Normality & Variance Homogeneity Tests (Shapiro-Wilk / Levene / Bartlett)
The two assumption checks before a t-test or ANOVA: Shapiro-Wilk tests whether each group is normally distributed (with a Q-Q plot), and Levene and Bartlett test whether multiple groups have equal variances. Use the results to decide between parametric and non-parametric methods.
① Enter data
One group per line, values within a group separated by spaces or commas. One group → normality test only; multiple groups → per-group normality + between-group variance homogeneity.
How to use & methodology
Why do these two checks first?
t-tests and ANOVA assume the data are approximately normal and the groups have equal variance. Testing these two points first lets you decide between parametric and non-parametric methods, avoiding misuse and unreliable conclusions.
Shapiro-Wilk or K-S test?
Shapiro-Wilk has higher power for normality with small-to-moderate samples (n<50) and is preferred; SPSS uses it as the default. This tool uses the Royston (1992) algorithm, with weights consistent with the original Shapiro-Wilk tables.
How do Levene and Bartlett differ?
Bartlett is very sensitive to departures from normality and easily misjudges non-normal data; Levene (especially the median-centered Brown-Forsythe version) is more robust and the more general choice. When both are given, relying on Levene is safer.
What if the test is significant (P<0.05)?
Normality fails: switch to a non-parametric test (two groups Mann-Whitney, multiple groups Kruskal-Wallis), available in the 'non-parametric test' tool. Unequal variance: use the Welch-corrected t-test/ANOVA. A data transformation is also an option.