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In statistics, Pearson’s correlation coefficient, also known as Pearson’s r, is defined as the measure of the strength of correlation between two variables or data sets. There are many types of correlation coefficients, but Pearson’s correlation coefficient is the most popular. As it is based on the method of covariance, it is known as the best method to measure the association between two variables of interest. It gives information on the strength, or magnitude, of the relation as well as direction.
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The following explains the statistical significance of strength and direction in regard to Pearson’s correlation coefficient:
Strength, or magnitude, of correlation refers to the relationship correlation between two data sets. It reflects the consistency at which one variable changes in reaction to a change in the other. When data points fall in a line or very close to a line, they have a really strong correlation. In this case values may be +1 or -1, or very close to them. If data points fall farther away from each other and aren’t close to being points on a line, they have a weaker linear relationship.
The direction of the line reflects whether the two variables have a positive linear relationship or a negative linear relationship. The line has a positive linear relationship when it has an upward slope. A positive linear relationship means an increase in the value of one variable leads to an increase in the value of the other. On the other hand, the line has a negative linear relationship when it has a downward slope. In this case, an increase in the value of one variable will lead to a decrease in the value of the other, or vice versa.
The following is the formula of Pearson’s Correlation Coefficient:
n = the number of pairs of scores
Σ(xy) = the sum of the products of paired scores
(Σx) = the sum of x scores
(Σy) = the sum of y scores
Σx2 = the sum of squared x scores
Σy2 = the sum of squared y scores
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The following depicts the guidelines for the interpretation of Pearson’s Correlation Coefficient:
Strength of Association
0.1 to 0.3
-0.1 to -0.3
0.3 to 0.5
-0.3 to -0.5
0.5 to 1
-0.5 to -1
The stronger the association between two variables, the closer the answer will be to +1 or -1 depending on whether it is a positive or negative linear correlation. The closer the answer is to 0, the more the variation there is between variables.
The following visual examples show a few types of correlations in order to understand Pearson’s correlation coefficient better.