Potencia

library(goft)

## Loading required package: fitdistrplus

## Loading required package: MASS

## Loading required package: survival

## Loading required package: sn

## Loading required package: stats4

## 
## Attaching package: 'sn'

## The following object is masked from 'package:stats':
## 
##     sd

library(mvnormtest)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:MASS':
## 
##     select

## The following object is masked from 'package:stats':
## 
##     filter

set.seed(1709)
DE<- sort.int(rnorm(30,5,0.8),partial = 10)+rnorm(30,0.1,0.05)
sim_2 = replicate(500,sort.int(rnorm(30,4,0.7),partial = 5))
data_sim = data.frame(DE,sim_2)
p_shapiro=c()
for(i in 2:c(dim(data_sim)[2]-1)){
  p_shapiro[i]=mshapiro_test(data_sim[,c(1,i)])$p.value
}
hist(p_shapiro)

potencia_shapiro=100*table(p_shapiro<0.05)/500

library(MVN)
p_mardia_sk_1=c()#skewness
for(i in 2:c(dim(data_sim)[2]-1)){
  p_mardia_sk_1[i]= as.numeric(as.character(mvn(data_sim[,c(1,i)],mvnTest = "mardia")$multivariateNormality[1,3]))
}

p_mardia_ku=c()#kurtosis
for(i in 2:c(dim(data_sim)[2]-1)){
  p_mardia_ku[i]=as.numeric(as.character(mvn(data_sim[,c(1,i)],mvnTest = "mardia")$multivariateNormality[2,3]))
}

hist(p_mardia_sk_1)

hist(p_mardia_ku)

potencia_mardia=100*table(p_mardia_ku<0.05 & p_mardia_sk_1<0.05)/500

library(royston)
##     The Royston's H test has been moved to 'MVN' package. 'royston'
##     package will no longer be supported. Please use 'MVN' package for
##     further analysis.
p_royston = c()
for(i in 2:c(dim(data_sim)[2]-1)){

  p_royston[i]=royston.test(data_sim[,c(1,i)])$p.value
}

potencia_royston= 100*table(p_royston<0.05)/500

# Histogramas
hist(p_royston)

hist(p_mardia_ku)

hist(p_mardia_sk_1)

hist(p_shapiro)

potencia_mardia

## 
## FALSE  TRUE 
##  98.6   1.2

potencia_royston

## 
## FALSE  TRUE 
##  97.8   2.0

potencia_shapiro

## 
## FALSE  TRUE 
##  72.6  27.2

En este caso la prueba mas rigurosa es la prueba de mardia, ya que presento un mayor cantidad de valores por fuera del rango de valor de rechazo (0.05), seguida de la prueba de royston, y por ultimo, la mas flexible, la prueba de Shapiro

Normalidad

Potencia