# Question 1315 Analyze Effect Design Variables Sacrifice Time Treatment Log Ratio Brain Cou Q11555531

Question 13.15

Analyze the effect of the design variables – sacrifice time andtreatment – on the log of the ratio of brain count to liver countin the data set described in Section 11.1.2. (a) Ignore thecovariates and use an analysis of variance procedure to fit thedata. Fit a model that includes interaction terms; plot theresiduals versus the fitted values. (b) Test whether there is aninteractive effect of treatment and sacrifice time. What are theF-statistic, the degrees of freedom, and the p-value? (c) If thereare no interactive effects, test whether there are main effects oftreatment and sacrifice time. (d) Complete the analysis bydescribing the effects of treatment and sacrifice time, either byestimating the appropriate contrasts or by using a regressionprocedure with indicator variables to model treatment (oneindicator) and sacrifice time (three indicators).

Data set described in Section 11.1.2:

 Brain Liver Time Treatment Days Sex Weight Loss Tumor 41081 1456164 0.5 BD 10 Female 239 5.9 221 44286 1602171 0.5 BD 10 Female 225 4.0 246 102926 1601936 0.5 BD 10 Female 224 -4.9 61 25927 1776411 0.5 BD 10 Female 184 9.8 168 42643 1351184 0.5 BD 10 Female 250 6.0 164 31342 1790863 0.5 NS 10 Female 196 7.7 260 22815 1633386 0.5 NS 10 Female 200 0.5 27 16629 1618757 0.5 NS 10 Female 273 4.0 308 22315 1567602 0.5 NS 10 Female 216 2.8 93 77961 1060057 3 BD 10 Female 267 2.6 73 73178 715581 3 BD 10 Female 263 1.1 25 76167 620145 3 BD 10 Female 228 0.0 133 123730 1068423 3 BD 9 Female 261 3.4 203 25569 721436 3 NS 9 Female 253 5.9 159 33803 1019352 3 NS 10 Female 234 0.1 264 24512 667785 3 NS 10 Female 238 0.8 34 50545 961097 3 NS 9 Female 230 7.0 146 50690 1220677 3 NS 10 Female 207 1.5 212 84616 48815 24 BD 10 Female 254 3.9 155 55153 16885 24 BD 10 Male 256 -4.7 190 48829 22395 24 BD 10 Male 247 -2.8 101 89454 83504 24 BD 11 Female 198 4.2 214 37928 20323 24 NS 10 Female 237 2.5 224 12816 15985 24 NS 10 Male 293 3.1 151 23734 25895 24 NS 10 Male 288 9.7 285 31097 33224 24 NS 11 Female 236 5.9 380 35395 4142 72 BD 11 Female 251 4.1 39 18270 2364 72 BD 10 Female 223 4.0 153 5625 1979 72 BD 10 Male 298 12.8 164 7497 1659 72 BD 10 Male 260 7.3 364 6250 928 72 NS 10 Male 272 11.0 484 11519 2423 72 NS 11 Female 226 2.2 168 3184 1608 72 NS 10 Male 249 -4.4 191 1334 3242 72 NS 10 Female 240 6.7 159

Question 13.22

The blocks in the Pygmalion study of Exercise 21 are thedifferent classrooms in the school. To model possible differencesamong the 17 classrooms (such as the effects of the differentclassroom teachers) as a categorical factor, 16 paramters areneeded. Some researchers would prefer to think of the classroomeffects as random, which would mean acting as if the 17 teacherswere a random sample from some larger population of teachers. Thetreatment effect would be handled in the usual way and would bereferred to as a “fixed effect.” A model that includes both fixedand random effects is called a mixed effects model. Analyze thedata of Exercise 21 but treat the block effects as random by usinga mixed linear model routine in a statistical computer program.

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