9.8 Suppose a researcher comes to you for advice about the analysis of an experiment she has conducted. She has used 5 treatments and she has 9 observations for each treatment. She shows you the following ANOVA from a computer printout:

The researcher wants to know from you whether the analysis is correct, and if so what it means. For each of the following scenarios answer the following questions: (i) What is the name of the design? (ii) What is the appropriate model? (iii) Based on the model in (ii) what is the corresponding ANOVA (include sources of variation, d.f., form of test for testing Ho T =72 = ... = 75). (iv) Is the ANOVA from the print-out above appropriate for testing Ho: T = ... = 73? (v) What are the SAS statements for doing (iii) and (iv)?

Scenario I: 45 animals were used for the study and each treatment was assigned to 9 animals at random; Scenario II: 45 animals were used but they came from 9 different litters of size 5 each and each treatment was assigned to one animal in each litter; Scenario III: 15 animals were used, each treatment was assigned to 3 ani- mals at random, and 3 observations were obtained from each animal.

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Source d.f. SS F-value Pr>F Treatments 4 100 8.33 .0001 Error 40 120