Zuckerman, Hodgins, Zuckerman, and Rosenthal (1993) surveyed over 500 people and asked a number of questions on statistical issues. In one question a reviewer warned a researcher that she had a high probability of a Type I error because she had a small sample size. The researcher disagreed. Subjects were asked, “Was the researcher correct?” The proportions of respondents, partitioned among students, assistant professors, associate professors, and full professors, who sided with the researcher and the total number of respondents in each category were as follows:
(Note: These data mean that 59% of the 17 students who responded sided with the researcher. When you calculate the actual obtained frequencies, round to the nearest whole person.)
a. Would you agree with the reviewer, or with the researcher? Why?
b. What is the error in logic of the person you disagreed with in (a)?
c. How would you set up this problem to be suitable for a chi-square test?
d. What do these data tell you about differences among groups of respondents?