Tests of the Equality of k Independent Samples

The natural extension of the two-sample problem is the k-sample problem, where observations are taken under a variety of different and independent conditions. Assume that we have k independent sets of observations, one from each of k continuous populations F ₁(x), F ₂(x), …, F_k (x) where the ith random sample is of size n_i, i = 1, 2, …, k and there are a total of ∑ i = 1 k n i   = N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203911563/4aee2b7e-4c1a-4282-8d9e-64e6349e54c1/content/eq1165.tif"/> observations. Note that we are again assuming the independence extends across samples in addition to within samples. The extension of the two-sample hypothesis to the k-sample problem is that all k samples are drawn from identical populations H 0 : F 1 ( x ) = F 2 ( x ) = ⋯ = F k ( x ) for all  x https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203911563/4aee2b7e-4c1a-4282-8d9e-64e6349e54c1/content/eq1166.tif"/>