Clase 3

Error estandar de la media

\[\LARGE{SEM=\frac{s}{\sqrt{n}}}\]

Desviación estandar de la muestra

set.seed(2023)
pH<-runif(100,4,6)

mean(pH)

## [1] 5.063379

sd(pH)

## [1] 0.5487565

se = sd(pH)/sqrt(100)
se

## [1] 0.05487565

sim1 = replicate(10000,runif(100,4,6))
#Función dim: Devuelve las dimensiones de una matriz
#dim(sim1)
mean_sim1=colMeans(sim1)
hist(mean_sim1)

#Error estandar tomado a partir de la variación de las 10000 muestras. 
sd(mean_sim1)

## [1] 0.05836866

ee = function(n){
  if(n>2){
  simf=replicate(1000,runif(n,4,6))
  e=sd(colMeans(simf)) #Hint: apply
  #Cacular error estandar de la mediana
  formula=sd(simf[,1])/sqrt(length(simf[,1]))
  return(list(e=e,formula=formula))
  }else{
    print("n<=2")
  }
 
}

y_1=c() #Simulacion
y_2=c() #Formula 
n_i=c() #N 
for(i in seq(3,1000,1)){
  y_e=ee(i)$e
  y_1=c(y_1,y_e)
  
  y_f=ee(i)$formula
  y_2=c(y_2,y_f)
  n_i=c(n_i,i)
}


library(ggplot2)
df=data.frame(y_1,y_2,n_i)

  ggplot(data=df,aes(x=y_1,y=y_2,col=n_i))+
  geom_point(size=3)+
  coord_equal()+
  geom_abline(slope=1)+
    labs(x="Simulado",y="Formula")

set.seed(2023)
ran = runif(100,4,6)
mediana = median(ran)
sem = sd(ran)/sqrt(length(ran))

sem

## [1] 0.05487565

sim2 <- replicate(1000,runif(100,4,6))
median_sim2<- colMedians(sim2)
hist(median_sim2)

## Error estandar de la mediana tomado a partir de la variación de las 1000 muestras.

sd(median_sim2)

## [1] 0.09966424

eem = function(n){
  if(n>2){
  simf=replicate(1000,runif(n,4,6))
  e=sd(colMedians(simf))
  #Calcular error estandar de la mediana
  formula=sd(simf[,1])/sqrt(length(simf[,1]))
  return(list(e=e,formula=formula))
  }else{
    print("n<=2")
  }
 
}

y_1=c() #Simulacion
y_2=c() #Formula 
n_i=c() #N 
for(i in seq(3,1000,1)){
  y_e=eem(i)$e
  y_1=c(y_1,y_e)
  
  y_f=eem(i)$formula
  y_2=c(y_2,y_f)
  n_i=c(n_i,i)
}

library(ggplot2)
df=data.frame(y_1,y_2,n_i)

  ggplot(data=df,aes(x=y_1,y=y_2,col=n_i))+
  geom_point(size=3)+
  coord_equal()+
  geom_abline(slope=mediana*0.1)+
    labs(x="Simulado",y="Formula")