R² Calculator from Cohen’s \( f^2 \) Effect Size

Given Cohen’s \( f^2 \) defined as $$ f^2=\frac{R^2}{1-R^2}, $$ the population \( R^2 \) is calculated as: $$ R^2=\frac{f^2}{1+f^2}. $$

* Enter Cohen’s \( f^2 \) (must be \( \ge 0 \)).

Step 1: Enter Cohen’s \( f^2 \)

e.g., 0.30

Formula: \( R^2=\frac{f^2}{1+f^2} \)

R² Calculator from Cohen's f² Effect Size - Educational Guide

R² Calculator from Cohen's f² Effect Size

Welcome to our R² Calculator from Cohen's f² Effect Size! This tool converts the observed Cohen’s f² effect size into the coefficient of determination (R²), which represents the proportion of variance explained by your regression model. It is an essential resource for understanding and interpreting the impact of predictors on your outcome variable.

Table of Contents

What is R²?

R², or the coefficient of determination, indicates the proportion of variance in the dependent variable that is explained by the predictors in a regression model. A higher R² value signifies a better model fit.

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What is Cohen's f²?

Cohen's f² is an effect size measure used in regression analysis to quantify the incremental impact of predictors. It is calculated from R² as a standardized metric.

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Conversion Formula

The conversion from Cohen's f² to R² is performed using the following formula:

$$R^2 = \frac{f^2}{1 + f^2}$$

Here, f² represents the effect size, and the formula provides the corresponding R² value.

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Key Concepts

  • R² (Coefficient of Determination): Measures the proportion of variance explained by the model.
  • Cohen's f²: A standardized effect size indicating the impact of predictors.
  • Conversion: The process of translating f² into R² using the formula above.
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Step-by-Step Calculation Process

  1. Obtain Cohen's f²:

    Compute or retrieve the observed Cohen's f² effect size from your regression analysis.

  2. Apply the Conversion Formula:

    Substitute the f² value into the formula to calculate R²:

    $$R^2 = \frac{f^2}{1 + f^2}$$

  3. Review the Result:

    The output gives the R² value corresponding to the observed effect size, indicating the proportion of variance explained by your model.

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Practical Examples

Example: Converting f² to R²

Scenario: Suppose your regression analysis yields an observed Cohen's f² of 0.20.

  1. Apply the Conversion Formula:

    $$R^2 = \frac{0.20}{1 + 0.20} = \frac{0.20}{1.20} \approx 0.167$$

  2. Interpretation:

    An R² value of approximately 0.167 indicates that about 16.7% of the variance in the dependent variable is explained by the model.

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Interpreting the Results

The R² Calculator from Cohen's f² Effect Size provides a straightforward conversion that helps you understand the explanatory power of your regression model. A higher R² indicates a stronger model fit, while the conversion from f² standardizes the effect size for easier interpretation.

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Applications

This calculator is useful in various fields, including:

  • Social Sciences: Evaluating the effectiveness of predictors in behavioral studies.
  • Economics: Assessing model fit in forecasting and regression analyses.
  • Health Sciences: Quantifying the explanatory power of clinical predictors.
  • Education Research: Determining the impact of educational interventions.
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Advantages

  • User-Friendly: Simple process for converting Cohen's f² to R².
  • Quick Computation: Provides rapid insights into your model's explanatory power.
  • Educational: Enhances understanding of effect sizes and variance explained.
  • Practical: Supports data-driven decision-making in regression model evaluation.
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Conclusion

Our R² Calculator from Cohen's f² Effect Size is an essential tool for researchers and analysts looking to quantify the proportion of variance explained in a regression model. By converting Cohen's f² into R², you gain a clear measure of your model's explanatory power, aiding in more informed statistical interpretation and decision-making. For further assistance or additional analytical resources, please explore our other calculators or contact our support team.

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