## Fixed Effects Analysis of Variance by Lloyd Fisher, Z. W. Birnbaum, E. Lukacs, John N. McDonald

By Lloyd Fisher, Z. W. Birnbaum, E. Lukacs, John N. McDonald

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9 [D. Shohori, I. Gedalia, A. E. Nizel, and V. Westreich, Fluoride uptake in rats given tea with milk, Journal of Dental Research 55, No. 5 (Sept-Oct 1976)] Shohori et al studied the fluoride uptake in rats given various drinking fluids. Fluoride uptake may be increased, decreased, or left unchanged, depending on its fluid medium. A total of 75 male rats were assigned to five groups. 9 ppm fluoride. A one-to-three dilution ratio was used. The fluids were sweetened with 100 g sugar per liter of fluid to increase consumption and consequently fluoride incorporation.

Do the following for n = m = 2, 10, 100: (a) Calculate the test statistic t. (b) Suppose one new observation is added to the X observations at the point x 0 · Write t as a function of x 0 . (c) Plot t(x0). (d) Does t seem robust against outliers? 13 (Robustness continued) One approach to making a two-sample test that is robust against outliers is to turn to a rank test. Let the X and Y observations be arranged in nondecreasing order from the smallest observation to the largest. The rank of an observation is its position in line; that is, the smallest observation has rank 1, the next smallest has rank 2, up to the largest observation which has rank m + n.

1, (a) compare the control men and women on the six scales; (b) compare the IM males with the IM females on the six scales. 2. What can you say about the p values from the tables in Appendix 2? 3. What can you say about the p values from the tables in Appendix 2? 18 Define a noncentral t-distribution with n df and noncentrality parameter δ to be the distribution resulting from division of a N(<5,1) random variable by the square root of an independent χ„2/η random variable. Denote the distribution by tn (δ).