Correlation Matrix

What is the Pearson Correlation Coefficient?

The Pearson Correlation Coefficient, denoted as r, is a statistical measure that calculates the strength and direction of the linear relationship between two variables on a scatterplot. The value of r ranges between -1 and 1, where:...

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:...

Pearson Correlation Coefficient Table

Pearson Correlation Coefficient (r) Range Type of Correlation Description of Relationship New Illustrative Example 0 < r ≤ 1 Positive An increase in one variable associates with an increase in the other. Study Time vs. Test Scores: More hours spent studying tends to lead to higher test scores. r = 0 None No discernible relationship between the changes in both variables. Shoe Size vs. Reading Skill: A person’s shoe size doesn’t predict their ability to read. -1 ≤ r < 0 Negative An increase in one variable associates with a decrease in the other. Outdoor Temperature vs. Home Heating Cost: As the outdoor temperature decreases, heating costs in the home increase....

Pearson Correlation Coefficient Origin

The Pearson correlation coefficient, although named after statistician Karl Pearson, has a more interesting backstory. The concept of correlation itself can be traced back to Francis Galton, a 19th-century scientist and explorer. Galton was fascinated by inheritance and explored relationships between traits in families....

Types of Pearson Correlation Coefficient

Each type of Pearson correlation coefficient offers unique insights and analytical tools for various research fields, from statistics and psychology to economics and engineering. Understanding these variations enhances the accuracy and depth of correlation analyses, enabling more informed decision-making and hypothesis testing....

Pearson Correlation Coefficient Interpretation

Pearson correlation coefficient (r) value Strength Direction Greater than .5 Strong Positive Between .3 and .5 Moderate Positive Between 0 and .3 Weak Positive 0 None None Between 0 and –.3 Weak Negative Between –.3 and –.5 Moderate Negative Less than –.5 Strong Negative...

Finding the Correlation Coefficient with Pearson Correlation Coefficient Formula

Steps to find the correlation coefficient with Pearson’s correlation coefficient formula:...

Assumptions of Pearson Correlation Coefficient

Linear Relationship: Karl Pearson’s correlation coefficient assumes a linear relationship between the two variables under consideration. It implies that as one variable changes, the other changes proportionally. Normality: The variables should follow a normal distribution. While Pearson’s correlation coefficient is robust to deviations from normality, extreme departures may affect the validity of the correlation analysis. Homoscedasticity: This assumption suggests that the variability in one variable should be consistent across all levels of the other variable. In other words, the spread of data points around the regression line should remain constant. Interval or Ratio Scale: Pearson’s correlation coefficient is appropriate for variables measured on an interval or ratio scale. These scales ensure meaningful numerical distances between observations. Independence: The observations used to compute the correlation coefficient should be independent of each other. Independence ensures that each data point contributes uniquely to the analysis without being influenced by other observations....

Correlation Coefficient Properties

Correlation Coefficient Range: The correlation coefficient r ranges from -1 to +1, inclusive. A value of -1 indicates a perfect negative linear relationship, +1 denotes a perfect positive linear relationship, and 0 represents no linear relationship. Directionality: The sign of the correlation coefficient indicates the direction of the relationship between variables. A positive r indicates a positive association (both variables increase or decrease together), while a negative r suggests a negative association (one variable increases as the other decreases). Magnitude: The magnitude of the correlation coefficient represents the strength of the relationship between variables. Values closer to -1 or +1 indicate a stronger linear relationship, while values closer to 0 suggest a weaker relationship. No Causation: Pearson’s correlation coefficient does not imply causation between variables. It only measures the degree of linear association and does not establish a cause-and-effect relationship. Symmetry: The correlation coefficient is symmetric, meaning the correlation between variables X and Y is the same as the correlation between Y and X. Invariance: The correlation coefficient remains unchanged under linear transformations of the variables (e.g., multiplication by a constant or addition of a constant), making it invariant to changes in scale and location....

Pearson Correlation Coefficient Interpretation

Interpreting the Pearson correlation coefficient (r) involves assessing the correlation strength, direction, and correlation significance of the relationship between two variables. Here’s a guide to interpreting r:...

Bivariate Correlation

Pearson’s correlation coefficient is a statistical tool used to measure bivariate correlation. This refers to the strength and direction of the linear relationship between two variables. It assesses how much one variable tends to change along with the other....

Correlation Matrix

The Pearson correlation coefficient is particularly useful when analyzing datasets with multiple variables. In such cases, a correlation matrix can be constructed. This is a square table that summarizes the correlation coefficients between all possible pairs of variables within the data set....

Pearson Correlation Coefficient Examples

Example 1: There is some correlation coefficient that was given to tell whether the variables are positive or negative?...

Pearson Correlation Coefficient Practice Problems

1. Given a Pearson correlation coefficient of r = 0.85 between the amount of time students spent studying and their score on a math test, interpret the strength and direction of the relationship....

Conclusion of Pearson Correlation Coefficient

The Pearson Correlation Coefficient (r) is a statistical measure of the strength and direction of a linear relationship between two variables on a scatterplot. It ranges from -1 to 1, with 1 indicating a perfect positive relationship, -1 indicating a perfect negative relationship, and 0 indicating no linear relationship. The formula involves summing products of paired scores and dividing by the square root of the product of the sums of squared scores. While r quantifies the degree of linear association, it doesn’t imply causation. Developed by Francis Galton, Auguste Bravais, and Karl Pearson, it’s foundational in fields like psychology and economics, aiding in the analysis of linear relationships under certain assumptions about the data....

Pearson Correlation Coefficient – FAQs

What is Karl Pearson’s coefficient of correlation?...