# Homogeneity of Coefficients of Variation

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: σ11 = σ22 = … = σkk) 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 = $\sum_{j=1}^k n_j$ 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).