Normality Test Calculator

Before a t-test or ANOVA you are usually asked whether the data are normal. Paste one or more columns and get the Shapiro–Wilk and K-S tests, skewness and kurtosis, a histogram and a Q-Q plot in one place.

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Data

One column per variable (or group). Paste from Excel or SPSS; a header row is optional.

Tests of normality

Variable	n	Shapiro–Wilk W	p	K-S D	p	Result
A	15	0.879	0.0460	0.181	0.2062	Not normal (p < 0.05)
B	15	0.994	1.0000	0.076	0.9995	No evidence against normality

The verdict uses Shapiro–Wilk, which is more powerful than K-S for most sample sizes. SPSS prints the K-S p as “.200*” when it is at least 0.2.

Descriptive statistics

Variable	Mean	SD	Median	Skewness	SE	Kurtosis	SE
A	3.74	1.663	3.3	1.334	0.58	1.542	1.121
B	10.253	1.121	10.2	-0.039	0.58	-0.298	1.121

Skewness and excess kurtosis are 0 for a normal distribution. A value more than about twice its SE away from 0 suggests skew or heavy tails.

Report asW(15) = 0.879, p = .046

Charts for

Histogram with the fitted normal curve

Normal Q-Q plot: points close to the line mean roughly normal data

Shapiro–Wilk matches R shapiro.test() and SPSS (3 to 5000 values); K-S uses the Lilliefors correction like SPSS. With large samples tiny departures become significant, so look at the Q-Q plot too.

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How to use

Paste one column per variable or group. A header row is optional.
Read the tests of normality table. A Shapiro–Wilk p of 0.05 or more means no evidence against normality.
Check skewness, kurtosis and the Q-Q plot; points close to the line are what you want.
For ANOVA, test each group separately, one column per group.

Options explained

Shapiro–Wilk: Works for 3 to 5000 values and is the most widely used and most powerful general test. The closer W is to 1, the more normal the data look.
K-S (Lilliefors): Uses the sample mean and SD, so it needs the Lilliefors correction. This is the K-S test SPSS shows under Explore.
Skewness and kurtosis: Both are 0 for a normal distribution. Positive skew means a long right tail; positive kurtosis means heavier tails. More than about twice the SE away from 0 suggests a real departure.

Worked example

The sample has two columns of 15 values:

Variable	Shapiro–Wilk W	p	K-S D	p	Skewness	Kurtosis
A	0.879	0.046	0.181	0.206	1.33 (SE 0.58)	1.54 (SE 1.12)
B	0.994	1.000	0.076	1.000	−0.04	−0.30

Column A has a Shapiro–Wilk p of 0.046, so it isn’t normal. Its skewness of 1.33 is more than twice its SE, a long right tail caused by the 7.9, and the top-right points of the Q-Q plot bend away from the line. K-S gives p = 0.21 and misses it, a typical example of how conservative it is. Column B looks normal on every measure.

APA style: W(15) = 0.879, p = .046.

Frequently asked questions

The two tests disagree. Which one should I use?

Usually Shapiro–Wilk, which has more power for most sample sizes. K-S is conservative and tends to say "normal".

With a large sample, even tiny departures are significant.

Yes. With hundreds of values the tests flag trivial departures, while t-tests and ANOVA are fairly robust at that size. Rely more on the Q-Q plot and skewness then.

My data aren't normal. What now?

For small, skewed samples use a nonparametric test (Mann–Whitney U, Wilcoxon signed-rank, Kruskal–Wallis), or try a log transform and test again.

What should I test for regression?

The residuals, not the raw variables. Paste the residuals from the regression calculator here.

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