Does this give the same result as SPSS?

Yes. It uses Royston's algorithm, which SPSS, R (shapiro.test), and SciPy also use, so W and p agree to several decimal places.

My Shapiro-Wilk test is significant. Can I still use a t-test?

With large samples (roughly 30+ per group) and only mild skew, t-tests are usually robust. With small samples or strong skew, use the non-parametric alternative such as the Mann-Whitney U test.

Should I test all my data together?

No. Test each group separately for t-tests and ANOVA, the differences for a paired t-test, and the residuals for regression.

SHAPIRO-WILK TEST CALCULATOR

Shapiro-Wilk normality test calculator with Q-Q plot.

Check whether your data are normally distributed before choosing a t-test or ANOVA. You get W, the p value, skewness, kurtosis, a histogram, a Q-Q plot, and an APA sentence.

DATA

One variable, 3 to 5,000 values

ROYSTON 1995

VALUES

Separate values with commas, spaces, or new lines. Test each group separately if you plan to compare groups.

Shapiro-Wilk test: interpretation, limits, and what to do next

How to interpret the result

p ≥ .05 → no significant departure from normality; parametric tests are reasonable
p < .05 → the data differ significantly from a normal distribution
W close to 1 means the data are close to normal; lower W means a bigger departure

Formula

W = (Σ aᵢ x₍ᵢ₎)² ÷ Σ (xᵢ − x̄)²

x₍ᵢ₎ are the sorted values and aᵢ are weights derived from expected normal order statistics. SolveGrid uses Royston's (1995) algorithm, the same one used by SPSS, R, and SciPy.

My normality assumption is violated. What now?

Two independent groups → Mann-Whitney U test instead of the t-test
Same people twice → Wilcoxon signed-rank test instead of the paired t-test
Three or more groups → Kruskal-Wallis instead of one-way ANOVA
Large samples (30+ per group) with mild skew → t-tests and ANOVA are usually robust
Right-skewed data → a log or square-root transformation may help

Test the right thing

For a t-test or ANOVA, check normality within each group separately, not on all the data pooled. For a paired t-test, check the differences. For regression, check the residuals.

How to report it (APA style)

“A Shapiro-Wilk test showed that exam scores were not normally distributed, W(11) = .79, p = .007; therefore a Mann-Whitney U test was used.” Report W with n, the p value, and what you did as a result.

References

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3–4), 591–611.
Royston, P. (1995). Remark AS R94: A remark on algorithm AS 181. Applied Statistics, 44(4), 547–551.
Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486–489.

Shapiro-Wilk Normality Test Calculator

Check the normality assumption before a t-test or ANOVA, see the histogram and Q-Q plot, and get advice on what to do if normality is violated.

Check normality before a t-test or ANOVA

Decide between parametric and non-parametric tests

Report the Shapiro-Wilk result in APA style

KEY FUNCTIONS

Royston (1995) algorithm, matches SPSS and RW statistic and p value for 3–5,000 valuesSkewness and excess kurtosisHistogram and normal Q-Q plotWhat-to-do-next guidance

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