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. H_{0}: *σ _{1}/μ_{1} = σ_{2}/μ_{2} = … = σ_{k}/μ_{k}*) when the

*k*samples are taken from normal distributions with positive means. The test statistic is

where the *V _{j}* are the coefficients of variation for the

*k*samples of size

*n*with

_{j}*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).