η²p for ANOVA repeated measures

[jorgesinval]

I am puzzled on how etasquared() is working with car objects for repeated designs:

ds <- data.frame(matrix(data = c(
      116,76,85,50,
      96,93,63,87,
      120,112,89,100,
      110,113,60,60,
      116,75,115,79,
      126,120,101,70,
      86,90,129,65,
      80,105,67,65),
    nrow = 8,
    ncol = 4,
    byrow = T
  ), id = 1:8)
names(ds) <- c("I","II","III","IV","id")

library(car)
#> Loading required package: carData
fit   <- lm(cbind(I,II,III,IV) ~ 1, data=ds)
in_rep    <- data.frame(ind_var=gl(4, 1))
Anova(fit, idata=in_rep, idesign=~ind_var) |> 
effectsize::eta_squared()
#> Note: model has only an intercept; equivalent type-III tests substituted.
#> # Effect Size for ANOVA (Type III)
#> 
#> Parameter | Eta2 (partial) |       95% CI
#> -----------------------------------------
#> ind_var   |           0.78 | [0.04, 1.00]
#> 
#> - One-sided CIs: upper bound fixed at (1).


ds_long <- rstatix::gather(ds,
                             "I", "II", "III", "IV",
                             key = ind_var, value = score)


afex::aov_ez(id = 'id',
       dv = 'score',
       fun_aggregate = mean,
       data = ds_long,
       within = 'ind_var',
       include_aov = T,
       type = "III") |> effectsize::eta_squared()
#> Warning in summary.Anova.mlm(model$Anova): HF eps > 1 treated as 1
#> # Effect Size for ANOVA (Type III)
#> 
#> Parameter | Eta2 (partial) |       95% CI
#> -----------------------------------------
#> ind_var   |           0.41 | [0.09, 1.00]
#> 
#> - One-sided CIs: upper bound fixed at (1).

^{Created on 2022-01-14 by the reprex package (v2.0.1)}

The same data, the same analysis, the same SS... but totally different results. I made it by hand and the second approach (ez object) is correct.

PS: I am aware that the Generalized η² might be more adequate to repeated measures designs. With the first approach is not possible to produce it using generalized =T but with the second one, yes.

[mattansb]

Originally, I couldn't figure out how to get the raw SS out of an Anova.mlm object, so instead I used the F-to-eta approximation (via F_to_eta2()) which gives only approx results.

But I see that I already solved this elsewhere but just didn't export the function... So now I've taken care of that (:

ds <- data.frame(I = c(116, 96, 120, 110, 116, 126, 86, 80),
                 II = c(76, 93, 112, 113, 75, 120, 90, 105), 
                 III = c(85, 63, 89, 60, 115, 101, 129, 67),
                 IV = c(50, 87, 100, 60, 79, 70, 65, 65),
                 id = 1:8)

ds_long <- data.frame(
  id = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
         1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
         1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 
         1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L),
  ind_var = c("I", "I", "I", "I", "I", "I", "I", "I", 
              "II", "II", "II", "II", "II", "II", "II", "II", 
              "III", "III", "III", "III", "III", "III", "III", "III", 
              "IV", "IV", "IV", "IV", "IV", "IV", "IV", "IV"),
  score = c(116, 96, 120, 110, 116, 126, 86, 80,
            76, 93, 112, 113, 75, 120, 90, 105, 
            85, 63, 89, 60, 115, 101, 129, 67,
            50, 87, 100, 60, 79, 70, 65, 65)
)


# Car -----
fit <- lm(cbind(I, II, III, IV) ~ 1, data = ds)
in_rep <- data.frame(ind_var = gl(4, 1))
car::Anova(fit, idata = in_rep, idesign =  ~ ind_var) |> 
  effectsize::eta_squared(ci = NULL)
#> Note: model has only an intercept; equivalent type-III tests substituted.
#> Warning in summary.Anova.mlm(model): HF eps > 1 treated as 1
#> # Effect Size for ANOVA (Type III)
#> 
#> Parameter | Eta2 (partial)
#> --------------------------
#> ind_var   |           0.41


afex::aov_ez(id = 'id',
             dv = 'score',
             data = ds_long,
             within = 'ind_var',
             anova_table = list(es = "pes"))
#> Anova Table (Type 3 tests)
#> 
#> Response: score
#>    Effect          df    MSE      F  pes p.value
#> 1 ind_var 2.22, 15.52 481.55 4.86 * .410    .021
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
#> 
#> Sphericity correction method: GG

^{Created on 2022-01-14 by the reprex package (v2.0.1)}

[jorgesinval]

Excellent! When will you upload that change to the package?

[mattansb]

Already on the main branch of Github