acknowledge the threat to validity explicitly.

Measurement invariance means that the scale or instrument measures the same latent construct in the same way at each wave. Without it, observed wave-to-wave differences in scores could reflect changes in how the instrument functions rather than true change in the underlying construct. Confirmatory factor analysis can test configural, metric, and scalar invariance before interpretating longitudinal latent variable change.

Sample size depends on the expected effect size for change, the number of waves, the within-person correlation across waves (higher correlation increases power), the acceptable Type I error rate, and desired power. Because the longitudinal structure induces within-person correlation, the effective sample size for a within-person change test is often larger than for an independent-samples test of the same effect, but power calculations must explicitly model the covariance structure. Simulation-based power analysis tools (e.g., the R package longpower) are recommended.