chapter 1

Chapter 14: The Analysis of Categorical Data28. With p ij denoting the probability of a type j response when treatment i is applied, H o : p 1j = p 2j2 2= p 3j =p 4j for j = 1, 2, 3, 4 will be rejected at level .005 if χ ≥ χ = 23. 587 ..005,9Ê ij 1 2 3 41 24.1 10.0 21.6 40.42 25.8 10.7 23.1 43.33 26.1 10.8 23.4 43.84 30.1 12.5 27.0 50.52χ = 27.66 ≥ 23.587 , so reject H o at level .00529. H o : p 1j = …= p 6j for j = 1, 2, 3 is the hypothesis of interest, where p ij is the proportion of the j thsex combination resulting from the i th genotype. H o will be rejected at level .10 if2 2χ ≥ χ = 15.987 ..10,10Ê ij 1 2 32χ 1 2 31 35.8 83.1 35.1 154 .02 .12 .442 39.5 91.8 38.7 170 .06 .66 1.013 35.1 81.5 34.4 151 .13 .37 .344 9.8 22.7 9.6 42 .32 .49 .265 5.1 11.9 5.0 22 .00 .06 .196 26.7 62.1 26.2 115 .40 .14 1.47152 353 149 654 6.46(carrying 2 decimal places in Ê yields χ2 = 6. 49 ). Since 6.46 < 15.987, H o cannot berejected at level .10.ij449