# Biostats SDS 328M Homework 12 Due Tuesday, December 1, 2015

August 30, 2017

Question

Biostats SDS 328M Homework 12
Due Tuesday, December 1, 2015 at 11am in UTC 3.134
Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name
and your lab time. Show your work and round all answers to at least 3 decimal places.
1. Scientists wanted to know if the strontium concentration (mg/ml) differed among several different
lakes within a state park so they took an equal number of measurements from each. You are using
their data, but only have the following partial ANOVA table to go on:
df SS MS F P-value
Lake 2193.4 56.155
Error 25
Total 2437.6
a. Fill in the table above. (4 pts)
b. How many lakes were measured? And how many measurements were made from each? (1 pt)
c. Write out the null and alternative hypotheses for testing if the mean concentration differs
among the lakes in the park. (2 pts)
d. What would you conclude based on the table above? (1 pts)
e. What percentage of the variation in barium concentration can be accounted for by which lake
you test? (2 pts)
f. Suppose that, instead of conducting an ANOVA, you had conducted two-sample t tests on all
possible pairwise comparisons between the lakes. How many t tests would you have
conducted? (1 pt)
g. Use a Bonferroni correction to limit the overall significance level to ? = 0.01 (across all tests).
What significance level would you use for each of your separate tests? (2 pts)

2. The parasitoid wasp, Leptopilina heterotama, injects eggs into young larvae of fruit flies,
Drosophila melanogaster. One reaction by the flies is to self-medicate by consuming alcohol
(ethanol), which is naturally present in the decaying fruits where they live. The ethanol reduces
oviposition by wasps, and it increases death rates of wasp larvae within parasitized flies.
Researchers investigated whether the presence of the wasp influences where female fruit flies
prefer to lay their eggs. They presented female flies in cages with two dishes of fly food, one
having 6% ethanol and the other with 0% ethanol. They recorded the proportion of eggs laid in the
6% ethanol dish when females were placed with female wasps, with male wasps, or with no wasps.
The data below give the proportion of eggs laid in the ethanol dish for multiple replicates of each
wasp treatment.
No wasp: 0.25, 0.40, 0.46, 0.44
Male wasp: 0.42, 0.47, 0.31, 0.52
Female wasp: 0.89, 0.83, 0.92, 0.93
The following table provides the means, standard deviations and sample sizes for the data. Note
that proportion data where groups have different means often also have different standard
deviations.
a. Apply a log transformation and an arcsine transformation ?! = ??????? ? to the data, and
assess whether either set of transformed data exhibits less heterogeneity across group standard
deviations. (3 pts)
b. Based on (b), state the null and alternative hypothesis you would use in conducting an ANOVA.
(2 pts)
c. Make a graph based on the transformed data you would use in your ANOVA. In addition to the
transformed data itself, show the means and standard errors of the means. (3 pts)
d. The table below shows partial results of a Tukey-Kramer multiple comparisons of means.
Complete the table by adding test conclusions. (2 pts)
Group i Group j ?? ? ?? SE q q0.05,4,12 Conclusion
Female No 0.572 0.0626 9.13 2.79
Female Male 0.527 0.0626 8.42 2.79
Male No 0.044 0.0626 0.71 2.79
e. Add symbols to the graph in part (c) to illustrate the results of the Tukey-Kramer test. That is,
show which means group together on the basis of statistical significance. (2 pts)

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