Just like the Spearman's Rank Correlation Coefficient, the Pearson
ProductMoment Correlation Coefficient is a complex tool (Excel
recommended) used to determine the strength or a correlation between two
sets of data. However the Pearson ProductMoment Correlation
Coefficient is more sophisticated that the Spearman's Rank Test: it
gives more accurate results because it uses the actual measured values
of the data rather than their relative rankings. For the Pearson
ProductMoment test to be used with validity however, the data MUST show a LINEAR correlation with NO outliers (use a scatter graph), and must come
from a normally distributed population. If unsure, use the Spearman's Rank Correlation Coefficient.
A simple way to calculate the coefficient is to first create a scatter graph (to check for the conditions above), and then simply use EXCEL's formula: =PEARSON(array1,array2) (Note: array1 = group of cells listing data of 1st sample / array 2 = group of cells listing data of 2nd sample)
A simple way to calculate the coefficient is to first create a scatter graph (to check for the conditions above), and then simply use EXCEL's formula: =PEARSON(array1,array2) (Note: array1 = group of cells listing data of 1st sample / array 2 = group of cells listing data of 2nd sample)
Determine the number of degrees of freedom (df = number of pairs  1) and the required significance level: you finally need to look up a table of critical values of the Pearson ProductMoment Correlation Coefficient Test (use the "onetail test" line on top) to interpret the result.
For example: if your sample has 10 pairs (ie degrees of freedom = N  1 = 9) and the Pearson coefficient found is, for example, 0.903. According to the table, at a significance level of 0.05 (ie: there is no more than a 5% chance the correlation occured by accident) and for Df = 9, we need a coefficient of at least 0.521. We can therefore safely say that the two sets of data have a strong positive correlation with a 95% certainty (or, that there is only a 5% chance that the correlation is just accidental).
Once you have calculated the Pearson ProductMoment Correlation Coefficient AND if you see a linear correlation (positive or negative) when you plot your data using a scatter graph, you can then predict values outside of the sample by using a Linear Regression analysis, or "line of best fit".
For example: if your sample has 10 pairs (ie degrees of freedom = N  1 = 9) and the Pearson coefficient found is, for example, 0.903. According to the table, at a significance level of 0.05 (ie: there is no more than a 5% chance the correlation occured by accident) and for Df = 9, we need a coefficient of at least 0.521. We can therefore safely say that the two sets of data have a strong positive correlation with a 95% certainty (or, that there is only a 5% chance that the correlation is just accidental).
Once you have calculated the Pearson ProductMoment Correlation Coefficient AND if you see a linear correlation (positive or negative) when you plot your data using a scatter graph, you can then predict values outside of the sample by using a Linear Regression analysis, or "line of best fit".
Watch this tutorial to learn more about the Pearson's test:

Watch this tutorial to learn how to perform the Pearson's test using Excel:
