Regression Effect Size Calculator Beta and N

Regression effect size measures the strength of the relationship between a predictor variable and an outcome variable in a regression model. This calculator helps you compute effect size using beta coefficients and sample size (n).

What is Regression Effect Size?

In regression analysis, effect size quantifies the magnitude of the relationship between independent and dependent variables. Unlike p-values, which only indicate statistical significance, effect size provides practical significance information.

Common effect size measures in regression include:

Beta coefficients (standardized regression coefficients)
R-squared (coefficient of determination)
Adjusted R-squared
F-statistic

This calculator focuses on beta coefficients, which are standardized to make them comparable across different studies.

How to Calculate Effect Size in Regression

The Formula

Effect Size (ES) = β / √(1 - R²)

Where:

β = Beta coefficient from regression
R² = Coefficient of determination (R-squared)

This formula standardizes the beta coefficient to account for the variance explained by other predictors in the model.

Alternative Formula

Effect Size (ES) = β * √(n - k - 1)

Where:

n = Sample size
k = Number of predictors

This alternative formula adjusts for sample size and number of predictors.

Note: The first formula is more commonly used when R² is available. The second formula is useful when you only have the beta coefficient and sample size.

Interpreting the Results

Effect size values are interpreted as follows:

Effect Size	Interpretation
0.00 to 0.19	Negligible effect
0.20 to 0.49	Small effect
0.50 to 0.79	Medium effect
0.80 to 1.00	Large effect

These guidelines are based on Cohen's (1988) conventions for interpreting effect sizes in social sciences. The actual interpretation may vary depending on the field of study.

Worked Example

Example Calculation

Suppose you have a regression model with:

Beta coefficient (β) = 0.6
Coefficient of determination (R²) = 0.49

Using the first formula:

ES = 0.6 / √(1 - 0.49) = 0.6 / √0.51 ≈ 0.6 / 0.714 ≈ 0.84

This indicates a large effect size (0.84).

Frequently Asked Questions

What is the difference between beta and effect size?: Beta coefficients are raw regression coefficients that may be difficult to interpret directly. Effect size standardizes these coefficients to provide a more meaningful measure of the relationship strength.
Can I use this calculator for multiple regression?: Yes, this calculator works for both simple and multiple regression models. Just ensure you use the appropriate beta coefficient from your regression output.
What if I don't have R-squared?: If you don't have R-squared, you can use the alternative formula that requires sample size and number of predictors instead.
How do I interpret negative effect sizes?: Negative effect sizes indicate an inverse relationship between the predictor and outcome variables. The magnitude still follows the same interpretation guidelines.