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# Effect size (contingency table)

An effect size estimates the magnitude of the difference of proportions or the association between two categorical variables.

The effect size that best describes a 2 x 2 contingency table depends on the study design that produced the data:

- When both variables are random variables, the odds ratio provides the best measure of association between the variables.
- When one variable is an explanatory variable (a fixed variable) and the other a response variable (a random variable), the effect size between the two groups of the response variable can be expressed as the odds ratio, the difference between proportions, or ratio of proportions.
- When the variables are matched-pairs or repeated measurements, the odds ratio or the difference between proportions are appropriate. The ratio of proportions is meaningless in this scenario.

A point estimate is a single value that is the best estimate of the true unknown parameter; a confidence interval is a range of values and indicates the uncertainty of the estimate.

For tables larger than 2 x 2, you must partition the contingency table into a series of 2 x 2 sub-tables to estimate the effect size.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Contingency table
- Creating a contingency table
- Creating a contingency table (related data)
- Grouped frequency plot
- Effect size
- Estimators
- Estimating the odds ratio
- Estimating the odds ratio (related data)
- Relative risk
- Inferences about equality of proportions
- Inferences about independence
- Mosaic plot
- Creating a mosaic plot
- Study design
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.40

Published 29-Jul-2019