Which of the following is a test that can be used to determine if data are normally distributed?

• A. Shapiro-Wilk Test
• B. ANOVA
• C. Durbin-Watson Test
• D. Levene's Test

Answer: (A)

Testing whether data are consistent with a normal distribution is about whether the assumption of normality holds for the data, which underpins many statistical methods. The Shapiro-Wilk test does this by comparing the observed order statistics of the sample to what would be expected if the data came from a normal distribution. It yields a W statistic; smaller values suggest the data deviate from normality, and the accompanying p-value guides whether to reject normality at your chosen significance level. This test is particularly powerful for small to moderate sample sizes and is widely used when the normality assumption is important for subsequent analyses.

ANOVA focuses on whether group means differ, not on the distribution shape. Durbin-Watson checks for autocorrelation in residuals from regression, not normality. Levene’s test assesses whether variances are equal across groups, not whether the data follow a normal distribution.