In: Statistics and Probability
You have been using the chi-square test of independence to test for association between two variables.
1) Give an example of a pair of variables for which you would expect to find no association.
2) Give an example of a pair of variables for which you would expect to find association, but not a causal relationship.
3) Finally, give an example of a pair of variables for which you would expect to find a causal relationship.
1) Give an example of a pair of variables for which you would expect to find no association.
ANs: variable1 = Gender
Variable 2 = Height
So, these two variables might not have any association
2) Give an example of a pair of variables for which you would expect to find association, but not a causal relationship.
Ans: A study shows that there is a negative correlation between a student's anxiety before a test and the student's score on the test. But we cannot say that the anxiety causes a lower score on the test; there could be other reasons—the student may not have studied well, for example. So the correlation here does not imply causation.
3) Finally, give an example of a pair of variables for which you would expect to find a causal relationship.
Ans: However, consider the positive correlation between the number of hours you spend studying for a test and the grade you get on the test. Here, there is causation as well; if you spend more time studying, it results in a higher grade.