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This paper deals with a multivariate extension of Friedman's chi[sup 2, sub tau]-test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest, when the block dispersion matrices differ and can be greater than unity when the differences are large. [ABSTRACT FROM AUTHOR]

Ellison has shown that the Wald-Wolfowitz tolerance limits for a normal distribution, x + lambda s, are good only to 0(n/N[sup 2]), rather than to 0(1/N[sup 2]). Here x is distributed normally with mean mu and variance sigma[sup 2]/N while s[sup 2]/sigma[sup 2] is distributed as chi[sup 2, sub n]/n independently of x. Thus, for n much greater than N[sup 2] the usual values of lambda are incorrect; Ellison has proposed an alternative in this case. This paper derives new lambda's which have two advantages over the Wald-Wolfowitz and the Ellison limits. First, they are shown to be better approximations. Secondly, they are easily calculated in the sense that only tables of the normal and chi[sup 2] distributions are required and the solution of a non-linear equation is not required. [ABSTRACT FROM AUTHOR]

This paper compares the Pearson Chi-Square and Kolmogorov goodness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are "small"; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test. [ABSTRACT FROM AUTHOR]

The article reports on the szondi test. In a previous paper, the researchers have shown the wide variation in the frequency with which pictures are chosen by Szondi test subjects. In the present study,the researcher test the homogeneity of the Szondi pictures from the standpoint of recognition by comparing sets 1 and V to see whether there is a significant difference in the frequency with which pictures are recognized. Should the pictures be associated with categories by chance, the researcher expect to find on the average one correct identification for each sample of eight pictures, or a total of 300 for the two sets in the experiment. The chi-square test is used to measure the significance of the difference between the number of correct identifications in the two sets.