Which Statistical Test Should I Use?

Before you start

You are comfortable with p-values and basic distributions. New to those? Start with Stats you cannot avoid.
Any term new? The Glossary has it.

Learning objectives

By the end of this lesson you will be able to: pick a sensible statistical test by asking three simple questions about your data, and know the safe default to reach for when you are unsure.

The question that freezes every beginner

"Which test should I use?" stops people cold. The good news: you do not need to memorize a hundred tests. Almost every everyday comparison comes down to three questions about your data, and a small map gets you to the right answer. This lesson is that map.

1The three questions

Before choosing a test, answer these about your data:

What kind of data is it? Numbers you measured (expression, height, concentration), or counts in categories (how many in group A vs B)?
How many groups are you comparing? One, two, or more than two?
Is the data roughly bell-shaped (normal), or is it skewed / very small / ranked? This decides whether you use a standard test or its rank-based ("non-parametric") cousin.

2The decision map

Follow your data down the tree. Green = standard (roughly normal) data; amber = the rank-based version for skewed, small, or ranked data.

You want to...	Standard data	Skewed / small / ranked
Compare 2 groups' averages	t-test (paired t-test if matched)	Wilcoxon (Mann-Whitney)
Compare 3+ groups	ANOVA	Kruskal-Wallis
Relate two numeric variables	Pearson correlation	Spearman correlation
Compare counts in categories	Chi-square test	Fisher's exact test (small counts)

3When you are not sure

If you cannot tell whether your data is normal (common with small samples), the rank-based tests are a safe default: Wilcoxon instead of a t-test, Spearman instead of Pearson. They make fewer assumptions and rarely mislead. And remember two things from the rest of this track: a significant result still needs an effect size to matter, and if you run many tests at once you must apply multiple-testing correction.

One honest caveat

This map covers the everyday cases, not every situation. Specialized data (survival times, RNA-seq counts, repeated measures) has its own purpose-built methods, for example DESeq2 for RNA-seq counts. But for "I measured a thing in two or three groups," this map is almost always right.

Check your understanding

You measured a numeric value in three treatment groups, and it is roughly normal. Which test?

Right. A t-test compares two groups; for three or more roughly-normal groups you use ANOVA (Kruskal-Wallis if non-normal).

Your sample is small and you cannot tell if it is normal. What is the safe default?

Correct. Rank-based tests make fewer assumptions, so they are the safe choice when normality is in doubt.

You have expression values for 4 treated and 4 control samples, and the data looks skewed. Which test fits best?

Right. Two groups of measured numbers that are small and skewed point to the rank-based two-group test, Wilcoxon.

You want to know whether two continuous measurements rise and fall together, but the relationship is not a straight line. Which correlation?

Correct. Spearman measures whether they move together in rank order, so it handles non-linear (monotonic) relationships and skew.

You have a 2x2 table counting how many samples fall into each category, and the counts are small. Which test?

Exactly. Categorical counts use chi-square, but when the counts are small, Fisher's exact test is the correct choice.

Next in Track 5