What is the Pearson correlation coefficient?

The Pearson correlation coefficient is a test that measures the statistical relationship between two continuous variables. If the relationship between the elements is not linear, the coefficient will not be represented appropriately.

The correlation coefficient can take a value between +1 and -1. A value of 0 means there is no relationship between the two variables. A value greater than 0 indicates a positive relationship. This means that if the value of one variable increases, the value of the other variable also increases. A value below 0 indicates a negative relationship, meaning that as the value of one variable increases, the value of the other variable decreases.

To perform Pearson correlation, the following is required:

• The measurement scale must be an interval or ratio scale.
• The variables must be approximately distributed.
• The relationship must be linear.
• There must be no outliers in the data.

How do you calculate the Pearson correlation coefficient?

The formula for the correlation coefficient by person is as follows:

Where:
“x” represents variable number one, “y” belongs to variable number two, “zx” is the standard deviation of variable one, “zy” is the standard deviation of variable two, and “N” is the number of data.

Interpretation of the correlation coefficient according to Karl Pearson

The Pearson correlation coefficient is intended to indicate how closely two variables are related to each other, like this:

• Correlation less than zero: If the correlation is less than zero, it means that it is negative, that is, the variables are inversely related to each other. If the value of one variable is high, the value of the other variable is low. The closer it is to -1, the more obvious the extreme covariation. If the coefficient is equal to -1, it is said to have a perfect negative correlation.
• Correlation greater than zero: If the correlation is +1, it means that it is completely positive. In this case, it means that the correlation is positive, that is, the variables are directly correlated with each other. When the value of one variable is high, the value of the other variable is also high, and the same happens when they are low. If the coefficient is close to +1, it is covariation.
• Correlation equal to zero: If the correlation is zero, it means that it is not possible to determine some covariation. However, this does not mean that there is no nonlinear relationship between the variables. If the variables are independent, it means that they are correlated, but that does not mean that the result is true.

Advantages and disadvantages of the Pearson correlation coefficient

Key benefits of Karl Pearson's correlation coefficient include:

• The value is independent of the unit used to measure the variable.
• When the sample is large, the accuracy of the estimate is more likely.

Some of the disadvantages of correlation coefficient are:

• The two variables must be measured at a continuous quantitative level.
• The distribution of the variable must be similar to the normal curve.

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KEYWORDS OF THIS BLOG POST

Pearson correlation coefficient | Correlation coefficient  | Pearson