Effect Size (Cohen’s f²) Calculator

Calculate the effect size for hierarchical regression using: $$ f^2=\frac{R^2_{\text{full}}-R^2_{\text{base}}}{1-R^2_{\text{full}}}. $$

* Enter the baseline model \( R^2 \) and full model \( R^2 \). Note: \( R^2_{\text{full}}>R^2_{\text{base}} \).

Step 1: Enter Model Parameters

e.g., 0.20

e.g., 0.35 (should be greater than baseline \( R^2 \))

Formula: $$ f^2=\frac{R^2_{\text{full}}-R^2_{\text{base}}}{1-R^2_{\text{full}}}. $$

Effect Size (Cohen’s f²) Calculator for Hierarchical Multiple Regression - Educational Guide

Effect Size (Cohen’s f²) Calculator for Hierarchical Multiple Regression

Welcome to our Effect Size (Cohen’s f²) Calculator for Hierarchical Multiple Regression! This tool helps you compute the incremental effect size (Cohen’s f²) when additional predictors are added to a regression model. By quantifying the change in explained variance, you can assess the practical significance of new predictors.

Table of Contents

What is Cohen’s f²?

Cohen’s f² is a measure of effect size used in multiple regression to assess the impact of a set of predictors. In hierarchical regression, it quantifies the incremental variance explained by adding new predictors to an existing model.

  • Incremental R²: The change in the coefficient of determination when additional predictors are included.
  • Cohen’s f²: Calculated as the ratio of the incremental R² to the unexplained variance of the full model.
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Calculation Formula

The formula for Cohen’s f² in hierarchical multiple regression is:

$$f^2 = \frac{R^2_{full} - R^2_{reduced}}{1 - R^2_{full}}$$

Where:

  • \(R^2_{full}\): The coefficient of determination for the full model with all predictors.
  • \(R^2_{reduced}\): The coefficient of determination for the reduced model without the additional predictors.
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Key Concepts

  • Hierarchical Regression: A method where predictors are added in steps to evaluate their incremental contribution.
  • Coefficient of Determination (R²): The proportion of variance in the dependent variable explained by the predictors.
  • Incremental Variance: The additional variance explained by the new predictors.
  • Effect Size: A standardized measure indicating the magnitude of an effect, with Cohen’s f² categorizing small, medium, and large effects.
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Step-by-Step Calculation Process

  1. Gather Model Data:

    Obtain the \(R^2\) values for both the reduced model (without the additional predictors) and the full model (with the additional predictors).

  2. Compute Incremental R²:

    Calculate the difference: \( \Delta R^2 = R^2_{full} - R^2_{reduced} \).

  3. Apply the Formula:

    Substitute the values into the formula:

    $$f^2 = \frac{R^2_{full} - R^2_{reduced}}{1 - R^2_{full}}$$

  4. Interpret the Result:

    The computed \(f^2\) value indicates the effect size of the additional predictors. Conventionally, \(f^2\) values of 0.02, 0.15, and 0.35 represent small, medium, and large effects, respectively.

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Practical Examples

Example: Calculating Cohen’s f²

Scenario: A reduced model yields \(R^2_{reduced} = 0.40\), and the full model yields \(R^2_{full} = 0.55\).

  1. Calculate Incremental R²:

    \( \Delta R^2 = 0.55 - 0.40 = 0.15 \)

  2. Apply the Formula:

    $$f^2 = \frac{0.15}{1 - 0.55} = \frac{0.15}{0.45} \approx 0.33$$

  3. Interpretation:

    An \(f^2\) value of approximately 0.33 indicates a medium-to-large effect size, suggesting that the additional predictors have a substantial impact on the model.

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Interpreting the Results

The calculator outputs Cohen’s \(f^2\) value, which quantifies the incremental effect size of the added predictors. Use the following guidelines:

  • Small Effect: \(f^2 \approx 0.02\)
  • Medium Effect: \(f^2 \approx 0.15\)
  • Large Effect: \(f^2 \approx 0.35\) or greater
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Applications

This calculator is particularly useful for:

  • Hierarchical Regression: Assessing the impact of adding new predictors.
  • Social Sciences & Psychology: Evaluating incremental predictive validity.
  • Economics & Business: Measuring the effect size of additional variables in forecasting models.
  • Educational Research: Quantifying the influence of new factors in academic performance models.
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Advantages

  • User-Friendly: Intuitive interface for entering \(R^2\) values.
  • Quick Computation: Instantly calculates Cohen’s \(f^2\) to help you assess effect size.
  • Educational: Enhances understanding of incremental effect sizes in regression analysis.
  • Practical: Supports data-driven decision-making in model building and evaluation.
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Conclusion

Our Effect Size (Cohen’s f²) Calculator for Hierarchical Multiple Regression is an essential tool for evaluating the incremental impact of additional predictors in your regression model. By computing Cohen’s \(f^2\), you gain valuable insights into the practical significance of new variables, helping you build more robust and interpretable models. For further assistance or additional analytical resources, please explore our other calculators or contact our support team.

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