Question

The values given below shows the aptitude test scores, x, and the intelligence quotient (IQ), y, for 9 people.
x : 68, 72, 65, 70, 62, 75, 78, 64, 69
y : 90, 85, 88, 100, 105, 98, 70, 65, 72

Resolve problem and find the correlation coefficient using Spearman Rank Correlation. Interpret the result accordingly. (15 pts)

Answer 1

We give rank for x variable data and y variable data based on the lowest to highest value and then used those ranks to calculate the correlation. Therefore we called Spearman Rank Correlation.

Now give ranks x and y variable data:

Now use these ranks to calculate correlation coefficient.

Use this formula to calculate the correlation coefficient.

From Above Table:

Now put these value in SSx SSy and SSxy formula.

Now put these values in Correlation formula.

Now understand correlation coefficent, correlation coefficient tells about direction and relationship between two variables.

If correlation coefficient is positive, it is mean when x increase then y also increases.

If correlation coefficient is negative, it is mean when x increase then y will be decreases.

Correlation coefficient lies between -1 to 1 and if correlation is zero then we say there is no correlation between two variables.

So, the Spearmen Correlation Coefficient is -0.167. That is negative and near to zero , it is mean when x increase then y will be decreases and there is low relationship between x and y.