Step 1: Paste your data

Comma, space or newline separated. Non-numeric tokens are skipped with a warning.
The Wilcoxon signed-rank test asks "does the median differ from μ0?" Enter your hypothesized reference — e.g., 120 for systolic BP against a reference value of 120 mm Hg, or 0 if your data are already centered (paired differences, log-ratios). Leave blank to skip the Wilcoxon panel entirely.

Results

How to read this

Q-Q plot: if the points fall roughly along the diagonal line, your data are approximately normal. Systematic curvature (S-shape or bow) indicates skew or heavy tails.

Skewness (S): 0 for normal; |S| > 1 is notable. Displayed as the bias-corrected G1 estimator (same convention as SPSS and R's e1071::skewness(type=2)). Excess kurtosis (K − 3): 0 for normal; positive is heavy-tailed, negative is light-tailed. Displayed as the bias-corrected G2.

Jarque-Bera test: combines skewness and excess kurtosis into a single χ²(2) statistic. Low p-value means "reject normality." Two footnotes. First: for n < 30 the chi-square approximation is loose — trust the Q-Q plot over the p-value for small samples. Second: JB internally uses the biased moments (not G1/G2) because its reference distribution is derived from them, so the S and K values inside JB will differ slightly from the bias-corrected numbers displayed above — this is by design, not a bug.

Shapiro-Wilk test: computed via Royston's (1992) polynomial approximation, valid for 4 ≤ n ≤ 2000. Generally the most powerful normality test for small n and the de-facto standard in R, SPSS, and jamovi. When S-W and JB disagree, prefer S-W at small n; trust the Q-Q plot over both.

Outliers: values outside Q1 − 1.5·IQR or Q3 + 1.5·IQR (Tukey's rule). Does not imply they are errors — just that they pull strongly on parametric summaries.

Recommendation: a rules-of-thumb traffic light. Not a substitute for your own judgment about the data-generating process and the inferential question.