Which test assesses whether a distribution deviates from normality?

Which test assesses whether a distribution deviates from normality?

• A. Shapiro-Wilk test
• B. Kolmogorov-Smirnov test
• C. Levene's test
• D. Bartlett's test

Answer: (B)

To determine if data deviate from a normal distribution, you use a goodness-of-fit test that compares the observed data to a normal curve. The Kolmogorov-Smirnov test calculates the maximum difference between the empirical distribution function of the sample and the theoretical normal distribution function; a significant result means the sample does not follow a normal distribution. This approach assesses the entire shape of the distribution, including tails, not just variability or central tendency. Levene's and Bartlett's tests, by contrast, focus on whether variances are equal across groups, which is about spread rather than distribution shape. Shapiro-Wilk is another normality test and can be more powerful in some cases, but the test in question directly performs a goodness-of-fit check against normality across the whole distribution, which is why it’s the appropriate choice here.

To determine if data deviate from a normal distribution, you use a goodness-of-fit test that compares the observed data to a normal curve. The Kolmogorov-Smirnov test calculates the maximum difference between the empirical distribution function of the sample and the theoretical normal distribution function; a significant result means the sample does not follow a normal distribution. This approach assesses the entire shape of the distribution, including tails, not just variability or central tendency. Levene's and Bartlett's tests, by contrast, focus on whether variances are equal across groups, which is about spread rather than distribution shape. Shapiro-Wilk is another normality test and can be more powerful in some cases, but the test in question directly performs a goodness-of-fit check against normality across the whole distribution, which is why it’s the appropriate choice here.