Question

A researcher is interested in the relationship between concussions and short-term memory loss. To explore this relationship, the researcher collects data on the number of concussions and number of words recalled on a memory test.

Assume SP = -34       SS_concussions =    58        SS_{number of words recalled} = 27

Interpret the Pearson correlation coefficient between concussions and number of words recalled in terms of the strength and direction of the relationship:

Answer 1

Solution:

Given:

SP = -34      

SS_concussions =    58       

SS_{number of words recalled} = 27

We have to find and interpret the Pearson correlation coefficient between concussions and number of words recalled in terms of the strength and direction of the relationship.

Formula:

following are the interpretations are for correlation coefficient r :

1) If r = -1 , then there is perfect negative correlation
2) if -1 < r ≤ -0.80 , then there is Strong negative correlation
3) if -0.80 < 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 < 0.80 , then there is moderate positive correlation
8) if 0.80 ≤ r < 1 , then there is strong positive correlation
9) if r = 1 , then there is perfect positive correlation

Since is between -1 < r ≤ -0.80 , there is Strong Negative Correlation  between concussions and number of words recalled.

(strength is strong and direction of the relationship is negative).