Normality tests

Practicing Statistics Interview Questions in R

Zuzanna Chmielewska

Actuary

Testing normality

Statistical tests

• Shapiro-Wilk test
• Kolmogorov-Smirnov test

Visual measure

• Q-Q plot

Shapiro-Wilk test

Shapiro-Wilk test

¹ Razali, Nornadiah; Wah, Yap Bee (2011). "Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests"

P-value

Shapiro-Wilk test

Kolmogorov-Smirnov test

Kolmogorov-Smirnov test

Kolmogorov-Smirnov test

Transforming data for normality

Transforming data for normality

Checking normality in R

Method	Function
Shapiro-Wilk test	shapiro.test(x)
Kolmogorov-Smirnov test	ks.test(x, y = "pnorm")
Q-Q plot	qqnorm(x); qqline(x)

Summary

• normality tests
  • Shapiro-Wilk test
  • Kolmogorov-Smirnov test
• p-value
• Q-Q plot
• data transformation
• checking normality in R

Let's practice!

Practicing Statistics Interview Questions in R