Derivation of pearson correlation coefficient
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Pearson Correlation Coefficient
The Pearson correlation coefficient is a very helpful statistical formula that measures the strength between variables and relationships. In the field of statistics, this formula is often referred to as the Pearson R test. When conducting a statistical test between two variables, it is a good idea to conduct a Pearson correlation coefficient value to determine just how strong that relationship is between those two variables.
Formula
In order to determine how strong the relationship is between two variables, a formula must be followed to produce what is referred to as the coefficient value. The coefficient value can range between -1.00 and 1.00. If the coefficient value is in the negative range, then that means the relationship between the variables is negatively correlated, or as one value increases, the other decreases. If the value is in the positive range, then that means the relationship between the variables is positively correlated, or both values increase or decrease together. Let's look at the formula for conducting the Pearson correlation coefficient value.
Step one: Make a chart with your data for two variables, labeling the variables (x) and (y), and add three more columns labeled (xy), (x^2), and (y^2). A simple data chart might look like this:
Person Age (x) Score (y) (xy) (x^2) (y^2)
1
2
3
More data would be needed, but only three samples are shown for purposes of example.
Step two: Complete the chart using basic multiplication of the variable values.
Person Age (x) Score (y) (xy) (x^2) (y^2)
1 20 30 600 400 900
2 24 20 480 576 400
3 17 27 459 289 729
Step three: After you have multiplied all the values to complete the chart, add up all of the columns from top to bottom.
Person Age (x) Score (y) (xy) (x^2) (y^2)
1 20 30 600 400 900
2 24 20 480 576 400
3 17 27 459 289 729
Total 61 77 1539 1265 2029
Step four: Use this formula to find the Pearson correlation coefficient value.
The Pearson correlation coefficient is a very helpful statistical formula that measures the strength between variables and relationships. In the field of statistics, this formula is often referred to as the Pearson R test. When conducting a statistical test between two variables, it is a good idea to conduct a Pearson correlation coefficient value to determine just how strong that relationship is between those two variables.
Formula
In order to determine how strong the relationship is between two variables, a formula must be followed to produce what is referred to as the coefficient value. The coefficient value can range between -1.00 and 1.00. If the coefficient value is in the negative range, then that means the relationship between the variables is negatively correlated, or as one value increases, the other decreases. If the value is in the positive range, then that means the relationship between the variables is positively correlated, or both values increase or decrease together. Let's look at the formula for conducting the Pearson correlation coefficient value.
Step one: Make a chart with your data for two variables, labeling the variables (x) and (y), and add three more columns labeled (xy), (x^2), and (y^2). A simple data chart might look like this:
Person Age (x) Score (y) (xy) (x^2) (y^2)
1
2
3
More data would be needed, but only three samples are shown for purposes of example.
Step two: Complete the chart using basic multiplication of the variable values.
Person Age (x) Score (y) (xy) (x^2) (y^2)
1 20 30 600 400 900
2 24 20 480 576 400
3 17 27 459 289 729
Step three: After you have multiplied all the values to complete the chart, add up all of the columns from top to bottom.
Person Age (x) Score (y) (xy) (x^2) (y^2)
1 20 30 600 400 900
2 24 20 480 576 400
3 17 27 459 289 729
Total 61 77 1539 1265 2029
Step four: Use this formula to find the Pearson correlation coefficient value.
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