Effect Size for ANOVA

Compute eta-squared and partial eta-squared for all terms in an ANOVA model.

See the Datanovia tutorial One-Way ANOVA in R for a worked walkthrough.

eta_squared(model, ci = NULL)

partial_eta_squared(model, ci = NULL)

Arguments

model

an object of class aov or anova.

ci

confidence level for a confidence interval on the effect size. If a number between 0 and 1 (e.g. 0.95), the function returns a tibble with one row per model term and the columns Effect, effsize, conf.low and conf.high instead of the bare named vector. The interval is computed in base R by inverting the noncentral F distribution (Steiger, 2004), and matches effectsize::eta_squared(ci = , alternative = "two.sided") — partial = FALSE for eta_squared() and partial = TRUE for partial_eta_squared() — to about four decimals for the non-partial bounds of a small pseudo-F (that function's inversion uses a looser tolerance), and more closely everywhere else. Default is NULL (no interval; the bare named vector is returned, unchanged).

Value

a named numeric vector of effect sizes, one per model term; or, when ci is a confidence level, a tibble with the columns Effect, effsize, conf.low and conf.high.

Functions

• eta_squared(): compute eta squared

• partial_eta_squared(): compute partial eta squared.

References

Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182.

See also

The Datanovia tutorial: One-Way ANOVA in R.

Examples

# Data preparation
df <- ToothGrowth
df$dose <- as.factor(df$dose)

# Compute ANOVA
res.aov <- aov(len ~ supp*dose, data = df)
summary(res.aov)
#>             Df Sum Sq Mean Sq F value   Pr(>F)    
#> supp         1  205.4   205.4  15.572 0.000231 ***
#> dose         2 2426.4  1213.2  92.000  < 2e-16 ***
#> supp:dose    2  108.3    54.2   4.107 0.021860 *  
#> Residuals   54  712.1    13.2                     
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Effect size
eta_squared(res.aov)
#>       supp       dose  supp:dose 
#> 0.05948365 0.70286419 0.03137672 
partial_eta_squared(res.aov)
#>      supp      dose supp:dose 
#> 0.2238254 0.7731092 0.1320279 

# Effect size with confidence interval
eta_squared(res.aov, ci = 0.95)
#> # A tibble: 3 × 4
#>   Effect    effsize conf.low conf.high
#>   <chr>       <dbl>    <dbl>     <dbl>
#> 1 supp       0.0595    0         0.214
#> 2 dose       0.703     0.562     0.787
#> 3 supp:dose  0.0314    0         0.146
partial_eta_squared(res.aov, ci = 0.95)
#> # A tibble: 3 × 4
#>   Effect    effsize conf.low conf.high
#>   <chr>       <dbl>    <dbl>     <dbl>
#> 1 supp        0.224  0.0586      0.402
#> 2 dose        0.773  0.662       0.838
#> 3 supp:dose   0.132  0.00147     0.295