Kenneth J. Levy

A Monte Carlo Study of Analysis of Covariance Under Violations of the Assumptions of Normality and Equal Regression Slopes

The present study indicates that ANCOVA is robust with respect to dual violations of the assumptions of equal regression slopes and normality of distributions provided that group sizes are equal. In ad dition, when regression slopes are equal, ANCOVA appears to be robust to violations of the assumption of normality whether group sizes are equal or not. In the present study ANCOVA did display disruptions of empirical significance levels when unequal regression slopes and unequal group sizes were coupled with nonnormal distri butions.

An empirical comparison of the ANOVA F-test with alternatives which are more robust against heterogeneity of variance

Monte Carlo techniques were employed to compare the familiar one-way fixed effects ANOVA F-test with Welchs v-test and Marascuilos slight variant of Welchs v-test. The three procedures were compared with respect to empirical significance levels under violations of homogeneity of variance and under violations of normality; power comparisons were performed only under conditions of homogeneity of variance because of the differing empirical significance levels which were produced under heterogeneous vaiance conditions. Welchs v-test is recommended as a reasonable alternative to the familiar F-test.

Pairwise Comparisons Associated with the K Independent Sample Median Test

Abstract In this article, a Tukey-type method is proposed that will allow simultaneous pairwise comparisons among all pairs of samples associated with Moods procedure. An example is also provided for illustrative purposes.

A Multiple Range Procedure for Independent Correlations.

Marascuilo (1966) proposes a χ2 analog of Scheffes multiple comparisons procedure. With respect to pairwise comparisons among k independent correlation coefficients, a multiple range procedure will produce lower critical values than the corresponding χ2 values, thereby increasing the power of the resulting tests. The basis of such a procedure is discussed and an example is provided for illustrative purposes.

Some Multiple Range Tests for Variances

Often times, the experimenter is interested in making inferences about treatment variances instead of, or in addition to, inferences about means. Three multiple range tests are proposed for the purpose of specifying which treatment variances or sets of variances are homogeneous. The procedures are based upon the F max statistic, Cochrans statistic, and a normalizing log transformation of the sample variances. All three tests depend heavily upon the underlying assumption of normality.

Nonparametric Applications of Shaffer's Extension of Dennett's Procedure

Abstract Shaffers extensions and generalization of Dunnetts procedure are shown to be applicable in several nonparametric data analyses. Applications are considered within the context of the Kruskal-Wallis one-way analysis of variance (ANOVA) test for ranked data, Friedmans two-way ANOVA test for ranked data, and Cochrans test of change for dichotomous data.

Testing Hypotheses Concerning Partial Correlations: Some Methods and Discussion

Summary A number of existing statistical procedures are reviewed which can be employed to test a variety of hypotheses involving partial correlations. Often in social science research investigators are interested in testing hypotheses concerning the values of specific simple population correlations, in testing that the differences between pairs of simple correlations are zero, and in testing that k simple population correlations are all equal. The procedures for making these tests are presented in numerous elementary and advanced social science statistics texts. Conceivably, investigators might also be interested in testing hypotheses concerning partial correlations that are similar to the types of hypotheses which are commonly tested involving simple correlations. The procedures for making such tests are not typically presented in elementary statistics texts. Although such procedures are alluded to in some advanced texts, specific results do not appear to be generally known by many social science researchers. The purpose of this paper is not to present new statistical methods for testing hypotheses concerning partial correlations; rather, this paper has been prepared for the purpose of reviewing a number of existing statistical procedures which can be employed to test hypotheses involving partial correlations. The procedures which are reviewed in the present paper involve applications of general statistical theory to data analyzing problems concerning partial correlations. The present authors feel that many of these procedures are not known to social

An empirical comparison of theZ-variance and Box-Scheffé tests for homogeneity of variance

This brief report provides a comparison of theZ-variance and Box-Scheffé tests for homogeneity of variance. Both procedures are relatively simple to perform and both may be readily utilized in complex, multifactor designs. TheZ-variance test is not robust against non-normality; the Box-Scheffé test is robust against non-normality but is not nearly as powerful as theZ-variance test.

Some empirical power results associated with welch's robust analysis of variance technique

Welchs (1951) V-test is useful for testing the equality of the means of k normal populations with heterogeneous variances. In the present paper, it is proposed that the non-null distribution of Welchs V statistic can be reasonably approximated by an appropriate non-central F distribution. Monte Carlo results are presented which suggest that the non-null distribution of V can be adequately approximated as suggested in the present paper.

An empirical comparison of several methods for testing the equality of dependent proportions

Three methods for testing the equality of nonindependent proportions were compared with, the use of Monte Carlo techniques. The three methods included Cochrans test, an ANOVA F test, and Hotellings T2 test. With respect to empirical significance levels, the ANOVA F test is recommended as the preferred method of analysis. Oftentimes an experimenter is interested in testing the equality of several proportions. When the proportions are independent Kemp and Butcher (1972) and Butcher and Kemp (1974) compared several methods for analysing large sample binomial data for the case of a 3 x 3 factorial design without replication. In addition, Levy and Narula (1977) compared many of the same methods for analyzing binomial data; however, Levy and Narula investigated the relative utility of the methods for small sample sizes.