How to choose the right statistical test
Test selection follows from three linked decisions: the type of your outcome variable (continuous, ordinal or categorical), the distribution of the data (whether the normality assumption holds), and the study design (independent observations versus repeated measures on the same participants).
With a continuous outcome that is approximately normally distributed, comparing two independent groups calls for an independent-samples t test; three or more groups call for a one-way ANOVA. When normality is violated, the Mann-Whitney U and Kruskal-Wallis H tests are the respective alternatives. For repeated measures, the paired-samples t test gives way to the Wilcoxon signed-rank test under the same conditions.
| Goal | Normally distributed | Not normally distributed |
|---|---|---|
| Two independent groups | Independent-samples t test | Mann-Whitney U |
| Two measures, same participants | Paired-samples t test | Wilcoxon signed-rank |
| Three or more groups | One-way ANOVA | Kruskal-Wallis H |
| Association between variables | Pearson r | Spearman rho |
Why effect size matters more than the p value
A p value tells you the probability of observing a result at least as extreme as yours if the null hypothesis were true — and nothing more. It depends heavily on sample size: with a large enough n, differences of no practical consequence become statistically significant. Effect sizes (Cohen's d, eta squared, r) quantify the magnitude of the phenomenon and are independent of n. This is why the APA Publication Manual (7th edition) requires reporting both, together with a confidence interval around the effect.
What this calculator reports, and in APA format
Every analysis returns the test statistic with its degrees of freedom, the exact p value (rendered as p < .001 when appropriate, per APA convention), the effect size with a verbal magnitude label, and a 95% confidence interval. The write-up panel produces a paragraph that follows APA 7 style conventions — italicised statistical symbols, no leading zero before decimals for bounded statistics, and the comparative direction stated explicitly — so you can paste it straight into your Results section and edit only the substantive wording.
Assumption checks
Normality is assessed with the Shapiro-Wilk test, applied within each group for independent designs and to the difference scores for paired designs. Homogeneity of variance is assessed with Levene's test. When variances are unequal, the calculator applies the Welch-Satterthwaite correction rather than the pooled-variance t test. When normality fails, it recommends the rank-based alternative. These recommendations are heuristics, not verdicts: with n < 30 the Shapiro-Wilk test is underpowered, and with very large samples it flags trivial departures from normality.
Frequently asked questions
My data are not normal. What now?
Use the corresponding non-parametric test: Mann-Whitney U, Wilcoxon signed-rank or Kruskal-Wallis H. The calculator detects the violation via Shapiro-Wilk and adjusts its recommendation automatically. In these cases, report the median and interquartile range rather than the mean and standard deviation.
Can I use these results in my thesis or manuscript?
Yes. The computations follow the same formulas implemented in SPSS and R. You should still confirm the choice of test with your advisor, because appropriateness depends on the study design — information no automated tool can infer from a spreadsheet.
Is my data uploaded to a server?
No. All processing happens in your browser in JavaScript. The spreadsheet is never transmitted or stored. You can disconnect from the internet after the page loads and the calculator keeps working.
How do I run a paired (pre–post) test?
Lay out your spreadsheet with two numeric columns —
for example Pre and Post —
keeping each participant's values on the same row. Select "Paired / repeated measures" under
Design and assign each column to its time point. Row-by-row alignment is what makes the pairing
valid.
See also: Which statistical test to use · Normality test · Sample size calculator