Archives

Pearson Correlation Analysis

 Pearson Correlation Analysis


Pearson correlation analysis is a statistical method used to quantify the strength and direction of the linear relationship between two continuous variables. It assesses how much one variable changes when the other variable changes and provides a measure of the extent to which the variables are associated.


When to Use Pearson Correlation Analysis:

Pearson correlation analysis is appropriate when:

There is an interest in examining the linear relationship between two continuous variables.

The relationship between the variables is expected to be linear.

The variables are measured on an interval or ratio scale.


Assumptions and Data Requirements:


Before conducting Pearson correlation analysis, several assumptions must be met:


Linearity: The relationship between the variables should be linear.

Normality: The variables should be approximately normally distributed.

Homoscedasticity: The variances of the variables should be approximately equal across different levels.

Additionally, the data required for Pearson correlation analysis should consist of continuous variables obtained from a random sample.


Interpreting Pearson's r:

Pearson's correlation coefficient (r) ranges from -1 to 1.

A correlation coefficient of 1 indicates a perfect positive linear relationship, while a correlation coefficient of -1 indicates a perfect negative linear relationship.

A correlation coefficient of 0 indicates no linear relationship between the variables.

The closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables. Conversely, values closer to 0 indicate a weaker linear relationship.


Sample Situation with Sample Data:

Suppose a researcher wants to examine the relationship between the number of hours students spend studying per week and their exam scores. The researcher collects data on study hours and exam scores for a sample of students.


In this scenario, Pearson correlation analysis can be conducted to determine the strength and direction of the linear relationship between study hours and exam scores.

Reporting the Results in a Research Paper:


The results of Pearson correlation analysis are typically reported with the following information:

The correlation coefficient (r) indicating the strength and direction of the linear relationship.
The significance level (p-value) indicating whether the correlation is statistically significant.
A brief interpretation of the findings in the context of the research question.

NOTE:

Other types of Correlation:

1. Spearman Correlation: Spearman's rank correlation coefficient (ρ) assesses the strength and direction of the monotonic relationship between two variables. It does not assume linearity and is based on the ranks of the data rather than the actual values.

2. Kendall Correlation: Kendall's tau (τ) is a non-parametric measure of correlation that assesses the ordinal association between two variables. It is suitable for data measured on an ordinal scale or when there are ties in the data.

For example:


"A Pearson correlation analysis was conducted to examine the relationship between students' study hours and their exam scores. The results revealed a significant positive correlation between study hours and exam scores (r = 0.65, p < 0.01), indicating that students who spent more time studying tended to achieve higher exam scores."

Tutorial Using JAMOVI: