Pearson’s Correlation Coefficient Formula
Karl Pearson’s correlation coefficient formula is the most commonly used and the most popular formula to get the statistical correlation coefficient. It is denoted with the lowercase “r”. The formula for Pearson’s correlation coefficient is shown below:
r = n(∑xy) – (∑x)(∑y) / √[n∑x²-(∑x)²][n∑y²-(∑y)²
The full name for Pearson’s correlation coefficient formula is Pearson’s Product Moment correlation (PPMC). It helps in displaying the Linear relationship between the two sets of the data.
Pearson’s correlation helps in measuring the correlation strength (it’s given by coefficient r-value between -1 and +1) and the existence (given by p-value ) of a linear correlation relationship between the two variables and if the outcome is significant we conclude that the correlation exists.
Cohen (1988) says that an absolute value of r of 0.5 is classified as large, an absolute value of 0.3 is classified as medium and an absolute value of 0.1 is classified as small.
The interpretation of the Pearson’s correlation coefficient is as follows:
- A correlation coefficient of 1 means there is a positive increase of a fixed proportion of others, for every positive increase in one variable. Like, the size of the shoe goes up in perfect correlation with foot length.
- If the correlation coefficient is 0, it indicates that there is no relationship between the variables.
- A correlation coefficient of -1 means there is a negative decrease of a fixed proportion, for every positive increase in one variable. Like, the amount of water in a tank will decrease in a perfect correlation with the flow of a water tap.
The Pearson correlation coefficient essentially captures how closely the data points tend to follow a straight line when plotted together. It’s important to remember that correlation doesn’t imply causation – just because two variables are related, it doesn’t mean one causes the change in the other.
Pearson Correlation Coefficient
Pearson Correlation Coefficient: Correlation coefficients are used to measure how strong a relationship is between two variables. There are different types of formulas to get a correlation coefficient, one of the most popular is Pearson’s correlation (also known as Pearson’s r) which is commonly used for linear regression.
The Pearson correlation coefficient, often symbolized as (r), is a widely used metric for assessing linear relationships between two variables. It yields a value ranging from –1 to 1, indicating both the magnitude and direction of the correlation. A change in one variable is mirrored by a corresponding change in the other variable in the same direction.
This article provides detailed information on the Pearson Correlation Coefficient, its meaning, formula, interpretation, examples, and FAQs.
Table of Content
- What is the Pearson Correlation Coefficient?
- Pearson’s Correlation Coefficient Formula
- Pearson Correlation Coefficient Table
- Pearson Correlation Coefficient Origin
- Types of Pearson Correlation Coefficient
- Adjusted Correlation Coefficient
- Weighted Correlation Coefficient
- Reflective Correlation Coefficient
- Scaled Correlation Coefficient
- Pearson’s Distance
- Circular Correlation Coefficient
- Partial Correlation
- Pearson Correlation Coefficient Interpretation
- Finding the Correlation Coefficient with Pearson Correlation Coefficient Formula
- Assumptions of Pearson Correlation Coefficient
- Correlation Coefficient Properties
- Pearson Correlation Coefficient Interpretation
- Bivariate Correlation
- Correlation Matrix
- Pearson Correlation Coefficient Examples
- Pearson Correlation Coefficient Practice Problems