We now extend the test to determine whether two coefficients of variation are equal (described in Coefficient of Variation Testing) to more than two samples.
For k samples you can test whether their populations have the same coefficient of variation (i.e. H0: σ1/μ1 = σ2/μ2 = … = σk/μk) when the k samples are taken from normal distributions with positive means. The test statistic is
where the Vj are the coefficients of variation for the k samples of size nj with n = and the pooled coefficient of variation is
The test works best when the sample sizes are at least 10 and the population coefficients are at most .33.
Example 1: Determine whether there is a significant difference between the population coefficient of variation for the three independent samples in range of A3:C14 of Figure 1.
Figure 1 – Testing for homogeneity of coefficients of variation
As you can see from Figure 1, there is a significant difference between the two coefficients of variation (p-value =.02567 < .05 = alpha).