Correlation Properties Suppose that you take a random sample of classes on campu
ID: 3309310 • Letter: C
Question
Correlation Properties
Suppose that you take a random sample of classes on campus and record the number of students enrolled in the class and the average evaluation score assigned by students to that teacher’s effectiveness (on an A = 4, B = 3, … scale).
(a) If the correlation coefficient turned out to be very close to zero, would you conclude that larger classes tend to have lower teaching evaluation averages? Explain.
(b) Suppose that the correlation coefficient turned out to be r = –0.5. Would you expect this to be more statistically significant if the sample size were n = 5 or if the sample size were n = 50, or would you expect sample size not to matter? Explain.
(c) Suppose that you also record whether the teacher was male or female. Would it make sense to calculate the correlation coefficient between class size and sex? Explain.
Explanation / Answer
a) The correlation coefficient very close to zero means there is no relationship between two variable. i.e. One variable can not affects the another variable. Therefore we would not conclude that larger classes tend to have lower teaching evaluation averages.
b) Larger sample size gives more significant statistic, i.e. sample size affects the statistic. If the correlation coefficient turned out to be r = –0.5 then we can expect this to be more statistically significant for sample size 50 and not for the size n = 5. Sample size matters in each statistic.
c) Sex is a categorical variable. Class size is a numerical variable. We can calculate the correlation coefficient only for two numerical variable. In this case, sex is not a numerical variable. So that, It doesn't make sense to calculate the correlation coefficient between class size and sex.