Question

Issue 1: Pearson Correlation Coefficient

One professor who teaches statistics gave students one homework assignment. He asked students to find a two-variable data set and compute the Pearson correlation coefficient. One student found a data set: one variable is students’ midterm test score in an introductory microeconomics class and total observations are 45 students; while the other one variable is also students’ midterm test score in another introductory microeconomics class and total observations are 57 students. Both of these two classes were taught by the same instructor in spring 2018. Does this student’s data set make sense? Why or why not? Discuss and explain your reasons. You must provide your statistical analysis and reasons.

Answer 1

If the sample size is different it is impossible to calculate Karl Pearson's correlation coefficient. But in the above case, definition of variables make sense as the instructor was same for both the classes. Hence the correlation indicates, given the same instructor i.e same teaching, what is the relationship between level of understanding among students of different classes

What the student can do is..re-design the 2 variables into matching pairs and calculate correlation coefficient for each group of 45 students. From the second variable, he will have to randomly select 45 obs out of 57 using and randomized model. The calculate correlation between N1 and new N2( containing 45 observation)