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# Measure of effect size (Cohen's d)

A researcher is studying nonverbal intelligence in elementary school students identified as having Asperger's syndrome (an autism spectrum disorder often characterized by higher verbal communication skills than individual's with autism). Specifically, the researcher wants to study whether students identified as having Asperger's syndrome have a level of nonverbal intelligence that is equal to that of the general population, as well as investigating how particular variables of interest are related to nonverbal intelligence in the population of individuals identified as having Asperger's. The researcher obtains a random sample of 16 elementary school students identified with Asperger's, and for each student records the gender (1 = female, 2 = male), the amount of maternal postsecondary education (1 = high school only, 2 = college/undergraduate degree, 3= Masters, 4 = PhD, MD, LLB), and the score on a nonverbal intelligence test. The obtained data are shown below.

Nonverbal Score Education Gender
38 1 1
47 1 1
43 1 2
47 1 1
40 2 2
59 2 2
60 2 1
40 2 1
49 3 1
53 3 2
50 3 2
53 3 2
51 4 1
47 4 1
56 4 2
55 4 2

3d. Compute a measure of effect size (Cohen's d) for the difference between nonverbal intelligence for male and female students identified with Asperger's syndrome. What does this value tell you?

3e. Test the null hypothesis that there is no difference in the mean nonverbal intelligence score for students identified with Asperger's syndrome who have mothers with different levels of education (where education is coded as 1, 2, 3, 4, as described above)? Be certain to clearly specify the statistical test you used in answering this question, and show all of the computations you used in answering this question.

5a. It has been hypothesized that Olympic marksmen shoot much better if they fire between heartbeats, rather than squeezing the trigger during a heartbeat due to the vibrations caused by the heartbeat. To test this hypothesis, a researcher collects shooting scores for a sample of 5 Olympic marksmen when the shots are taken during heartbeats and between heartbeats. The obtained scores are as follows:

Participant During Heartbeats Between Heartbeats
A 93 98
B 90 94
C 95 96
D 92 93
E 95 97

Use this data to test the null hypothesis that there is no difference in shooting score when shots are taken during or between heartbeats. Be certain to clearly specify the statistical test you used in answering this question, and show all of the computations you used in answering this question.

#### Solution Summary

Step by step method for computing measure of effect size (Cohen's d) is given in the answer.

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