Bartlett€™s homogeneity-of-variance test.* Suppose there are k independent sample variances s²₁, s²₂, . . . , s²_kwith f₁, f₂, . . . , f_kdf, each from populations which are normally distributed with mean μ and variance σ²_i. Suppose further that we want to test the null hypothesis H₀: σ²₁ = σ²₂ = · · · =σ²_k = σ²; that is, each sample variance is an estimate of the same population variance σ². If the null hypothesis is true, then

provides an estimate of the common (pooled) estimate of the population variance σ², where f_i = (n_i ˆ’ 1), n_i being the number of observations in the ith group and where f Σ^k_{i = 1} f_i . Bartlett has shown that the null hypothesis can be tested by the ratio A/B, which is approximately distributed as the χ² distribution with k ˆ’ 1 df, where

And

Apply Bartlett€™s test to the data of the following table and verify that the hypothesis that population variances of employee compensation are the same in each employment size of the establishment cannot be rejected at the 5 percent level of significance. Note: fi, the df for each sample variance, is 9, since ni for each sample (i.e., employment class) is 10.

Transcribed Image Text:

Σi Σi3 Σ1 A=fns? - ΣUng) (fi In s