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🎲intro to statistics review

Pearson Correlation

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Pearson correlation is a statistical measure that quantifies the linear relationship between two variables. It determines the strength and direction of the association between these variables, providing insights into how changes in one variable are related to changes in another.

5 Must Know Facts For Your Next Test

  1. The Pearson correlation coefficient (r) ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and 1 indicating a perfect positive linear relationship.
  2. The strength of the linear relationship is determined by the magnitude of the correlation coefficient, with values closer to 1 or -1 indicating a stronger relationship.
  3. Pearson correlation is sensitive to outliers, which can significantly influence the value of the correlation coefficient.
  4. The statistical significance of the Pearson correlation coefficient is determined by the p-value, which represents the probability of obtaining the observed correlation coefficient (or a more extreme value) if the null hypothesis of no linear relationship is true.
  5. Hypothesis testing is used to determine whether the observed Pearson correlation coefficient is statistically significant, meaning the relationship between the variables is unlikely to have occurred by chance alone.

Review Questions

  • Explain the interpretation of the Pearson correlation coefficient and its range of values.
    • The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. The coefficient can range from -1 to 1, with -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and 1 indicating a perfect positive linear relationship. The magnitude of the coefficient, regardless of its sign, represents the strength of the linear relationship, with values closer to 1 or -1 indicating a stronger relationship.
  • Describe the role of hypothesis testing in the context of Pearson correlation.
    • Hypothesis testing is used to determine the statistical significance of the observed Pearson correlation coefficient. The null hypothesis typically states that there is no linear relationship between the two variables (i.e., the true correlation coefficient is zero). The p-value is then calculated to assess the probability of obtaining the observed correlation coefficient (or a more extreme value) if the null hypothesis is true. If the p-value is less than the chosen significance level (e.g., 0.05), the null hypothesis is rejected, and the researcher can conclude that the observed correlation is statistically significant, meaning the relationship between the variables is unlikely to have occurred by chance alone.
  • Analyze the potential impact of outliers on the Pearson correlation coefficient and its interpretation.
    • Pearson correlation is sensitive to outliers, which are data points that are significantly different from the rest of the data. Outliers can have a disproportionate influence on the value of the correlation coefficient, potentially leading to a misrepresentation of the true linear relationship between the variables. If outliers are present, it is important to carefully examine the data and consider their impact on the Pearson correlation. Depending on the research question and the context, outliers may need to be addressed or removed to obtain a more accurate assessment of the linear relationship between the variables.