I am going to type the excerpt from my textbook in its entirety. There are 2 questions at the end, but I am looking for further information/understanding regarding the 2nd question.

Multivitamins and Cancer

The following New York Times article on multivitamins appeared on October 17th, 2012. The article addresses a clinical trial that unfolded over more than a decade. Male doctors were followed during that period of time, and those taking a daily multivitamin were compared to those who took a placebo.

Title: Multivitamin Use Linked to Lowered Cancer Risk

Author: Roni Caryn Rabin

Source: New York Times

After a series of conflicting reports about whether vitamin pills can stave off chronic disease, researchers announced on Wednesday that a large clinical trial of nearly 15,000 older male doctors followed for more than a decade found that taking a daily multivitamin experienced 8% fewer cancers than the subjects taking dummy pills.

The findings were to be presented Wednesday at an American Association for Cancer Research conference on cancer prevention in Anaheim, Calif., and the paper was published online in the Journal of the American Medical Association.

The reduction in total cancers was small but statistically significant, said the study's lead author, Dr. J. Michael Gaziano, a cardiologist at Brigham and Women's Hospital and the VA Boston Healthcare System. While the main reason to take a multivitamin is to prevent nutritional deficiencies, Dr. Gaziano said, "It certainly appears there is a modest reduction in the risk of cancer from a typical multivitamin."

We aren't told how many doctors were in each group, but let's assume for sake of this exercise that there were 7,500 doctors in the vitamin group and 7,500 in the placebo group.

a. The results say that there were 8% fewer TOTAL cancers in the vitamin group than in the placebo group. If there were 1000 total cancers in the placebo group, what was the difference in the average number of cancers reported between the two groups?

80

b. Suppose you could plan this study all over again. Given the seriousness of cancer, you decide you want to be able to detect a small effect size (Cohen's d), with a Type I error rate of 0.05 and a Type II error rate of 0.20. What percentage of the 7,500 that were studied in each group would actually have been needed? Assume you were conducting a two-sided test.

i. About 5%

ii. About 50%

iii. About 0.5%

iv. About 500%