Correlation Formula

CORRELATION= is a measure of relationship between two variables.
Coefficient of correlation determine validity, reliability and objectivity of an examination prepared. It also indicates the amount of agreement or disagreement between groups of scores, measurements, or individuals.
Interpretation of Ranges
+ 0.00 to + 0.20 –Slight correlation, almost negligible relationship
+ 0.21 to + 0.40 –Slight correlation, definite but small relationship
+ 0.41 to + 0.70 –moderate correlation, substantial relationship
+ 0.71 to + 0.90 –High correlation, marked relationship
+ 0.91 to + 1.00 –Very high correlation, very dependable relationship
Coefficient of correlation Spearman’s Formula:
R=1-[(6(ΣG)/N2-1]
Where:
G=Difference of the two ranked scores
N=Number of scores
Procedure:
1. Write the scores or measures of the two variable under column x and column y
2. Rank the scores under column x , with the highest score as rank 1 and the lowest score as rank N. Write the ranks of the scores under column Rx which means rank of x
3. Rank the scores under column y with the highest scores as rank 1 and the lowest score as rank N.
4. Subtract the Ry values from the Rx values. Write the difference under column G, means gain. Consider only the positive values.
Coefficient of correlation by the use of the Rank-Difference Method:
rho=1-[(6(ΣD2)/N(N2-1)]
Procedure:
1. Follow the same steps from 1 to 3 in the Spearman’s Formula.
2. Find the difference between the two steps of ranks or values under column Rx and Ry. Subtract the larger value from the smaller value.
3. Write the difference of Rx and Ry under column D, which means difference.
4. Square the difference, D and write under column D2.
5. Get the sum of the values under D2.
Coefficient of correlation by the Product-Moment Method:
rxy=Σdxdy/square root[(Σd2x)(Σd2y)]
Procedure:
1. Get the total of the data under test x and test y and find the mean of x and mean of y.
2. Get the deviations dx and dy by getting the difference between the mean and the scores.
3. Square dx to obtain d2x and dy to obtain d2y.
4. Get the summation of each.
5. Get the product of dx and dy to have dxdy
6. Get the summation of dxdy.