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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 purposes instead of concept, yet offers sufficient concept to permit the reader to use the tools intelligently instead of automatically. finished, and masking the real concepts within the box, together with new tools of put up hoc checking out. The relationships among diverse study designs are emphasised, and those relationships are exploited to improve normal rules that are generalized to the analyses of a big variety of probably differentdesigns. essentially for graduate scholars in any box the place data are used.

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If the variance of the scores in Group Al is larger than the variances in the other three groups, the ratio will be too large. The problem exists, moreover, even when sample sizes are large and equal. One solution is to find a transformation on the data that will make the variances in all I groups approximately the same. The advantages and disadvantages of such a transformation were discussed in Chapter 2. ApPROXIMATE F TEST Another solution is an approximate F test. 4. The null hypothesis specifies that 'Ij;~ is zero, so when the null hypothesis is true, E(C~) = EiC~kO'; /ni' We can form an appropriate F ratio if we can find a denominator that depends only on the variances within groups and has the same expected value as c~ under the null hypothesis.

Finally, dividing by MSw , we get The square root of this has a t distribution: (SSk/M Sw)1/2 '" t(N-I). , can be made using noncentral F as described in the previous chapter, with If every group has the same number of scores, then Xi. C~ N(l-'i,tT~/n)' = Ck(n/E ic'fk)1/2, 52 3. 2. 1. Al Ho(l) Ho(2) Ho(3) Xi. 625 -1/3 -1/3 -1/2 -1/2 -1 1 Et? 21 and = 0'; + n'I/JV(EiC~k)' 'l/JV(20';EiC~k)' We can now apply these formulas to the other two experimental questions asked at the beginning of this section.

Make the transformation you suggested in part c, and do the analysis of variance on the transformed data. Compare your results with those in part a. 1. Suppose that a fourth group had also been run and the data were A4 : 3,1,2,5,4. ) Do an analysis of variance on the four groups, finding the p value and w'2bet . , suppose the data are A4 : 3,1,2. Do the analysis of variance again on the four groups. 05 level, but those in part b were. 1) and then by removing some of the added data, we decreased it again.

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