Method Of Unweighted Means Research Articles

Two Factor Data Analysis with Unequal Cell Frequencies and Interaction

This paper proposes a non parametric method for two factor data analysis with unequal cell frequencies and interaction. Chi-square test statistic was developed for testing the null hypothesis of no treatment effect and interaction between factor A and factor B. The proposed methods are illustrated with some data and compared with the usual unweighted mean method. The result showed that the proposed method is more powerful than the method of unweighted mean.

Graphical evaluation of the adequacy of the method of unweighted means

A graphical technique is introduced to assess the adequacy of the method of unweighted means in providing approximate F -tests for an unbalanced random model. These tests are similar to those obtained under a balanced ANOVA. The proposed technique is simple and can easily be used to determine the effects of imbalance and values of the variance components on the adequacy of the approximation. The one-way and two-way random models are used to illustrate the proposed methodology. Extensions to higher-order models are also mentioned.

The Method of Unweighted Means in Univariate and Multivariate Analysis of Variance

The method of unweighted means (MUM) is an alternative to the least squares method (LSM) for analyzing nonorthogonal data. The MUM was investigated empirically to determine Type I error rates associated with various degrees of imbalance among the cell frequencies. The MUM was found to have acceptable error rates in both univariate and multivariate cases when the ratio of largest to smallest cell frequency, a, is less than or equal to 5. Previously, the MUM was thought to be inappropriate when a - 2. The issue of the power is also addressed. The LSM has more power on average; however, cases for which the MUM has more power are described.

The Method of Unweighted Means in Multivariate Analysis of Variance

The method of unweighted means in the multivariate analysis of variance with unequal sample sizes is investigated. By approximating the distribution of the hypothesis SSCP with a Wishart distribution, multivariate test statistics are derived that are analogous to the usual ones except the eigenvalues and hypothesis degrees of freedom are adjusted in accordance with the discrepancies in sample size. Monte Carlo methods are used to show the approximate test statistics are accurate over a range of conditions. Conditions are given under which the method of unweighted means yields exact results. A numerical example illustrates the technique.

The Method of Unweighted Means in Multivariate Analysis of Variance

The Method of Unweighted Means in Multivariate Analysis of Variance

Variance-Component Estimation from Human Sibship Data

The large-sample relative efficiencies of the analysis-of-variance (ANOVA) estimators of variance components and the intraclass correlation coefficient rho are investigated for the unbalanced single classification in the context of family studies. The efficiency of an analysis based on the method of unweighted group means is also investigated. From a Monte Carlo study which generates the group sizes from typical family-size distributions it is found that the relative efficiency of the ANOVA estimators of the between-group variance component exceeds 95% for values of .2 less than or equal to rho less than or equal to .4, but can fall below 60% for values of rho that are very close to zero. For the estimation of the between-group variance component the method of unweighted means tends to be preferable to the ANOVA method only if rho greater than .5.

ExactFTests for the Method of Unweighted Means in a 2kExperiment

Abstract The analysis of a general k-factor factorial experiment having unequal numbers of observations per cell is complex. For the special case of a 2 k experiment with unequal numbers of observations per cell, the method of unweighted means provides a simple vehicle for analysis that requires no matrix inversion and can be used with existing software programs for the analysis of balanced data. All numerator sums of squares for testing main effects and interactions are χ2 with one degree of freedom. In addition, for tests having one degree of freedom in any factorial experiment, the method of unweighted means may be modified to yield exact tests.

Exact F Tests for the Method of Unweighted Means in a 2 k Experiment

Exact F Tests for the Method of Unweighted Means in a 2 k Experiment

Estimating Variance Components for Two-Way Disproportionate Data with Missing Cells by the Method of Unweighted Means

Abstract The method of unweighted means, which is a simple analysis based on cell means, has been limited to designs where every cell has at least one observation. Here, the method of unweighted means is examined with regard to estimating the variance components for a two-way classification with unequal numbers of observations in the cells and with one or more cells having no observations. In particular, two estimating procedures based upon the method of unweighted means are developed to estimate the variance components for a design with missing cells. These two unweighted means procedures are then examined numerically.

Treatment conditions, dogmatism, and perception of demand characteristics.

In an attitude study 158 Ss' perceptions of demand characteristics were investigated in relation to treatment condition and dogmatism (Rokeach, 1960). Ss receiving the experimental treatment were expected to show greater awareness of E's purpose than control Ss because of less confusing cues for the former Ss. Dogmatism was expected to be either negatively related to accurate perception of demand cues or unrelated to such awareness. Analysis of responses to a five-question awareness scale was performed by a 3 by 2 analysis of variance using the method of unweighted means (Winer, 1962). Experimental Ss showed significantly more accurate perceptions of demand cues ( p < .01) than control Ss, but dogmatism had no significant effects. Tentative interpretations of these data were provided in terms of the phenomena of perceptual synthesis and perceptual analysis (Levy & Rokeach, 1960), and suggestions for further research were given.

Analysis of Variance of Disproportionate Data When Interaction is Present

The disturbance to the level of significance of additive sums of squares methods of analyzing disproportionate data is studied for several patterns of subclass numbers in the two-way classification. These methods yield too many significant results for main effects under the null hypothesis although this disturbance is judged to be moderate for the method of unweighted means. Factors to remove the bias in the method of expected subclass numbers are given. A procedure for computing the power of the exact methods, similar to the computations for equal subclass numbers, and approximate procedures for determining the power of the method of unweighted means are described.