By Albert R. Wildt
This booklet provides a strategy for interpreting 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 in addition the results of workforce situations.
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Extra resources for Analysis of Covariance (Quantitative Applications in the Social Sciences)
If analysis of variance is conducted without considering these characteristics, the results may be biased. In those cases where the disturbing variables are quantitative (interval- or ratio-scaled), analysis of covariance may be employed in an effort to remove the bias introduced because the groups have not been matched on these disturbing variables. In other words, differences may exist in these disturbing variables from group to group, and covariance analysis provides a means to statistically adjust the dependent variable for these preexisting differences.
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.
Furthermore, as in experiments with intact groups, it is more difficult to eliminate the possibility that the group membership of a test unit has been influenced by the covariate or vice versa, which would bias the results. As previously mentioned, three distinct problem perspectives may be employed in conjunction with analysis of covariance. Here we address the analysis procedures for one-way layouts associated with all three perspectives. However, primary consideration is given to the experimental perspective, which includes those cases, both observational and experimental, in which primary interest is in the effect of a single qualitative independent variable on the dependent variable and the covariates are considered nuisance variables.
Analysis of Covariance (Quantitative Applications in the Social Sciences) by Albert R. Wildt