Which test should I use?
The best method depends on what you measure and how you collected it. Choose your question below, then check the assumptions before calculating.
One-sample t-test
For independent numerical observations with unknown population standard deviation. Check for severe skew and outliers, especially with a small sample.
Welch’s two-sample t-test
Use for two unrelated groups with numerical outcomes. Welch’s method does not require equal variances. Independence and suitable distribution assumptions still matter.
Paired t-test
Calculate the difference within each pair, then test the mean difference. Pairs must be independent of one another; assess the distribution of the differences.
One-way ANOVA
For a numerical outcome grouped by one categorical factor. The standard ANOVA model assumes independent observations, roughly normal errors, and equal variances. Consider Welch’s ANOVA if variances differ.
Chi-square test of independence
Use counts in a contingency table, with independent observations and sufficient expected cell counts. Sparse tables may need an exact test. Use goodness-of-fit instead when comparing one categorical distribution to specified proportions.
Pearson correlation
For paired numerical variables with a roughly linear relationship. Inspect a scatterplot and influential outliers. The usual significance test assumes independent pairs and appropriate distribution conditions; correlation does not establish causation.
Don’t let sample size choose the test for you
“Use z when n ≥ 30” is too simple. Inference about a mean with population standard deviation estimated from your sample generally uses t. A large sample makes t and z cutoffs closer; it doesn’t make the population standard deviation known.
Decide before looking at the result
State your null and alternative hypotheses, choose a significance level, and decide whether a directional test is justified before analyzing the data. Trying multiple tests until one gives p < 0.05 changes the error rate.
Report more than a p-value
Include the estimated effect, an uncertainty interval when appropriate, the sample size, and the test assumptions. A statistically significant result can be practically small; a non-significant result does not prove there is no effect.