A scientist postulates that grazing by gastropod snails affects the settlement of Spirorbid worms in estuaries. She sets up a manipulative experiment to test this by using cages to exclude grazers, and she repeated the whole experiment three different times. The full experimental design had the following factors:
Factor 1: Treatment, 3 levels (open surfaces, caged surfaces and a procedural control consisting of a partial cage), fixed;
Factor 2: Time, 3 levels, random, crossed with factor 1;
Factor 3: Sticks, 3 levels, random, nested in Treatment and also nested in Time
She counted the number of Spirorbid worms settling after a period of 6 months on each of n = 4 replicate panels per combination of the above factors. Data are given in the file "Spirorbids.txt".
a. Analyse these data, using ANOVA, using the full model associated with the above experimental design. Summarize your conclusions from this study as you would for a scientific journal.
b. What is a "mixed model"?
c. Which term in the above model yields a test of generality of effects of treatments among the three different trial runs?
d. Which term in the model yields a test of consistency in the overall direction of the effects of treatments across the three different trial runs, even in the presence of a potentially significant interaction with Time?