Stat 401: lab 6 – self assessment The data in cavity.txt are measurements of nesting cavity size for 9 species of birds and mammals that nest in cavities in southern Colorado. Specifically, the measurement is the area of the cavity entrance, although I will call that nest size throughout. The data in cavity2.txt are the subset of data for two species: Plain Titmouse and American Kestrel. Consider first the data from Plain Titmouse and American Kestrel (cavity2.csv). 1) Is it reasonable to assume that variability in nest size is the same for the two species? Why or why not? 2) Consider log transformed nest size for those two species. Is it reasonable to assume equal variances after log transformation? Why or why not? 3) Thinking about the ratio of nest sizes, how much larger are American Kestrel nests? 4) Calculate a 95% confidence interval for that ratio of nest sizes. Using all 9 species (cavity.txt): 5) Test the null hypothesis that all species have the same median nest size. Report the p-value and a one-sentence conclusion. 6) What is the estimated difference of log transformed nest sizes between American Kestrel and Plain Titmouse? 7) Estimate the ratio of nest sizes between American Kestrel and Plain Titmouse and a 95% confidence interval for that ratio. Do not use any multiple comparisons adjustment. 8) Why is the confidence interval in question 7 different from that in question 4? Answers: 1) No – variability much larger in Am Kestrel. See this in a box plot or by computing the sd for each species: 3183 and 830. 2) Yes – variability much more equal (although Kestrel still more variable). See this in a box plot or computing the sd of each species: 0.59 and 0.33. 3) Kestrel nest entrances are 2.8 times larger than Plain Titmouse nest entrances. Note: on log scale, difference is 1.033 (= 8.598 – 7.565). Estimated ratio is exp(1.033) 4) 95% confidence interval for the ratio is (1.86, 4.25). Note: on log scale, ci is (0.619, 1.446). Reported ci is obtained by exponentiating each endpoint. 5) p < 0.0001, very strong evidence that at least one species has a nest size that differs from the others. 6) 1.03 (Same as in log scale result in 3) 7) ratio = 2.8. 95% confidence interval is (1.84, 4.28) 8) Two differences: pooled sd is not the same (0.414 for two species, 0.448 for nine species) and t quantile used to calculate the ci is smaller in the nine species analysis (285 df, instead of 20).