An online statistics instructor wants to know if students’ statistics self-effic

Question

An online statistics instructor wants to know if students’ statistics self-efficacy increases from the beginning to end of an online introductory statistics course. Through the American Statistical Association (ASA) she finds 99 other researchers who are also interested in this topic. Together they organize a series of 100 research studies comparing online introductory students’ statistics self-efficacy at the beginning and end of a semester.

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 100 tests, there were 30 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 30 tests with statistically significance results were published, and not the 70 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*100 = 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 90 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 30 studies which are statistically significant , this does not provide convincing evidence

D)

There is publication bias when you publish only 30 significant results because the results might be different if you increase your sample size or perform the same test over different set of 100 observations.

So, only publishing the significant results would create a bias in reader's mind which is not right.

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