How to Calculate the Strength in a Correlational Study

Correlation coefficients can be calculated using a calculator and defining values on a piece of paper.

Scientists use correlation to show the relationship between two groups or changing variables. When a study is trying to relate two seemingly independent variables, the correlation coefficient is the most robust available statistic to show how these variables change relative to one another. Correlation strength is defined by the correlation coefficient. The closer this coefficient is to one, the stronger the correlation. Correlations can be negative, which shows an inverse relationship; as one variable increases, the other decreases. Correlation measurements are often used as statistical measurements to define how reliably variables shift in relation to one another.

Things You'll Need

• Two normalized groups of the same number of values

Instructions

1. Define N. This is the number of values in each group. This number should be the same across groups. For example, if there are five values in the first group and five in the second, N = 5.

2. Define Sum(X). Sum all the values in group one.

3. Define Sum(Y). Sum all the values in group two.

4. Define Sum(XY). Multiply the first value in group one with the first value in group two. Continue down the list of values until each value in the first group has been multiplied by a value in the second group. Sum all the products.

5. Define Sum(X^2). Square all the values in group one and sum them.

6. Define Sum(Y^2). Square all the values in group two and sum them.

7. Find the square root of [N*Sum(X^2)-(Sum(X))^2]*[N*Sum(Y^2)-(Sum(Y))^2]. Call this value "SqRt."

8. Calculate the correlation coefficient by plugging the defined values into the following equation: N*SumXY - Sum(X)*Sum(Y) / SqRt. The answer to this equation will be a number between -1 and 1. A correlation of zero indicates the two variables are not correlated at all. As the correlation value approaches 1, the groups are more strongly correlated.

Tips & Warnings

• Correlation calculations can be applied to more than just two categories by adding a Z definition and changing the Sum(XY) value to Sum(XYZ) and including the Z category in the formulas.

References

• Learn Correlation Co-efficient Tutorial, Definition, Example, Formula
• Correlation Coefficients

Resources

• Correlation
• AP Statistics Tutorial: Linear Correlation and Linearity