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By Albert R. Wildt

This publication offers a method for studying the consequences of variables, teams, and coverings in either experimental and observational settings. It considers not just the most results of 1 variable upon one other, but additionally the consequences of workforce instances.

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Analysis of Covariance (Quantitative Applications in the Social Sciences)

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Mean comparisons may be classified as orthogonal or non-orthogonal, and as a priori or a posteriori. Two comparisons among k means are said to be orthogonal to each other if they utilize nonoverlapping pieces of information. A maximum of k1 mutually orthogonal comparisons are possible in the analysis containing k groups or treatment levels, though the k1 comparisons are not unique. , sum to equal the treatment/group sum of squares, and correspond to an orthogonal comparison. Mathematically, two contrasts, C1 and C2, are considered orthogonal if where cji is the coefficient of the ith group mean in the jth contrast and ni is the number of observations in group i.

Also, all discussion of experimental designs that follows considers only fixed effects models. ) Covariance Model For the one-way layout, the covariance model considers the observed value of the dependent variable to be influenced by the effect of the particular treatment level or group from which the observation comes, and the values of the concomitant variables (covariates). Verbally, an additive model representing this situation is: Page 19 Algegraically, the analysis of covariance model for the one-way layout with one covariate is represented as: where Yij is the observed value of the dependent variable for the jth observation within the ith group or treatment level, u is the true mean effect, ti is the effect due to the ith group or level of the categorical independent variable (treatment) with Sniti = 0, b is the (regression) coefficient representing the average effect of a one unit change in the covariate on the dependent variable, Xij is the observed value of the covariate, X * is the general mean of the covariate, eij is a random error which is normally and independently distributed with mean zero and variance s2, k is the number of groups, and ni is the number of observations in group i.

The quantitative independent variable (covariate) is included in the analysis either to remove extraneous variation from the dependent variable, and thereby, increase the precision of the analysis, or to remove bias due to the groups not being matched on that quantitative independent variable. The analysis procedure in this case can be viewed as adjusting the dependent variable for differences in the covariate and Page 9 then investigating the relationship between the qualitative independent variable(s) and the adjusted values of the dependent variable.

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