Search

Eight asymptotically robust tests of population correlation coefficient equality are proposed and are studied along with two parametric tests. Monte Carlo simulation is used to compare the small sample performance of these ten procedures. The sampled distributions consist of the normal distribution, two mixed normal distributions and four nonnormal distributions. (Author/PN)

When several variates are measured on the individuals of a single sample, it is often of interest to test whether or not two population correlation coefficients are equal. For example, in the behavioral sciences, it is often desirable to know whether two mental tests have equal test-retest reliability. In the present paper, eight asymptotically robust tests are proposed and are studied along with two parametric tests recommended by previous studies. Monte Carlo simulation is used to compare the small sample performance of these ten tests under the null hypothesis Ho: ρ12 = ρ34 where ρab is the population product moment correlation coefficient between variables Xa and Xb. Seven distributions are considered; a normal distribution, two mixed normal distributions, and four other nonnormal distributions. [ABSTRACT FROM PUBLISHER]

Probabilities of correct classification under several commonly used methods of handling missing values ore studied by Monte Carlo methods. The methods include use of only complete observation vectors; use of all observations with no replacement; substitution of means for missing observations; Buck's regression method; and, Dear's principal component method. Discriminant functions were formed using independent random samples from two multivariate normal distributions with equal covariance matrices. Missing values occur randomly in each variable and independently of missing values in other variables. The mean substitution method and principal component method are, in general, superior to the other methods for cases considered. [ABSTRACT FROM AUTHOR]

Monte Carlo methods are used to study the effect of inequality of covariance matrices on the distribution of Hotelling's T² statistic. Samples are drawn from multivariate normal distributions and from them the distribution of T² is approximated. One minus the significance level is calculated for various departures from equality, for tests with a supposed significance level of .05 and .01. The power of the tests is also given. The number of variates considered is 1, 2, 3, 5, 7, and 10. The effect of sample size on level of significance and power is studied; both equal and unequal sample sizes are used. Let σ1 and σ2 be the two covariance matrices. Graphs are presented for one minus the significance level versus d, for the case where all eigenvalues of the matrix σ2σ1-1, are equal to d. One minus the significance level is also plotted against the sample size for the case of equal sample size and equal eigenvalues of σ2σ1-1. Power curves are also included for several ratios of sample size. In general it may be said that as the number of variates increases, or as the sample size decreases, the actual level of significance increases. Equal sample sizes help in keeping the level of significance close to the supposed level, but do not help in maintaining the power of the test. [ABSTRACT FROM AUTHOR]

Monte Carlo methods are used to study the effect of inequality of covariance matrices on the distribution of Hotelling's T² statistic. Samples are drawn from multivariate normal distributions and from them the distribution of T² is approximated. One minus the significance level is calculated for various departures from equality, for tests with a supposed significance level of .05 and .01. The power of the tests is also given. The number of variates considered is 1, 2, 3, 5, 7, and 10. The effect of sample size on level of significance and power is studied; both equal and unequal sample sizes are used. Let σ1 and σ2 be the two covariance matrices. Graphs are presented for one minus the significance level versus d, for the case where all eigenvalues of the matrix σ2σ1-1, are equal to d. One minus the significance level is also plotted against the sample size for the case of equal sample size and equal eigenvalues of σ2σ1-1. Power curves are also included for several ratios of sample size. In general it may be said that as the number of variates increases, or as the sample size decreases, the actual level of significance increases. Equal sample sizes help in keeping the level of significance close to the supposed level, but do not help in maintaining the power of the test. [ABSTRACT FROM AUTHOR]