Bommae Kim

Note: This post is not about hierarchical linear modeling (HLM; multilevel modeling). Hierarchical regression is model comparison of nested regression models.

Let’s say previous studies have suggested that higher grades predict higher happiness: X (grades) → Y (happiness). (This research example is made up for illustration purposes. Please don’t consider it a scientific statement.)

You ran a linear regression analysis and the stats software spit out a bunch of numbers. The results were significant (or not). You might think that you’re done with analysis. No, not yet. After running a regression analysis, you should check if the model works well for the data.

When I first learned data analysis, I always checked normality for each variable and made sure they were normally distributed before running any analyses, such as t-test, ANOVA, or linear regression. I thought normal distribution of variables was the important assumption to proceed to analyses. That’s why stats textbooks show you how to draw histograms and QQ-plots in the beginning of data analysis in the early chapters and see if variables are normally distributed, isn’t it?