Start with the question, not the test menu
Every statistical test answers one shape of question. Picking the right one takes three facts: what you are asking (a mean? a proportion? a relationship?), what your data look like (one sample or two, paired or independent, counts or measurements), and whether the classic assumptions roughly hold (bell-shaped data, decent sample size). Answer those and the test usually names itself. The table below routes the common questions to the tests this site computes.
| Your question | Your data | Test | Calculator |
|---|---|---|---|
| Is one mean different from a target value? | One sample of measurements | One-sample t test | One-sample t test |
| Do two groups differ on average? | Two independent samples | Two-sample t test (Welch) | Two-sample t test |
| Did the same subjects change? | Paired measurements (before/after) | Paired t test | Paired t test |
| Do three or more groups differ? | Three-plus independent samples | One-way ANOVA | One-way ANOVA |
| Is one proportion different from a target? | Counts of successes out of trials | One-proportion z test | One-proportion z test |
| Do two proportions differ? | Success counts in two groups | Two-proportion z test | Two-proportion z test |
| Do observed counts match expected proportions? | Counts across categories | Chi-square goodness of fit | Chi-square goodness of fit |
| Are two categorical variables associated? | A contingency table of counts | Chi-square independence test | Chi-square independence |
| Are two measurements related? | Paired numeric data | Correlation significance test | Correlation test |
| Two groups, but the data are skewed or ranked | Independent samples, non-normal | Mann-Whitney U | Mann-Whitney U |
| Paired data, skewed or ranked | Paired differences, non-normal | Wilcoxon signed-rank | Wilcoxon signed-rank |
| Did pairs mostly move one way? (no magnitudes trusted) | Paired signs only | Sign test | Sign test |
The three decisions behind the table
Paired or independent? Pairing is the most expensive mistake in the menu. If the same person, shop or plot appears in both groups, the observations lean on each other and a paired test is required; treating them as independent invents sample size you do not have. Measurements or counts? Means get t tests and ANOVA; counts and proportions get z-proportion and chi-square machinery. Normal-ish or not? The t family tolerates mild departures, especially with larger samples. Strong skew, heavy outliers or purely ranked data argue for the rank-based row of the table.
A bakery owner asks whether new ovens changed daily sales: she has 8 days before and 8 different days after. Independent samples, measurements, roughly symmetric: the two-sample t test. Had she matched the same weekdays before and after (8 Mondays, 8 Tuesdays...), the pairing would route her to the paired test instead. Same question in words, different design, different test.
Choosing the test after seeing which one gives p < 0.05. Running three tests and reporting the winner inflates the false-positive rate quietly. Decide the test from the design, before the results, and report the one you chose.
Estimates deserve equal billing
A confidence interval often serves better than any test: it answers "how big?" rather than only "is it zero?". The interval calculators sit beside every test on this site for that reason. And when the honest answer is "my sample is too small to tell", the power and sample-size calculators say how big the study needs to be next time.
Frequently asked questions
What is the most common test-selection mistake?
Ignoring pairing. Before-and-after data on the same subjects analysed with a two-sample test treats linked observations as independent, and understates or overstates the evidence. If subjects appear in both conditions, use a paired test.
My data are not normal. Can I still use a t test?
Often, yes, with moderate samples: the t test cares about the sampling distribution of the mean, which the central limit theorem regularizes. With small samples and strong skew or outliers, switch to the rank-based tests in the table.
When is ANOVA better than several t tests?
Whenever three or more groups are compared. Each t test adds its own false-positive risk; ANOVA first asks the joint question at one controlled rate, then follow-up comparisons can be adjusted.
What if none of the table rows match my study?
You may be outside the classic menu: time series, clustered data and repeated measures over many waves each have their own machinery. The honest move is to name the design first and look for the method built for it, not to squeeze it into a t test.