# Module 2

## Foundations of Complex Multilevel and Longitudinal Designs

In the second module, we are going to dive into the many facets of research design and important considerations related to power and sample size analysis. Specifically, we will examine independent sampling unit factors, power and error, and variance and correlation structure. We will explore the appropriate statistical tests for use in specific models, criteria for evaluating these different tests, and how to choose an appropriate test for a data analysis problem. Finally, we will note how clusters of observations or multivariate designs can induce correlation. This module provides the details for specifying research designs, and the beginning steps in aligning the research design to sample size and power analysis. The module concludes with summarizing research designs for GLIMMPSE software. You will walk through a guided exercise problem to solve for sample size analysis for a longitudinal study.

### Key Concepts

• Define between-independent and within-independent sampling unit factors.
• Describe how statistical models facilitate outcome prediction and hypothesis testing.
• Define between-ISU hypothesis, within-ISU hypothesis, and an interaction.
• Define type 1 error, type 2 error, and power.
• Describe which hypothesis test statistics are used for a specific model.
• Evaluate criteria for comparing different statistical tests.
• Choose an appropriate statistical test for data analysis aligned to power and sample size analysis.
• Define standard deviation, variance, and correlation structure.
• Describe how correlation structure influences power and data analysis.
• Describe how clusters of observations induce compound symmetric correlation structures.
• Describe how multivariate study designs can induce a variety of different correlation structures.