Undergraduate students writing a scientific paper, lab report, or senior thesis frequently have to decide how to formalize statistical analyses. How do you know if values in an experimental group are different from those in a control group? While many students have been taught about general statistical concepts—such as p-values and confidence intervals—choosing the right test for statistical significance can be daunting without a framework. As someone who has worked on dozens of translational and clinical research manuscripts, I make this sort of choice in almost every table or figure. I’ve found that the decision can often be boiled down to the following four questions:

- Is my data parametric or non-parametric?
- Is my data numeric or categorical?
- How many groups do I have?
- Are my groups paired or unpaired?

Let’s go through these questions to better understand how they can be helpful.

*Is my data parametric or non-parametric?*

It is important to decide whether your data follows a normal distribution curve, in which case parametric statistical tests are most appropriate. When plotted in a histogram, values for normally distributed variables lie in an approximately symmetrical fashion around the mean. Parametric tests are usually reasonable for continuous variables that are not measured on a unique, experimenter-derived scale. Examples of such variables include age, height, weight, blood pressure, and temperature.

If the underlying distribution of the data is not normal—or you are not sure about the distribution—then it is safer to use non-parametric statistical tests. These tests are often well-suitable for scores on a known scale. For example, the Glasgow Coma Scale (GCS) is a clinical score used to measure a person’s level of consciousness after a brain injury. The GCS is quantitative (with scores ranging from 3 to 15) but it is neither continuous nor normally distributed.

*Is my data numeric or categorical?*

Parametric and non-parametric variables differ in their distributions, but still have a hierarchy of smaller and greater values. In contrast, a categorical variable is a variable that can take on only a fixed number of possible values—and whose values differ from each other *qualitatively* rather than quantitatively. Examples of categorical variables include polical party, blood type, and gender. Determining whether two or more distributions of categorical variables are different requires applying distinct statistical tests.

*How many groups do I have?*

Different statistical tests are also applied when comparing more than two groups. This collection of statistical tests is often referred to as ANOVA (or analysis of variance). When comparing more than two sets of numerical data, an ANOVA-like test for more than two groups should be used initially. If this test returns a significant result, then one can apply another “post hoc” test to determine between which exact groups the difference lies, depending on whether the data is parametric or non-parametric.

*Are my groups paired or unpaired?*

Pairing means that your data includes repeated measurements (e.g. multiple measurements across time) on the same set of subjects. Pairing can also mean that data points for one group of subjects are somehow linked or related to values in another group (e.g. studies on pairs of twins). The relationship between sets of measurements with paired data necessitates the use of different statistical tests.

An overall algorithm for picking an appropriate test is summarized in the graphic below:

One caveat to this graphic is that it assumes you are interested in testing for a *difference* rather than an *association*. As with the tests listed above, the best approach for investigating associations between variables depends on what kinds of variables (e.g., parametric, non-parametric) that you are dealing with.

To sum it up, the key to analyzing your data is understanding your variables. Choosing the right statistical test can be challenging, but hopefully the algorithm above makes this decision a little bit easier!

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