Log transformations and bee handout with partial solutions
As part of a study to investigate reproductive strategies in plants, biologists recorded the time spent at sources of pollen and the proportions of pollen removed by bumble-bee queens and honeybee workers pollinating a species of lily. (Data from L. D. Harder and J. D. Thompson, “Evolutionary Options for Maximizing Pollen Dispersal of Animal-pollinated Plants,” American Naturalist 133 (1989): 323-44.) Their data appear in Display 3.12.
pollen_removed duration_of_visit bee_type 1 0.07 2 Queen 2 0.10 5 Queen 3 0.11 7 Queen 4 0.12 11 Queen 5 0.15 12 Queen 6 0.19 11 Queen
Welch Two Sample t-test data: pollen_logprop by bee_type t = -3.9744, df = 20.249, p-value = 0.0007322 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -1.7504675 -0.5460731 sample estimates: mean in group Queen mean in group Worker -0.3812734 0.7669968
Which of the three scales seems most appropriate for use of the \(t\)-tools?
Compute a 95% confidence interval to describe the difference in means on the chosen scale.
What are relative advantages of the three scales as far as interpretation goes?
Based on your experience with this problem, comment on the difficulty in assessing equality of population standard deviations from small samples.