The Degrees of Freedom of the Chi square-Test of Dimensionality
SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE
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Wani and Kabe abbreviated as W K hereafter have recently given an elegant derivation of the likelihood ratio criterion for testing the hypothesis H sub 0 that the dimensionality of the space of the means of k p-variate normal populations is s. The main difference between their derivation and the one given in Rao is that Rao uses geometrical terminology while W Ks derivation is completely analytical. However, Their proof is incomplete without the degrees of freedom of the Chi square -test. The object of this note is therefore to derive the number of d.f. here analytically and complete the W K derivation.
- Statistics and Probability