Psychology, 5th Edition by Robert A. Baron (eBook)
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?

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 1: Organize Data

Mean 𝑋 = (∑𝑋)/𝑛 = 80/10 = 8

Mean 𝑌 = (∑𝑌)/𝑛 = 75/10 = 7.5
Step 2: Compute means of X and Y

Compute deviation of each score from its mean (see table)
Step 3: Calculate Deviations

Calculate squares of deviation.

Then calculate sum of these deviations. (see table)
Step 4: Calculate squares of deviation.

𝑆_x = √((∑(𝑋 − Mean 𝑋)^2 ) / 𝑛) = √(144/10) = 3.79

𝑆_y = √((∑(𝑌 − Mean 𝑌)^2 ) / 𝑛) = √(124.5/10) = 3.53
Step 5: Calculate standard deviations for X and Y.

Pearson’s ProductMoment 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 6: Calculate correlation coefficient

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.
Step 7: Interpretation of Result
If you found this useful, do remember to like Psychology Learners on Facebook and subscribe by email.
For 'SuperNotes' click here.
For Free eBook previews click here.
For other IGNOU MAPC material click here.
For IGNOU related information and material click here.
IGNOU Students  please visit the FREE IGNOU Help Center for latest updates.
IGNOU Solved Assignments: Q4  MAPC MPC006 Statistics in Psychology  MPC006/ASST/TMA/201415
Comment using Facebook
What others like...
Introduction to Psychology, 7th Edition by Clifford T. Morgan, Richard A. King, John R. Weisz, John Schopler (eBook)
Social Psychology, 12th Edition by Robert A. Baron, Nyla R. Branscombe, Donn R. Byrne, Gopa Bhardwaj (eBook)
Statistics in Psychology and Education by S. K. Mangal (eBook)
IGNOU  Practicum File for MPCL007 MAPC 1st Year
Psychology, South Asian Edition by Saundra K. Ciccarelli and Glenn E. Meyer (eBook)
Personality Development  Psychological and Environmental Determinants
IGNOU  Examination Results  Final Score Calculator
Chi Square Method  Numerical
Start the discussion!