The correlation coefficient is a statistical value that measures the linear dependence between two variables. Pearson's Correlation Coefficient, in particular, is the most commonly reported correlation value for normally distributed data in scientific research. It is denoted as "r" and ranges in value from +1 to -1. The square of the coefficient, or r^2 value, may also be used which ranges from 0 to 1 with 1 identifying a perfect linear relationship. There are several assumptions that must be made in order to use the correlation coefficient which include, but are not limited to: paired "x" and "y" samples, independent "x" and "y" values, normally distributed data and independent observations. Although scientific calculators and statistical programs are the preferred method for determining the correlation coefficient for data sets, the formula and calculation are fairly straightforward and able to be done without the use of these tools.
- Simple calculator
- Two independent data sets of equal size
Show More
Instructions
-
-
1
Determine the sum of all the "x" variables.
Sum(X)=x1 + x2 + x3...
-
2
Determine the sum of the square of each "x" variable.
Sum(X^2)= x1^2 + x2^2 +x3^2...
-
-
3
Repeat Steps 1 and 2 for the "y" variables.
-
4
Find the cross product of each corresponding "x" and "y" variable and add these resulting values.
Sum(XY) = x1*y1 + x2*y2 + x3*y3...
-
5
Plug all of the previously calculated values into the correlation coefficient formula.
r = [Sum(XY) - (Sum(X)*Sum(Y)) / N)] / [sqrt(Sum(X^2) - (Sum(X^2) / N))*sqrt(Sum(Y^2) - (Sum(Y^2) / N)) ]
where N is equal to the number of paired observations. A link to a more easily interpreted representation of the formula is provided in the resources section.
-
6
Ensure that the resulting coefficient value lies between +1 and -1.
-
7
Use a scientific calculator, if possible, to check the answer as it is a fairly tedious calculation and errors can easily be made. A link for determining the correlation coefficient on a TI-84 calculator is also provided in the resource section.