Measures Of Association
- Quantify how strongly and in what direction two variables are related.
- Apply different measures depending on data type (e.g., Pearson for continuous, chi-square for categorical).
- Inform hypothesis testing, decision making, and prediction based on observed relationships.
Definition
Section titled “Definition”Measures of association are statistical tools used to measure the strength and direction of a relationship between two variables.
Explanation
Section titled “Explanation”Measures of association provide a quantitative assessment of how two variables relate. Different measures target different kinds of relationships and data types. For example, the Pearson correlation coefficient assesses the linear relationship between two continuous variables and ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. The chi-square test assesses the relationship between two categorical variables by comparing observed frequencies to expected frequencies under the assumption of independence; a significant chi-square value indicates a relationship, while a non-significant value indicates no relationship.
Examples
Section titled “Examples”Pearson correlation coefficient (continuous variables)
Section titled “Pearson correlation coefficient (continuous variables)”The Pearson correlation coefficient measures the linear relationship between two continuous variables. It can range from -1 to 1, with:
- 1 indicating a perfect positive linear relationship,
- -1 indicating a perfect negative linear relationship,
- 0 indicating no linear relationship.
Example: A study examining the relationship between age and blood pressure might find a Pearson correlation coefficient of 0.6, indicating a moderately strong positive linear relationship between these two variables.
Chi-square test (categorical variables)
Section titled “Chi-square test (categorical variables)”The chi-square test measures the relationship between two categorical variables by calculating how observed frequencies deviate from expected frequencies under independence. A significant chi-square value indicates a relationship between the variables; a non-significant value indicates no relationship.
Example: A study examining the relationship between gender and political party affiliation might find a significant chi-square value, indicating a relationship between these two variables.
Use cases
Section titled “Use cases”- Hypothesis testing
- Making decisions and predictions based on observed relationships
- Understanding underlying mechanisms and causes of a relationship
- Providing insights for further research and analysis
Notes or pitfalls
Section titled “Notes or pitfalls”- The Pearson correlation coefficient measures linear relationships specifically; a value of 0 indicates no linear relationship but does not rule out non-linear relationships.
- For the chi-square test, a significant chi-square value indicates a relationship between the categorical variables, while a non-significant value indicates no relationship.
Related terms
Section titled “Related terms”- Pearson correlation coefficient
- Chi-square test