Kolmogorov–Smirnov test
Compare two samples, or ask whether one sample matches a normal curve.
When to use it
The two-sample test asks whether two numeric columns could come from the same distribution. The normality option is an assumption check. On that option Tensr runs Shapiro–Wilk and labels the result normality_shapiro. For the Lilliefors correction, use Lilliefors K-S. For Shapiro–Wilk by name, use Shapiro–Wilk.
Assumptions
Two-sample mode needs two numeric columns. Normality mode needs one numeric column with at least three values and at most 5000.
Running it in Tensr
Options
Prop
Type
Reading the output
Two tutorial groups of 40, each drawn from a normal curve near 70 with the same spread. The columns are the two groups.
No significant difference between the distributions of score_a and score_b (two-sided K–S: D = 0.1, p = .990; n = 40, 40). Critical D at α = .05 = 0.304. The primary result is not significant (p = .990). This is not large enough to treat the comparison this page is about as a reliable association. The result is non-significant: the data are still compatible with no effect. Metrics: D statistic = 0.1; p-value = .990; n (score_a) = 40; n (score_b) = 40; Critical D (α = .05) = 0.304.
Reporting (APA 7)
No significant difference between the distributions of score_a and score_b (two-sided K–S: D = 0.1, p = .990; n = 40, 40). Critical D at α = .05 = 0.304. This result is not significant (p = .990). Report the estimate with that p, and do not describe the pattern as a reliable effect.
Coming from SPSS
Analyze → Nonparametric Tests → 1-Sample K-S, or 2 Independent Samples with the K-S box. SPSS’s one-sample K-S against a normal distribution uses the Lilliefors correction when the mean and SD are estimated from the data. Tensr’s normality option does not. Use Lilliefors K-S for that check.