MEASURES OF

CORRELATION

Correlation

| A measure to determine the degree of relationship of two sets of variables, X and Y.

Perfect Positive Correlation

Perfect Negative Correlation

Pearson Product Moment

Correlation Coeffi cient

Pearson r

| A linear correlation necessary to find the degree of the association of two sets of variables X and Y.

Formula:

2222 YYNXXN

YXXYNrxy

xyr = correlation between X and Y

X = sum of test X

Y = sum of test Y

∑XY= sum of the product of X and Y

N = number of cases

2X = sum of squared X scores

2Y =sum of squared Y scores

For example:

r=0.99

Spearman Rank

Correlation Coeffi cient

or Spearman

Rho

Spearman Rho

| A statistic which is used to measure the relationship of paired ranks assigned to individual scores on two variables.

Formula:

sr = Spearman rho

2D = sum of the squared differences between

ranks

N = Number of cases

Computation of Spearman rho Between Capital (X) and Profit (Y) of Dried Fish

Businessmen X Y 1 Php 20,000 Php5,000 2 50,000 15,000 3 10,000 3,000 4 100,000 30,000 5 18,000 4,000 6 25,000 9,000 7 11,000 6,000 8 150,000 70,000 9 5,000 3,000

10 40,000 15,000

Computation of Spearman rho Between Capital (X) and Profit (Y) of Dried Fish

Businessmen X Y xR Ry

1 Php 20,000 Php5,000 6 7 2 50,000 15,000 3 3.5 3 10,000 3,000 9 9.5 4 100,000 30,000 2 2 5 18,000 4,000 7 8 6 25,000 9,000 5 5.0 7 11,000 6,000 8 6.0 8 150,000 70,000 1 1 9 5,000 3,000 10 9.5

10 40,000 15,000 4 3.5

Computation of Spearman rho Between Capital (X) and Profit (Y) of Dried Fish

Businessmen X Y D

1 Php 20,000 Php5,000 6 7 1.0 1.00

2 50,000 15,000 3 3.5 -0.5 0.25

3 10,000 3,000 9 9.5 -0.5 0.25

4 100,000 30,000 2 2 0 0

5 18,000 4,000 7 8 -1.0 1.00

6 25,000 9,000 5 5.0 0 0

7 11,000 6,000 8 6.0 2.0 4.00

8 150,000 70,000 1 1 0 0

9 5,000 3,000 10 9.5 0.5 0.25

10 40,000 15,000 4 3.5 0.5 0.25

xR Ry2D

Computation of Spearman rho Between Capital (X) and Profit (Y) of Dried Fish

very high relationship

Interpretation of

Correlation Value

Consider the following:| An r from 0.00 to +0.20 denotes

neglible correlation| An r from +0.20 to + 0.40 denotes

low or slight relationship| An r from +0.41 to + 0.70 denotes

marked or moderate correlation| An r from +0.71 to + 0.90 denotes

high relationship| An r from +0.91 to + 0.99 denotes

very high relationship| An r from +1..00 denotes perfect

relationship

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