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Problem Set 1:

A scientist is interested in how chemotherapy affects spatial memory. The first phase of the experiment is to train a large group of rats (N=25) to learn a complex maze. After training for 30 days, the researcher wants to show that during the last 5 days of training all rats have hit their steady state performance in terms of completion time (in seconds). The collected data are in animal_maze_learning.csv. These data are the completion times for each rat over the last five days of training.

1. Provide a compelling graph of the data.

2. What is the statistical hypothesis and which statistical test is most appropriate? Are follow-up comparisons needed?

The statistical test used is Repeated measures ANOVA.

3. Provide the appropriate descriptive statistics.

4. Provide a numeric description of the statistical hypothesis test result and follow-up comparisons (if needed).

5. Provide a verbal description of the scientific result (not just reject/fail to reject the null hypothesis). Should the second phase of the experiment be started?

Problem Set 2: compare_three_drugs.csv

A scientist is examining whether three current drugs for nausea are equally effective at reducing self-reported nausea. The collected data are in compare_three_drugs.csv. These data show symptom severity (on a scale of 0 through 10, 10 being the most severe) for 60 adults taking one of three common over-the-counter nausea medications.

1. Provide a compelling graph of the data.

2. What is the statistical hypothesis and which statistical test is most appropriate? Are follow-up comparisons needed?

The statistical test used here is One-way ANOVA. Follow up test used is

3. Provide descriptive statistics.

4. Provide a numeric and verbal description of the output of the statistical test and follow-up comparisons (if needed).

5. Is one drug demonstrably the best? Why or why not?

Problem Set 3: seizures.csv

A group of researchers are testing a new drug that should reduce seizures by suppressing activity of a particular class of neurotransmitter receptors. The dataset seizures.csv contains the results of a pilot study. Assume the pilot study is accurate.

1. What is the expected effect size (Cohen's d)?

2. How many animals (in each group) are needed to have a 90% chance of detecting a statistically significant (p < 0.05) effect of the drug?

3. The researchers are considering a pre/post design where the same animals are observed for a period with and without the drug. Assuming the effect size stays the same, how many total animals would be needed for this kind of research design?

4. The company rep sends out an email that a new version of the drug is available. This version has a stronger binding affinity and blocks receptors at a higher rate. The claim is that this should increase the effect of the drug by 20%. Unfortunately, the drug costs 50% more than the original drug. Discuss how you could use power analysis to determine the relevant ethical and financial trade-offs in using this new drug (for the purposes of this question, let's assume the company rep is telling the truth about the effectiveness of the new drug)

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