By Albert R. Wildt
This booklet provides a strategy for interpreting the results 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 consequences of workforce circumstances.
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Additional resources for Analysis of Covariance (Quantitative Applications in the Social Sciences)
If b were known, this would be an appropriate approach to the problem. However, b must be estimated from the data and that estimate is made by utilizing all data observed under all treatment levels. Under these conditions, the adjusted treatment means are not independent of each other, and the assumptions necessary for establishing the ratio of mean squares as an F-distribution are violated. Therefore, some alternative approach must be employed. Consistent with the above rationale, this alternate approach should yield the appropriate sum of squares and mean square terms (necessary for the F-test), which are adjusted for the covariate.
However, according to Kirk (1968: 78), "for planned orthogonal comparisons, contemporary practice in the behavioral sciences favors setting the type I error probability level at a for each comparison. " A Posteriori Nonorthogonal Comparisons In many situations the researcher is not sufficiently knowledgeable concerning the effect of the independent variable to a priori specify the appropriate mean comparisons. However, if the overall F-test leads to the rejection of the null hypothesis of no treatment/group effects, the researcher is usually interested in further "exploring" the data in an effort to uncover the sources of the treatment/gorup effect.
With knowledge of only the value of the covariate. At this point a question may arise as to how one might obtain an estimate for the coefficient of the covariate term. A close look reveals that equation 3 can be viewed as a simple regression model with (YijY)* as a dependent variable and (XijX)* as the independent variable. It is a relatively easy matter to obtain bT by the method of least squares. bT will be referred to as the overall regression coefficient and is computed: With this estimate of bT, the total sum of squares of Y adjusted for the covariate (and grand mean), which is also the sum of squared residuals about the regression line, may be computed.