How to Calculate the Value of Pearson Product-Moment Correlation
Calculating the Pearson product-moment, also known as Pearson's r or regression line, is done to determine the form of a relationship between two interval data variables. Interval data are considered parametric or data that measures of central tendency can be performed on. According to Data Construction and Data Analysis for Survey Research, "The objective is to be able to predict or estimate the value of one variable corresponding to a given value of the other." A "best fit" line will show the level of correlation. A value of 1.00 equals a perfect positive correlation; -1.00 equals a perfect negative correlation.
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Instructions
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1
Make a table of all variables. Subtract the mean of X from each individual X variable and the mean of Y from each individual Y variable.
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2
Multiply the X and Y values obtained in Step 1 together for each individual in the study. Total these quotients.
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3
Square each answer you obtained in Step 1 for both the X and Y values and total these answers for both columns.
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4
Multiply the total of X and the total of Y from Step 3.
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Find the square root of the quotient from Step 3 and divide this into the total from Step 2. This will give you the final r value. As can be seen from the given table, in this case r = .843, which is generally a strong positive correlation.
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Tips & Warnings
Although it is important to know how to figure Pearson's regression line to understand the statistic, in doing research it is best to use a software program such as SPSS or Minitab to run the statistic.
If the relationship is clearly not linear or the data are not intervals to begin with, a different calculation needs to be used to determine potential relationships between the variables. You will need multiple pairs of samples to determine the real level of significance of the r value.
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Comments
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The pearson product moment correlation math sucks.
