Product Moment Method of correlation (r)

Introduction

Broadly speaking the collected data can be classified into two major categories i.e., parametric and non-parametric. More often parametric tests are used for analyzing the data when it are in interval and/or ratio scale, and non-parametric tests are used when data are in nominal and/or ordinal scale. The Product Moment Method of Correlation is used to find the degree of association or correlation for interval or ratio scale data.

Salient Features and Requirements for Using Product Moment Correlation

1.       Denoted by English letter r

2.       Lies between -1 and +1

3.     The Product Moment correlation coefficient represents linear (straight line) relationship between the variables.

4.       Both variables between which correlation is to be calculated must have data in interval scale or ratio scale.

5.       The data have been collected in independent pairs.

6.     The two variables on which Product moment method is applied should be continuous.

7.       The data must be collected using random sampling.

Example

10 Psychology students were assessed on their Memory and Intelligence Quotient. Using the Product Moment method find out the degree and direction of their relationship.

Student	Memory Score (X)	IQ Score (Y)
Sujal	42	131
Saloni	39	118
Rohit	48	109
Dinesh	24	98
Suji	32	107
Priyanka	41	100
Raman	38	110
Monika	44	122
Rakesh	29	101
Veronica	33	111

First Step (Calculation of Mean)

 

Student	Memory Score (X)	IQ Scores (Y)
Sujal	42	130
Saloni	39	118
Rohit	48	107
Dinesh	24	98
Suji	32	105
Priyanka	41	100
Raman	38	110
Monika	44	120
Rakesh	29	100
Veronica	33	112
	Mean (x) = 370/10=37	Mean (y) = 1100/10=110

 

Second Step (Calculate Deviations)

 

Student	Memory Score (X)	(X-Mean)	x	IQ Scores (Y)	(Y-Mean)	y
Sujal	42	42 – 37	5	130	130 – 110	20
Saloni	39	39 – 37	2	118	118 – 110	8
Rohit	48	48 – 37	11	107	107 – 110	-3
Dinesh	24	24 – 37	-13	98	98 – 110	-12
Suji	32	32 – 37	-5	105	105 – 110	-5
Priyanka	41	41 – 37	4	100	100 – 110	-10
Raman	38	38 – 37	1	110	110 – 110	0
Monika	44	44 – 37	7	120	120 – 110	10
Rakesh	29	29 – 37	-8	100	100 – 110	-10
Veronica	33	33 – 37	-4	112	112 – 110	2

Third Step (Square the Deviations)

 

Student	Memory Score (X)	x-Mean	x	X Sqr	IQ Scores (Y)	Y-Mean	y	Y Sqr
Sujal	42	42 – 37	5	25	130	130 – 110	20	400
Saloni	39	39 – 37	2	4	118	118 – 110	8	64
Rohit	48	48 – 37	11	121	107	107 – 110	-3	9
Dinesh	24	24 – 37	-13	169	98	98 – 110	-12	144
Suji	32	32 – 37	-5	25	105	105 – 110	-5	25
Priyanka	41	41 – 37	4	16	100	100 – 110	-10	100
Raman	38	38 – 37	1	1	110	110 – 110	0	0
Monika	44	44 – 37	7	49	120	120 – 110	10	100
Rakesh	29	29 – 37	-8	64	100	100 – 110	-10	100
Veronica	33	33 – 37	-4	16	112	112 – 110	2	4

 Fourth Step (Calculate Product of Deviations)

Student	Memory Score (X)	x-mean	x	x Sqr	IQ Scores (Y)	Y-mean	y	y sqr	xy
Sujal	42	42 – 37	5	25	130	130 – 110	20	400	100
Saloni	39	39 – 37	2	4	118	118 – 110	8	64	16
Rohit	48	48 – 37	11	121	107	107 – 110	-3	9	-33
Dinesh	24	24 – 37	-13	169	98	98 – 110	-12	144	156
Suji	32	32 – 37	-5	25	105	105 – 110	-5	25	25
Priyanka	41	41 – 37	4	16	100	100 – 110	-10	100	-40
Raman	38	38 – 37	1	1	110	110 – 110	0	0	0
Monika	44	44 – 37	7	49	120	120 – 110	10	100	70
Rakesh	29	29 – 37	-8	64	100	100 – 110	-10	100	80
Veronica	33	33 – 37	-4	16	112	112 – 110	2	4	-8

 

Fifth Step (Find the Sum of Squared Deviations and Product of Deviations)

Student	Memory Score (X)	x-mean	x	x Sqr	IQ Scores (Y)	y-mean	y	y Sqr	xy
Sujal	42	42 – 37	5	25	130	130 – 110	20	400	100
Saloni	39	39 – 37	2	4	118	118 – 110	8	64	16
Rohit	48	48 – 37	11	121	107	107 – 110	-3	9	-33
Dinesh	24	24 – 37	-13	169	98	98 – 110	-12	144	156
Varsha	32	32 – 37	-5	25	105	105 – 110	-5	25	25
Priyanka	41	41 – 37	4	16	100	100 – 110	-10	100	-40
Raman	38	38 – 37	1	1	110	110 – 110	0	0	0
Monika	44	44 – 37	7	49	120	120 – 110	10	100	70
Rakesh	29	29 – 37	-8	64	100	100 – 110	-10	100	80
Veronica	33	33 – 37	-4	16	112	112 – 110	2	4	-8
Total (∑)	---	---	---	490	---	---	---	946	366

 

Interpretation of Correlation coefficient

The value of the coefficient r = 𝟎.𝟓𝟑𝟕 indicates that the correlation between memory and IQ moderate and positive. This means that if there is any change in the memory of a person, then there will be a moderate change in his IQ in the same direction.

 

References:

Levin, J. & Fox, J. A. (2006). Elementary Statistics. New Delhi: Pearson.

Guilford, J. P. and Fruchter, B. (1978). Fundamental Statistics in Psychology and Education, 6th ed. Tokyo: McGraw-Hill.

Garrett, H. E. (2014). Statistics in Psychology and Education. New Delhi: Pragon International.

 

 

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