Probability Statistics

Analysis of Variance in Experimental Design by Harold R. Lindman

By Harold R. Lindman

As an introductory textbook at the research of variance or a reference for the researcher, this article stresses functions instead of concept, yet provides adequate idea to allow the reader to use the equipment intelligently instead of robotically. accomplished, and protecting the $64000 concepts within the box, together with new tools of put up hoc checking out. The relationships among assorted study designs are emphasised, and those relationships are exploited to increase basic rules that are generalized to the analyses of a giant variety of doubtless differentdesigns. essentially for graduate scholars in any box the place statistics are used.

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21 is W~et = = fT~et/fT~ [SSbet - (I - l)MSwl/(SSt + MSw) (F -l)/[F -1 + N/(J - 1)]. 22) This is not an unbiased estimate of W~et. It tends to underestimate W~et' but with large samples the bias is small. 31. 21. This estimate is used in many standard computer programs. It has one minor disadvantag~although W~et can never be negative, W~et can. In fact, whenever F < 1, W~et will be negative. When that happens, you may either report that W~et = 0 or report the negative estimate, assuming that the reader can interpret the estimate correctly.

The error term should be based only on the variances of the two groups being compared. If, for example, the two specific groups being compared have population variances larger than the average for all I groups, MSw will underestimate the average for those two groups. The obtained t (or F) will then be too large and the p value will be too small. The opposite will be true if the two groups in question have population variances smaller than the average over all I groups. More complicated comparisons produce additional difficulties.

00 1 2 a E(F) 5 a E(F) 00 a Source: a values taken from Scheffe, 1959, p. 340. aUnattainable limiting cases to show bounds. i, and O"~ = [l:i(ni - l)O";Jj(N - I), so that O"~ is a weighted average of the true group variances, then MSw is an unbiased estimate of O"~. That is, E(MSw) = O"~. Similarly, we can let O"~ = [l:I 0"; Jj I so that O"~ is the unweighted average of the group variances. 12) E(MSbet) = O"~ + [(N - l)/N][I/(I -1)](0"~ - O"~). 13) 1 + [(N -l)/N][I/(I -1)][(0"~/0"~) -1]. 13. We already know that MSw is an unbiased estimate of 2.

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