An online statistics instructor wants to know if students’ statistics self-effic
ID: 2921319 • Letter: A
Question
An online statistics instructor wants to know if students’ statistics self-efficacy increases from the beginning to the end in an online introductory statistics course. Through the American Statistical Association (ASA) she finds 49 other researchers who are also interested in this topic. Together they organize a series of 50 research studies comparing online introductory students’ statistics self-efficacy at the beginning and end of a semester. [28 points]
A. If there is not difference between students’ statistics self-efficacy at the beginning and end of the semester, how many tests would you expect to be statistically significant at the 0.05 alpha level just by random chance?
B. If you were conducting one of these research studies, what alpha level would you use and why?
C. Suppose that of 50 tests, there were 24 tests with statistically significant results. Would this be convincing evidence that statistics self-efficacy changes from beginning to end of a semester? Explain why or why not.
D. If only the 24 tests with statistically significance results were published, and not the 26 tests without statistically significant results, explain why publication bias is a problem.
Explanation / Answer
A. At 0.05 level we would expect 5% = 0.05*50 = 2.5 of the studies to be statistically significant just by random chance
B.We would use a alpha level of 0.1 because it an observational study and we do not want the probability of type two error to be too high.
C.At an alpha level of 0.1 we would expect at least 45 studies to be statistically significant for there to be convincing evidence that statistics self-efficacy changes from beginning to end of a semester. Since we have only 20 studies which are statistically significant , this does not provide convincing evidence