How to Calculate Pearson Correlation Coefficient

Step-by-Step Guide

1. 1

   Step 1: Find the average of chocolate consumption (Mx) by adding up all of the people's scores and dividing by the number of people.

   Then we would subtract each individual score (X) from the mean.
   
   This tells us how far away this person is from the average.
   
   You should have a new score for each person.      In the formula that is:
   X-Mx
2. 2

   Step 2: Do the same for happiness.

   We find the average level of happiness (My); then subtract each individual score (Y) from the mean.
   
   Again, you'll have a score for each person.      In the formula that is:
   Y-My , Once again, you'll have a new score for each person.      In the formula that is: (X-Mx)(Y-My) , That's what the funny-shaped "E" means in the formula. "Σ" is the Greek symbol for Sigma, and is used in stats to signify that you should add everything up.      In the formula that is: Σ(X-Mx)(Y-My) ,      In the formula that is:
   N-1 , If you're not sure how to calculate these values, check out How to Calculate Standard Deviation.
   
   In the formula that is:
   SxSy ,      In the formula that is: (N-1)SxSy ,, r is the symbol used to denote the Pearson Correlation Coefficient).
   
   A score of .1-.3 indicates a small relationship 31-.5 is a moderate relationship .51-.7 is a large relationship anything above .7 is a very strong (sometimes called "isomorphic") relationship.   A positive number means they move the same direction (as chocolate consumption goes up, so does a person’s happiness, and if chocolate consumption goes down, so does happiness).
   
   It doesn’t mean they both go UP—but it means they move together.
   
   A negative number means the variables move in opposite directions.
   
   That would mean that people were less happy as they ate chocolate, or people ate less chocolate when they were happy.
3. 3

   Step 3: Multiply each person's deviation from the mean for their X score by their deviation from the mean for their Y score.

4. 4

   Step 4: Add up all of the people's multiplied scores.

5. 5

   Step 5: Take the number of people in the sample (N) and subtract by 1.

6. 6

   Step 6: Multiply the standard deviation of chocolate consumption (Sx) by the standard deviation of happiness (Sy).

7. 7

   Step 7: Multiply that number by the number of people in your sample minus one.

8. 8

   Step 8: Take the number you calculated first and divide it by the number you just got .

9. 9

   Step 9: Interpret your result.

Detailed Guide

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