11.4: Simulación de ANOVA de un factor

A continuación se construyen datos simulados para un ANOVA de un factor, apropiado para un diseño entre sujetos. Construimos el marco de datos con una columna para los niveles de factor de grupo y una columna para el DV. Entonces, ejecutamos el ANOVA y lo imprimimos.

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library(xtable)
N <- 10
groups <- rep(c("A","B","C"), each=10)
DV <- c(rnorm(100,10,15),   # means for group A
        rnorm(100,10,15),   # means for group B
        rnorm(100,20,15)    # means for group C
        )
sim_df<-data.frame(groups,DV)
aov_results <- summary(aov(DV~groups, sim_df))
knitr::kable(xtable(aov_results))

library(xtable)
N <- 10
groups <- rep(c("A","B","C"), each=10)
DV <- c(rnorm(100,10,15),   # means for group A
        rnorm(100,10,15),   # means for group B
        rnorm(100,20,15)    # means for group C
        )
sim_df<-data.frame(groups,DV)
aov_results <- summary(aov(DV~groups, sim_df))
knitr::kable(xtable(aov_results))

	Df	Suma Sq	Cuadrados medios	Valor F	Pr (>F)
grupos	2	1187.127	593.5635	2.683555	F)" style="vertical-align:middle;">0.0699765
Residuales	297	65692.093	221.1855	NA	F)" style="vertical-align:middle;">NA

En este siguiente ejemplo, simulamos el mismo diseño 100 veces, guardamos$p$ los valores -y determinamos la proporción de simulaciones significativas.

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N <- 10
save_p<-length(100)
for(i in 1:100){
  groups <- rep(c("A","B","C"), each=10)
  DV <- c(rnorm(100,10,15),   # means for group A
          rnorm(100,10,15),   # means for group B
          rnorm(100,20,15)    # means for group C
          )
  sim_df<-data.frame(groups,DV)
  
  aov_results <- summary(aov(DV~groups, sim_df))
  save_p[i]<-aov_results[[1]]$`Pr(>F)`[1]
}
length(save_p[save_p<0.05])/100

N <- 10
save_p<-length(100)
for(i in 1:100){
  groups <- rep(c("A","B","C"), each=10)
  DV <- c(rnorm(100,10,15),   # means for group A
          rnorm(100,10,15),   # means for group B
          rnorm(100,20,15)    # means for group C
          )
  sim_df<-data.frame(groups,DV)
  
  aov_results <- summary(aov(DV~groups, sim_df))
  save_p[i]<-aov_results[[1]]$`Pr(>F)`[1]
}
length(save_p[save_p<0.05])/100

0.07