Here are the answers to exam 2. For some of the questions, I have provided explanatory material in regular type, and the answer in **bold**; all you need to write down is the answer. If you don't understand why your answer was wrong, you may e-mail me, talk to me before or after class, or set up a time to talk to me in my office. The exam is worth 25% of your grade for the class.

**1. **One measurement variable, penis length; two nominal variables, food type and mother; each mother is nested within one food type: **nested anova**

**2. **One measurement variable, flying time; two nominal variables, plugged vs. unplugged and the identity of the individual pigeons (since you have two observations per pigeon): **paired t-test** or **two-way anova, no replication**

**3. ****Partitioning the variance helps you decide how to allocate your effort in the big experiment, for example it will help you decide whether to have more rabbits and fewer liver samples per rabbit.**

**4. **One measurement variable, number of food pellets eaten; one nominal variable, joint vs. brownie vs. control; **one-way anova**. Note that you only have one observation per pigeon, so pigeon is not a nominal variable, and this is not a nested anova.

**5. **One measurement variable, grip strength; two nominal variables, right vs. left and person (because you have multiple observations per person); each person is found in combination with right and with left: **two-way anova with replication**. Note that you have three observations for each person-hand combination, so it's not a paired t-test or two-way anova without replication.

**6. **One measurement variable, jumping height; two nominal variables, dog breed and castrated vs. uncastrated; each dog breed is found in combination with castrated and with uncastrated; multiple dogs for each breed/castration combination: **two-way anova with replication**. Note that I randomize the order of questions after I write them, so it can happen that the same answer appears twice in a row, as it did here.

**7. ****You should try transformations and try to find one that makes the data look more normal.** Note that if you said you would just use one specific transformation, such as the log transformation, you got a little off; you would need to try different transformations.

**8. ****The unbalanced design is bad because if your data have heteroscedasticity, the combination of heteroscedasticity and an unbalanced design could increase your chance of a false positive.**. Remember that an unbalanced design doesn't

**9. **One measurement variable, balance time; two nominal variables, point stared at, and person (since you have multiple observations per person); each person is found in combination with each point stared at; just one observation per person/point combination: **two-way anova without replication**.

**10. **Three nominal variables, professor, asleep vs. awake, day:** Cochran-Mantel-Haenszel test**.

**11. **You are given effect size (0.1 m/s) and alpha (0.05), so you need **beta (or power) and standard deviation.**

**12. ****The larger standard deviation for A. vulgare means there's more variation of individual observations around the mean for A. vulgare than for A. nasatum.**

**13. **Two measurement variables, humidity and time rolled up; **linear regression/correlation.** Humidity is a measurement variable because there are 10 different values.

**14. **One measurement variable, arsenic content; two nominal variables, species and location; multiple individuals of each species found at each location: **Two-way anova with replication**

**15. **Two nominal variables, lure type and fish species; total sample size greater than 1000 (about 800 fish for each of 4 lures): **Chi-square test of independence** or **G-test of independence**

**16. **One measurement variable, moisture content; two nominal variables, person and before vs. after, each person has one measurement for before and after: **Paired t-test** or**two-way anova, without replication**

**17. **One measurement variable, weight; two nominal variables, person and date; each person is weighed once on each date: **two-way anova without replication**.

**18. **One ranked variable, relative color of urine; one measurement variable, food: **Kruskal-Wallis test**

**19. ****The effect of caffeine on crawling speed was different on different days**. Note that the significant *interaction* does not tell you that caffeine affects speed, or that day affects speed, or that caffeine affects day. Also note that saying that a significant interaction term tells you that there's an interaction was not enough, you had to explain what "interaction" means.

**20. ****With 10 breeds of chicken, there are a lot of pairwise comparisons, so comparing the highest and lowest means has a strong chance of giving a false positive if the null is true. You should have done a one-way anova, followed by the Tukey-Kramer test.**.

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