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This paper presents the results of a Monte Carlo study of the accuracy of an approximation to the power of the chi-square goodness of fit test with small but equal expected frequencies. Various combinations of sample size, number of groups, and alpha level are considered, and in most instances the actual power of the test is estimated to be less than the nominal power. The degree of accuracy appears to be more related to the size of the sample than to the size of the expected frequencies. The following rule of thumb is offered for obtaining crude estimates of the actual power from the nominal power for sample sizes from 10 to 50: The actual power of the test equals about eight-tenths of the nominal power. [ABSTRACT FROM AUTHOR]

Let X[sub 1], ... , X[sub m] and Y[sub 1], ... , Y[sub n] be independent random samples from populations having continuous d.f.'s psi((x-micro)/sigma) and psi((y-nu)/tau) respectively. The classical F-test of a hypothesis concerning angle = tau/sigma is known to be non-robust. This paper examines several robust alternative procedures and compares them on the basis of Pitman a.r.e and Monte Carlo studies of power functions. An approximate permutation test [13] and a "jackknife" procedure [9] are found to be most satisfactory; while a class of "rank-like" tests [10] are found to be "useful inefficient statistics" [ABSTRACT FROM AUTHOR]