Be the unbiased estimate of the population variance, obtained from the ith sample Xij,(j=1, 2, …….ni)and based on vi = (ni – 1) degrees if freedom, all the k samples being independent.
Under the null hypothesis that the samples come from the same population with variance σ2, that is the independent estimates , (i =1,2,….k) of σ2are homogeneous, Bartlet proved that the statistic
Follows chi-square distribution with (k-1) degrees of freedom.
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