# Biological Data Analysis: Exam 2 Answers

Here are the answers to the exam questions. The answer is in bold and the explanation for the answer is in regular type. If you have quick questions about your exam, you can talk with me before or after class. If you'd like to talk with me about the exam outside of class, e-mail me to set up a time to meet.

1. One nominal variable, fate of the turtle, with more than two values; one measurement variable, hatching time: Fisher's one-way anova or Welch's one-way anova

2. One nominal variable, which side they sleep on; one ranked variable, order in which they wake up; Kruskal-Wallis test

3. One nominal variable, which quadrant they fly to; theoretical expectation under the null is equal numbers in each quadrant; total sample size 95 butterflies; exact test of goodness-of-fit.

4. Two nominal variables, turtle species, east vs. west coast; Fisher's exact test of independence, chi-squared test of independence, G-test of independence. Need to know the sample size; if sample size is greater than 1000, need to know what is commonly used in your research area

5. Two nominal variables, food eaten, morning vs. evening; total sample size 144; Fisher's exact test of independence

6. Comparing two means out of 15 possible pairs of means: Tukey-Kramer test.

7. Two nominal variables, species of isopod, habitat; total sample size 54+33+65+49=201: Fisher's exact test of independence

8. Because you are doing 90 statistical tests when the null is always true, you expect 5% of 90 = 4.5 tests to have P<0.05, so you can use these results to convince gullible people that no-touch reiki works for some diseases. (And "no-touch reiki" is a real thing; some people even claim they can channel the healing life forces of the universe via an expensive phone call.)

9. One nominal variable, species of giraffe; one measurement variable, neck length: Fisher's one-way anova or Welch's one-way anova.

10a. One nominal variable, apples vs. no apples, with two values; one measurement variable, collagen:
Student's two-sample t-test, Welch's two-sample t-test, Fisher's one-way anova, Welch's one-way anova.

10b. If the data are unbalanced and heteroscedastic, you should not use Student's two-sample t-test or Fisher's one-way anova.

11. significance level (alpha): use what is common in your field (usually 0.05);
power or beta: use what is common in your field;
effect size: look at the effect sizes found in similar experiments, or decide what would be a large enough difference to be interesting to you;
standard deviation of collagen content: look at prior literature or do a pilot experiment

12. Three nominal variables, red vs. white eyes, light vs. dark, date; experiment is repeating a test of independence (red vs. white in light vs. dark) on different dates: Cochran-Mantel-Haenszel test.

13. One measurement variable, distance from starting point; theoretical expectation that mean distance will be 0 if the null is true: Student's one-sample t-test

14a. If the error bars are standard deviations, they tell you that the individual observations of tail length in DBA/2 mice are more spread out than in other strains of mice.

14b. If the error bars are standard errors, they tell you that the estimate of the mean tail length in DBA/2 mice is likely to be not as accurate as the estimates of the mean for other strains of mice

14c. If the paper does not tell you what the error bars represent, they tell you that the authors are either sloppy, or they don't know very much about statistics.

15. One nominal variable, strain of mice, with two values; one measurement variable, time on the wheel; experiment is unbalanced (26 of one strain, 59 of the other), and heteroscedastic (standard deviation is 0.48 in one strain, 0.22 in the other): Welch's two-sample t-test, Welch's one-way anova.

Return to the Biological Data Analysis syllabus