Not Everything Is Normal: Three Statistical Distributions and When to Use Them

Be mindful of linear regressions. They’re not always the indicated statistical analysis.

René F. Najera, MPH, DrPH
9 min readMay 28, 2024
Three side-by-side histograms illustrating the distributions of Normal, Poisson, and Chi-square distributions. Each histogram is overlaid with a red density curve. The first histogram, labeled ‘Normal Distribution,’ shows a symmetrical bell curve with blue bars. The second histogram, labeled ‘Poisson Distribution,’ displays a right-skewed distribution with green bars. The third histogram, labeled ‘Chi-square Distribution,’ presents a right-skewed distribution with purple bars.
They all look bell-shaped because of the Central Limit Theorem, but be mindful of what each is presenting.

A few days ago, a friend sent me a picture of a graph. The graph showed his weight over the last few years, and the projected date when he would hit his desired weight. He was upset because the app he used was forecasting him getting back to his college weight sometime in 2032, eight years from now.

“That’s ridiculous,” I said. “No one ever returns to their college weight, unless they have something seriously bad happen to them.” My attempt at levity was not received well, so I turned on the math. “Look,” I said. “The model they’re using is a linear model. They’re taking all the points before and getting the average, then drawing a straight line to your desired weight. The thing is, you don’t lose weight linearly under normal circumstances. It’s more like a Poisson regression.”

A Statistical What-tribution?

Statistical distributions are essential tools in the field of statistical inference, providing a foundation for analyzing data and making predictions. The most basic definition I use for students who are not statistics majors is that distributions are “the way numbers…

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René F. Najera, MPH, DrPH

DrPH in Epidemiology. Public Health Instructor. Father. Husband. "All around great guy."