Question

The Spearman correlation for a sample of data on two variables is –1. What can you say about the value of the Pearson correlation for the data? Justify your answer briefly.

Answer 1

Solution:

Given:The Spearman correlation for a sample of data on two variables is –1.

following are the interpretations are for correlation coefficient r :

1) If r = -1 , then there is perfect negative correlation
2) if -1 < r ≤ 0.70 , then there is Strong negative correlation
3) if -0.70 < r ≤ -0.30, then there is moderate negative correlation
4) if -0.30 < r < 0 , then there weak negative correlation
5) if r = 0 , then there no or zero correlation
6) if 0 < r < 0.30 then there is weak positive correlation
7) if 0.30 ≤ r < 0.70 , then there is moderate positive correlation
8) if 0.70 ≤ r < 1 , then there is strong positive correlation
9) If r = +1 , then there is perfect positive correlation

Since r = -1 , there is perfect negative correlation between two variables.

In this case all points of scatter plot lie exactly on straight line and there is downward trend.