## Alliant International University

Research II: Data Analysis & Advanced Statistics

Due Date:

# Saturday, Mar. 22, 2003

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.

• (HW_4_1) A study was conducted to compare the effectiveness of two suspect interrogation techniques. 180 criminal suspects are chosen to participate in the study. They are categorized in one of nine groups (1 = minor crimes, and 9 = most violent criminals). Within each of the nine groups the suspects are randomly assigned to one of two different interrogation techniques. The state-of-the-art police interrogation method (method A) was applied to the first 90 suspects and the remaining 90 underwent a hypnosis-based interrogation (method B).  For each crime severity level (group 1, 2, ..., 9), the percentage of true confessions obtained from all suspects is recorded. The resulting data (confession rates using interrogation methods A or  B) are as follows:

 Violence Group 1 2 3 4 5 6 7 8 9 Mean Standard Deviation Method A: 23% 17% 28% 48% 10% 36% 15% 22% 94% _______ ________ Method B: 36% 22% 25% 60% 16% 34% 28% 22% 100% _______ _________ Difference: ___ ___ ___ ___ ___ ___ ___ ___ ___ _______

• Complete the table.
• In this question you will perform 2 different types of analyses on the above data. Both of these tests may not be appropriate; you will discuss this issue in part (c). For the two tests please clearly state your hypotheses, show your work to get the statistics and interpret the results.
• Treating the data as from two independent samples (with interrogation method A data as sample 1 and method B data as sample 2), carry out a 2-sided t-test to investigate whether there is a difference between the two interrogation schemes based upon the percentages of true confessions obtained.
• Treating the data as paired, carry out a 2-sided t-test to investigate whether there is a difference between the two interrogation schemes based upon the percentages of true confessions obtained.
• Should we  treat these data as two independents samples or as paired observations? Briefly justify your answer. Draw an appropriate dotplot  for this data. Which of the tests from part (b) is most appropriate for this data? Justify your answer. Construct the corresponding 95% CI for the parameter of interest (?) which indicates whether the two interrogation techniques yield different results.

• (HW_4_2) In a recent test of the effectiveness of a new sleeping pill, 75 patients were randomly assigned to three groups of 25. The first group was given the new drug, the second group was given a placebo and the third group was given no treatment at all. The number of minutes it took for the patient to fall asleep was measured and the results of the experiment are shown in the table below.

 Drug 12 11 18 37 12 10 63 19 8 17 5 27 50 27 4 22 28 34 42 2 32 21 33 41 29 Placebo 44 30 3 13 56 28 24 4 67 32 22 12 27 32 22 9 13 28 12 42 54 37 22 20 42 Neither 32 12 55 44 38 89 6 56 59 33 15 67 60 49 63 8 28 21 14 72 36 66 23 9 39

• Comment on the validity of the assumptions for the F-test.

• Complete the ANOVA table. State the hypotheses for the F-test. Interpret your results in plain English. Make recommendations.

• (HW_4_3) In the early 1990s, aspirin, well known as a mild painkiller, was recognized to have blood-thinning properties. If a small dosage of aspirin is taken regularly, the risk of a heart attack caused by blood clotting can be reduced substantially. A drug company in the United States is presently interested in testing a new drug which it believes has similar properties to aspirin. A total of 19,000 people will take part in the study. The number of deaths due to heart attacks will be recorded over a 10-year period.

• Describe an experiment you could use to investigate the problem posed. Include details of how you would allocate treatments to subjects. Justify your choice of experimental design.
• Describe the hypotheses you would test.
• List all the assumptions that should be satisfied so that your chosen method is valid.