Question

1. (60)Define a situation where you would chose to use Spearman Correlation rather than Pearson Correlation. Define a case when you should not use either. Be sure to include the null and alternative hypothesis, a description of the data, and an interpretation of a significant result.

Answer 1

Spearman correlation-

Suppose, there are 122 students in a class.

We want to find relation between marks (X) in mathematics and number (Y) of prizes won annually in cultural program.

In this case it is better to use Spearman's rank correlation coefficient to compare these two variables.

We have to test for null hypothesis

against the alternative hypothesis

Interpretation of significant result is that marks obtained by students in mathematics is significantly related (may be positively or negatively) with number of prizes they won annually in cultural programs.

Use neither-

There may be different instances.

1. Nonsense correlation- Suppose number of cars in road of America is compared with population in Japan during different times. Though we shall get highly positive correlation, these are not at all related. They are both related to third variable time.
2. Non-linear relation- Spearman correlation and Pearson correlation coefficients denotes linear relations only. So non-linear relations can not be determined using these. Suppose we have data set X={-2, -1, 0, 1, 2} and Y={4, 1, 0 , 1, 4}. Clearly Spearman correlation and Pearson correlation coefficient values are 0 signifying that there is no relation among variables. But clearly, there is an exact relation Y=X2. This is non-linear relation and can not be determined with these correlation coefficients.