Spearman Rank Difference Method of correlation (SRDM) (ρ)

 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 employed when data are in nominal and/or ordinal scale. The Spearman’s Rank Difference Correlation method is used to find the degree of association or correlation for ordinal data. Ordinal data means that the data are in order or ranks.

 Salient Features and Requirements for Using SRD Correlation

1.       Denoted by Greek letter rho ρ.

2.       Lies between -1 and +1

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

4.       Both variables between which correlation is to be calculated must have data in ordinal scale so that data can be given ranks.

5.       The data must be collected using random sampling.

Example

Suppose 11 Psychology students were assessed on their Memory and Socio-Economic Status. Compute the Spearman Rank Difference Correlation coefficient.

Student	Memory Score (X)	SES Score (Y)
Pooja	21	12
Sujal	42	15
Saloni	39	11
Rohit	48	20
Dinesh	24	18
Varsha	32	9
Priyanka	41	16
Raman	38	10
Monika	44	13
Rakesh	29	19
Veronica	33	14

 

Assign ranks to each score, starting with 1 to the lowest score and so on.

Student	Memory Score (X)	Rank	SES (Y)	Rank
Pooja	21	1	12	4
Sujal	42	9	15	7
Saloni	39	7	11	3
Rohit	48	11	20	11
Dinesh	24	2	18	9
Varsha	32	4	9	1
Priyanka	41	8	16	8
Raman	38	6	10	2
Monika	44	10	13	5
Rakesh	29	3	19	10
Veronica	33	5	14	6

 

Calculate Rank Difference

 

Student	Memory Score (X)	Rank	SES (Y)	Rank	Rank Difference (d)
Pooja	21	1	12	4	-3
Sujal	42	9	15	7	2
Saloni	39	7	11	3	4
Rohit	48	11	20	11	0
Dinesh	24	2	18	9	-7
Varsha	32	4	9	1	-3
Priyanka	41	8	16	8	0
Raman	38	6	10	2	4
Monika	44	10	13	5	5
Rakesh	29	3	19	10	-7
Veronica	33	5	14	6	-1

Calculate Square of Difference (d2)

Student	Memory Score (X)	Rank	SES (Y)	Rank	Rank Difference (d)	d2
Pooja	21	1	12	4	-3	9
Sujal	42	9	15	7	2	4
Saloni	39	7	11	3	4	16
Rohit	48	11	20	11	0	0
Dinesh	24	2	18	9	-7	49
Varsha	32	4	9	1	-3	9
Priyanka	41	8	16	8	0	0
Raman	38	6	10	2	4	16
Monika	44	10	13	5	5	25
Rakesh	29	3	19	10	-7	49
Veronica	33	5	14	6	-1	1
Total						178

 

Where, ρ = Spearman Rank Difference Correlation Coefficient

     6 Summation d Square = Sum of Squared Rank Differences

           n = Total sample size

If the Ranks are Tied?

More often it happens that two or more scores have similar ranks. In such situations we must add the tied ranks and divide by the number of ties.

 

Interpretation of Correlation coefficient

The value of the coefficient ρ = 0.190 indicates that the correlation between memory and Socio-Economic Status is negligible. It means SES has nothing to

do with Memory.

References:

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

Siegel, S. (1956). Nonparametric Statistics for Behavioural Sciences. Tata McGraw Hill.

  

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