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**Additional resources for Analysis of Variance in Experimental Design**

**Sample text**

The only solution to this problem is to obtain the data in such a way that you can be reasonably certain the assumption of independence is justified. 26 2. Analysis of Variance, One-Way, Fixed Effects POWER OF THE F TEST We have found so far that the F test may be a useful test of the null hypothesis that the means of I independently sampled populations are all equal. In addition, we have found that the F test is relatively insensitive to departures from the normality and equal variance assumptions.

What conclusions can you draw for application to practical problems of experimental design? 9 for detecting a difference as large as 10 between any two means. 05. ) How large, approximately, must n be if I = 4? How large must N be? ) How large, approximately, must nand N be if I = 3? Compare these values with those in part a. 2. 12. ) Prove that SSt = SSbet + SSw' 44 2. 16. ) Do an analysis of variance on the data assuming that all of the assumptions for a one-way test are met. Find the p value and W~et.

SSm = RSM) because it is at the top. Second, note that each raw sum of squares is found by squaring the appropriate totals (or raw scores in the case of RSw ), adding them up (if there is more than one), and then dividing by the number of scores that entered into each total. Both of these principles will be generalized to higher-way designs in later chapters. Unequal Sample Sizes So far, we have assumed that the same number of scores was sampled from each group. In general, it is better if the number of scores in each group is the same (for reasons that will be evident later).