# Biological Data Analysis: Homework 4

## Due Tuesday, Oct. 30

You must type this and all other homework assignments. Do not e-mail the assignment to me; turn it in early (at 322 Wolf) for a foreseeable absence, or turn it in late after an unexpected absence from class.

1. You're going to use the balance data set again. Analyze the same measurement variable that you analyzed in homework 3. Get the histogram spreadsheet (linked from the textbook page on normality) and enter the values of the measurement variable for people who disliked math. Print the histogram.

2. Plot two more histograms; one for the data from question 1 after it has been log transformed, and one with a square-root transformation. Say whether you think the untransformed data looks close enough to normal, and if not, say which transformation you think is best.

3. Print a table showing the standard deviation of your chosen measurement variable and sample size for each disliked class (math, English, gym, etc.). For each disliked class, you should give the standard deviation of the untransformed data; the standard deviation of the log-transformed data; and the standard deviation of the square-root transformed data. Based on comparing the standard deviations and sample sizes, say whether you think the data are homoscedastic enough to use Fisher's one-way anova. (Note that there is not absolute rule about how homoscedastic the data have to be; just give your opinion.)

4. Analyze the untransformed data using Fisher's one-way anova. Report the F-statistic, the degrees of freedom, and the P-value. Also do the Tukey-Kramer test and report the results in either a graph or table. Write a couple of sentences interpreting your results.

5. Analyze the untransformed data using Welch's one-way anova. Report the F-statistic, the degrees of freedom, and the P-value. Also do the Games-Howell test and report the results in either a graph or table. We didn't talk about Games-Howell in class; it's the same idea as the Tukey-Kramer test, only you do Tukey-Kramer after a Fisher's one-way anova and Games-Howell after a Welch's one-way anova. Write a couple of sentences interpreting your results.

6. Even though I think it's kind of stupid, analyze the untransformed data using the Kruskal-Wallis test. Report the adjusted-H statistic, the degrees of freedom, and the P-value. Write a couple of sentences interpreting your results.

7. Even if you thought the untransformed data were normal and homoscedastic enough, pick the best transformation and analyze the transformed data using Fisher's one-way anova, Welch's one-way anova, and Tukey-Kramer.

8. You've now analyzed the data six different ways: Fisher's one-way anova, Welch's one-way anova, and Tukey-Kramer, on both untransformed and transformed data. If you were analyzing data for your own research, would it be a good idea to analyze it six different ways? Why or why not?