Why does SPSS show 0.200* for Kolmogorov-Smirnov?

SPSS uses a table that stops at 0.200, so when the p-value is higher it shows "0.200*" (a lower bound). Here you see the approximate value; the conclusion is the same.

The Shapiro-Wilk W and the Kolmogorov-Smirnov D match. The Kolmogorov-Smirnov p-value may differ in the decimals because each program uses a different approximation, but the decision at 0.05 is the same.

What data do I paste?

A single column with one value per person: usually the total score of the variable or of each dimension. Don’t paste item-by-item answers.

How much data do I need?

At least 3 for Shapiro-Wilk and 5 for Kolmogorov-Smirnov, though with so few the tests rarely detect anything. Shapiro-Wilk accepts up to 5,000 values.

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Normality test: Shapiro-Wilk and Kolmogorov-Smirnov

Before correlating or comparing groups you need to know whether your data is normal: it decides between Pearson and Spearman, or a t-test and Mann-Whitney U. Paste one column of numbers (for example, each person’s total score on a variable) and the tool runs the two tests most research projects ask for.

Paste your data (one column, one value per person)

Significance level

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How it’s calculated

Shapiro-Wilk compares your sorted data with what a normal distribution would produce. It uses Royston’s (1995) algorithm, the same as SPSS, R and SciPy.

Kolmogorov-Smirnov measures the largest gap between your data’s distribution and a normal one with the same mean and standard deviation. It applies the Lilliefors correction, as SPSS does, because the mean and deviation come from the same data.

In both tests the null hypothesis is that the data is normal. If the p-value is below 0.05, you reject it: the data is not normal.

How to read the result

Common rule: with 50 data points or fewer report Shapiro-Wilk; with more than 50, Kolmogorov-Smirnov. The tool marks which one applies.
p > 0.05: no evidence against normality, so you can use parametric tests (Pearson, t-test, ANOVA).
p ≤ 0.05: the data is not normal, so use non-parametric tests (Spearman, Mann-Whitney U, Kruskal-Wallis).
If you will correlate two variables, test each one. If either is not normal, Spearman is the usual choice.

Frequently asked questions

Why does SPSS show 0.200* for Kolmogorov-Smirnov?: SPSS uses a table that stops at 0.200, so when the p-value is higher it shows "0.200*" (a lower bound). Here you see the approximate value; the conclusion is the same.
Does it match SPSS?: The Shapiro-Wilk W and the Kolmogorov-Smirnov D match. The Kolmogorov-Smirnov p-value may differ in the decimals because each program uses a different approximation, but the decision at 0.05 is the same.
What data do I paste?: A single column with one value per person: usually the total score of the variable or of each dimension. Don’t paste item-by-item answers.
How much data do I need?: At least 3 for Shapiro-Wilk and 5 for Kolmogorov-Smirnov, though with so few the tests rarely detect anything. Shapiro-Wilk accepts up to 5,000 values.

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