The Eta Squared Calculator determines the proportion of variance in a dependent variable that is explained by an independent variable in the context of an ANOVA (Analysis of Variance) test. This value, known as eta squared (η²), is a measure of effect size and is widely used in social sciences, psychology, education, and behavioral research to understand the strength of relationships between variables.
By calculating η², researchers can quantify how much of the total variability in the data is associated with the factor being studied. It provides more interpretive power than significance testing alone, offering a practical understanding of the impact size of treatments, interventions, or group differences.
formula of Eta Squared Calculator
Primary Eta Squared Formula:
η² = SS_effect / SS_total
Where:
η² = eta squared (effect size)
SS_effect = sum of squares for the treatment or effect
SS_total = total sum of squares (explained + unexplained)
This formula calculates the proportion of total variance explained by the treatment.
Using ANOVA Output:
η² = SS_effect / (SS_effect + SS_error)
or
η² = (F × df_effect) / (F × df_effect + df_error)
Where:
F = F-ratio from ANOVA test
df_effect = degrees of freedom for the effect
df_error = degrees of freedom for the error (residual)
These alternative formulas are helpful when only ANOVA output is available, such as from statistical software.
Helpful Reference Table
This table helps interpret η² values and categorize effect sizes based on common thresholds in behavioral sciences.
| η² Value | Effect Size Interpretation |
|---|---|
| 0.01 | Small effect |
| 0.06 | Medium effect |
| 0.14 | Large effect |
| 0.30+ | Very large effect |
These benchmarks are commonly accept and assist researchers in communicating their findings clearly and meaningfully.
Example of Eta Squared Calculator
A researcher runs an ANOVA to test the effectiveness of three teaching methods on test performance. From the analysis, they find:
- SS_effect = 120
- SS_error = 280
- SS_total = SS_effect + SS_error = 400
Step 1: Apply the formula
η² = SS_effect / SS_total = 120 / 400 = 0.30
Step 2: Interpret the result
An η² value of 0.30 indicates a very large effect, meaning the teaching method explains 30% of the variance in test scores.
Alternatively, using the F formula:
- F = 6.0
- df_effect = 2
- df_error = 27
η² = (6.0 × 2) / (6.0 × 2 + 27) = 12 / (12 + 27) = 12 / 39 ≈ 0.31
This confirms the large effect size using another method.
Most Common FAQs
Eta squared is use to measure the effect size in ANOVA results. It tells you how much of the variability in the outcome is due to the factor or treatment being studied.
They are similar in that both represent the proportion of explained variance, but R-square is typically use in regression, while eta squared is used in ANOVA. Their interpretations are comparable.