# Pearson’s Product Moment Correlation- Numerical

The numerical below is an example of the process of performing the performing the Pearson’s Product Moment Correlation Analysis. This approach can be extended to similar cases by replacing the data.

## Calculate the coefficient between the following sets of scores using Pearson’s Product Moment method.

 Individuals A B C D E F G H I J Test A 1 6 7 3 11 9 7 11 14 11 Test B 2 3 5 6 6 8 10 10 12 13

### How to calculate the Pearson's Product Moment Coefficient of Correlation?

#### Step 1: Organize Data

• Organize the data into a table – test scores reflected in columns X and Y
•  Subject Test A (X) Test B (Y) X - Meanx Y - Meany (X - Meanx)2 (Y - Meany)2 (X - Meanx) x (Y - Meany) A 1 2 -7 -5.5 49 30.25 38.5 B 6 3 -2 -4.5 4 20.25 9 C 7 5 -1 -2.5 1 6.25 2.5 D 3 6 5 -1.5 25 2.25 7.5 E 11 6 3 -1.5 9 2.25 -4.5 F 9 8 1 0.5 1 0.25 0.5 G 7 10 -1 2.5 1 6.25 -2.5 H 11 10 3 2.5 9 6.25 7.5 I 14 12 6 4.5 36 20.25 27 J 11 13 3 5.5 9 30.25 16.5 Total 80 75 144 124.5 102

#### Step 2: Compute means of X and Y

• Mean 𝑋 = (∑𝑋)/𝑛 = 80/10 = 8
• Mean 𝑌 = (∑𝑌)/𝑛 = 75/10 = 7.5

#### Step 3: Calculate Deviations

• Compute deviation of each score from its mean (see table)

#### Step 4: Calculate squares of deviation.

• Calculate squares of deviation.
• Then calculate sum of these deviations. (see table)

#### Step 5: Calculate standard deviations for X and Y.

• 𝑆_x = √((∑(𝑋 − Mean 𝑋)^2 ) / 𝑛) = √(144/10) = 3.79
• 𝑆_y = √((∑(𝑌 − Mean 𝑌)^2 ) / 𝑛) = √(124.5/10) = 3.53

#### Step 6: Calculate correlation coefficient

• Pearson’s Product-Moment correlation cofficient, r:
• r = ∑((𝑋 − Mean 𝑋) x (Y − Mean Y))/(n x Sx x Sy) = 102/(10 x 3.53 x 3.79) = 0.762

#### Step 7: Interpretation of Result

• r = 0.762. This indicates a high positive correlation between the scores of the two tests. A student who scores well in one subject can be expected to score high in the other test too.

### If you found this useful, do remember to like Psychology Learners on Facebook and subscribe by email.

IGNOU Students - please visit the FREE IGNOU Help Center for latest updates.
IGNOU Solved Assignments: Q4 - MAPC MPC006 Statistics in Psychology - MPC006/ASST/TMA/2014-15