Testing Populations for Equal Variances

Learn how to test populations for equal variances

The choice among various difference-of-means tests depends partially on the assumption that two populations have a common variance. In the chapter, we did not discuss how to test whether this assumption holds or not. Here we offer an F test for whether the variances of growth are the same between 1960 and 1990.

Null hypothesis H0H_0: σ19602=σ19902\sigma^2_{1960}= \sigma^2_{1990},i.e., σ19602σ19902=1\frac{\sigma^2_{1960}}{\sigma^2_{1990}}=1

Alternative hypothesis HaH_a: σ19602σ19902\sigma^2_{1960} \not= \sigma^2_{1990}

The test statistic for the null hypothesis is: F=σ19602σ19902F = \frac{\sigma^2_{1960}}{\sigma^2_{1990}}

We reject the null hypothesis if the pp value for the FF test statistic is smaller than the acceptable Type I error, 0.05.

The R code and output below indicate that the pp value is much smaller than 0.05. Hence, we reject the null hypothesis that growth in 1960 and growth in 1990 are of equal variance.

Get hands-on with 1200+ tech skills courses.