Shapiro–Wilk test
Test whether one numeric column looks normally distributed.
When to use it
Use Shapiro–Wilk before a t-test or ANOVA when you want a direct check of normality. A small p-value means the column does not look normal. A large p-value does not prove normality. It means this sample did not show a clear departure.
Assumptions
The column is numeric, with at least three values and at most 5000. The test is sensitive in large samples, so a tiny departure can be “significant” when N is big.
Running it in Tensr
Options
Prop
Type
Reading the output
A column of 120 standard-normal draws, separate from the exam scores. The exam scores are a mixture of three teaching groups, so they are the wrong column for a clean normality check.
No significant deviation from normality detected for noise (W = 0.995, p = .968). Parametric tests are appropriate. The primary result is not significant (p = .968). 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: W statistic = 0.995; p-value = .968; N = 120.
Reporting (APA 7)
No significant deviation from normality detected for noise (W = 0.995, p = .968). Parametric tests are appropriate. This result is not significant (p = .968). Report the estimate with that p, and do not describe the pattern as a reliable effect.
Coming from SPSS
Analyze → Descriptive Statistics → Explore → Plots → Normality plots with tests. SPSS also prints Kolmogorov–Smirnov with the Lilliefors correction.