Table 13.8 reports the results of a study of fish hatching under three environments. Eggs from seven
Question:
Table 13.8 reports the results of a study of fish hatching under three environments. Eggs from seven clutches were randomly assigned to three treatments, and the response was whether an egg hatched by day 10. The three treatments were (1) carbon dioxide and oxygen removed, (2) carbon dioxide only removed, and (3) neither removed.
a. Let πit denote the probability of hatching for an egg from clutch i in treatment t. Assuming independent binomial observations, fit the model
logit(πit) = β1 z1 + β2 z2 + β3 z3,
where zt = 1 for treatment t and 0 otherwise. What does your software report for β̂1, and what should it be? (Note that treatment 1 has no successes.)
b. Analyze these data using an approach that allows overdispersion. Interpret. Indicate whether evidence of overdispersion occurs for treatments 2 and 3.
Table 13.8:
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