Taller 2

Taller 2: Intervalos de confianza con R

Plantilla de todo el trabajo:

Datos: Definición formal de las muestras, variables, tamaños muestrales y niveles de confianza

Ejemplo de funciones (Para no olvidar)

# ============================================================
# 1. Intervalo Z para una media con sigma conocida
# ============================================================

ic_media_z <- function(media, sigma, n, conf = 0.95,
                       digitos = 4) {
  
  alpha <- 1 - conf
  z <- qnorm(1 - alpha / 2)
  error_estandar <- sigma / sqrt(n)
  margen_error <- z * error_estandar
  
  inferior <- media - margen_error
  superior <- media + margen_error
  
  resultado <- data.frame(
    Medida = c(
      "Media",
      "\u03c3",
      "Error estándar",
      "n",
      "Grado de confianza",
      "Valor crítico",
      "Margen de error",
      "Extremo inferior",
      "Extremo superior",
      "Intervalo"
    ),
    
    Resultado = c(
      round(media, digitos),
      round(sigma, digitos),
      round(error_estandar, digitos),
      n,
      round(conf, digitos),
      round(z, digitos),
      round(margen_error, digitos),
      round(inferior, digitos),
      round(superior, digitos),
      paste0(
        round(media, digitos),
        " ± ",
        round(margen_error, digitos)
      )
    ),
    
    check.names = FALSE
  )
  
  knitr::kable(
    resultado,
    format = "html",
    col.names = c("Medida", "Valor"),
    align = c("l", "r")
  )
}

# ============================================================
# 2. Intervalo t para una media con sigma desconocida
# ============================================================

ic_media_t <- function(media, s, n, conf = 0.95,
                       digitos = 4) {
  
  alpha <- 1 - conf
  gl <- n - 1
  t_critico <- qt(1 - alpha / 2, df = gl)
  error_estandar <- s / sqrt(n)
  margen_error <- t_critico * error_estandar
  
  inferior <- media - margen_error
  superior <- media + margen_error
  
  resultado <- data.frame(
    Medida = c(
      "Media",
      "s",
      "Error estándar",
      "n",
      "Grados de libertad",
      "Grado de confianza",
      "Valor crítico",
      "Margen de error",
      "Extremo inferior",
      "Extremo superior",
      "Intervalo"
    ),
    
    Resultado = c(
      round(media, digitos),
      round(s, digitos),
      round(error_estandar, digitos),
      n,
      gl,
      round(conf, digitos),
      round(t_critico, digitos),
      round(margen_error, digitos),
      round(inferior, digitos),
      round(superior, digitos),
      paste0(
        round(media, digitos),
        " ± ",
        round(margen_error, digitos)
      )
    ),
    
    check.names = FALSE
  )
  
  knitr::kable(
    resultado,
    format = "html",
    col.names = c("Medida", "Valor"),
    align = c("l", "r")
  )
}


# ============================================================
# 3. Intervalo Z para una proporción
# ============================================================

ic_proporcion <- function(exitos, n, conf = 0.95,
                          digitos = 4) {
  
  if (exitos < 0 || exitos > n) {
    stop("El número de éxitos debe estar entre 0 y n.")
  }
  
  alpha <- 1 - conf
  z <- qnorm(1 - alpha / 2)
  
  proporcion <- exitos / n
  error_estandar <- sqrt(proporcion * (1 - proporcion) / n)
  margen_error <- z * error_estandar
  
  inferior <- max(0, proporcion - margen_error)
  superior <- min(1, proporcion + margen_error)
  
  resultado <- data.frame(
    Medida = c(
      "Éxitos",
      "n",
      "Proporción",
      "Error estándar",
      "Grado de confianza",
      "Valor crítico",
      "Margen de error",
      "Extremo inferior",
      "Extremo superior",
      "Intervalo"
    ),
    
    Resultado = c(
      exitos,
      n,
      round(proporcion, digitos),
      round(error_estandar, digitos),
      round(conf, digitos),
      round(z, digitos),
      round(margen_error, digitos),
      round(inferior, digitos),
      round(superior, digitos),
      paste0(
        round(proporcion, digitos),
        " ± ",
        round(margen_error, digitos)
      )
    ),
    
    check.names = FALSE
  )
  
  knitr::kable(
    resultado,
    format = "html",
    col.names = c("Medida", "Valor"),
    align = c("l", "r")
  )
}

Crear base de datos

library(lsm)        # Para acceder a la base de datos survey
library(knitr)      # Para construir tablas
library(kableExtra)

datosCompleto <- lsm::survey

Muestra1 <-datosCompleto[1:100,27:34]
Muestra1

## # A tibble: 100 × 8
##    Definitive Expense Income   Gas Course       Law             Economic Race  
##         <dbl>   <dbl>  <dbl> <dbl> <chr>        <chr>           <chr>    <chr> 
##  1       4       48.9   1.61  27.4 Face-to-Face Agree           Regular  Ethnic
##  2       3.55    72.1   2.07  24.2 Virtual      Agree           Good     Ethnic
##  3       2.72    85.2   2.84  22.3 Face-to-Face Agree           Regular  Ethnic
##  4       3.55    56.6   1.55  23.1 Virtual      Agree           Bad      Ethnic
##  5       3.65    64.6   2.32  27.3 Face-to-Face In disagreement Bad      None  
##  6       4.35    63     2.1   17.2 Virtual      Agree           Good     Ethnic
##  7       3.78    40.8   1.69  27.0 Virtual      Agree           Regular  Ethnic
##  8       3.8     65.4   2.18  25.0 Face-to-Face In disagreement Regular  None  
##  9       2.88    37.3   1.71  25.1 Virtual      In disagreement Regular  Ethnic
## 10       3.58    63     2.1   21.8 Virtual      In disagreement Bad      Ethnic
## # ℹ 90 more rows

Muestra2 <- datosCompleto[1:29,27:34]
Muestra2  

## # A tibble: 29 × 8
##    Definitive Expense Income   Gas Course       Law             Economic Race  
##         <dbl>   <dbl>  <dbl> <dbl> <chr>        <chr>           <chr>    <chr> 
##  1       4       48.9   1.61  27.4 Face-to-Face Agree           Regular  Ethnic
##  2       3.55    72.1   2.07  24.2 Virtual      Agree           Good     Ethnic
##  3       2.72    85.2   2.84  22.3 Face-to-Face Agree           Regular  Ethnic
##  4       3.55    56.6   1.55  23.1 Virtual      Agree           Bad      Ethnic
##  5       3.65    64.6   2.32  27.3 Face-to-Face In disagreement Bad      None  
##  6       4.35    63     2.1   17.2 Virtual      Agree           Good     Ethnic
##  7       3.78    40.8   1.69  27.0 Virtual      Agree           Regular  Ethnic
##  8       3.8     65.4   2.18  25.0 Face-to-Face In disagreement Regular  None  
##  9       2.88    37.3   1.71  25.1 Virtual      In disagreement Regular  Ethnic
## 10       3.58    63     2.1   21.8 Virtual      In disagreement Bad      Ethnic
## # ℹ 19 more rows

dim(Muestra1)

## [1] 100   8

dim(Muestra2)

## [1] 29  8

str(Muestra1)

## tibble [100 × 8] (S3: tbl_df/tbl/data.frame)
##  $ Definitive: num [1:100] 4 3.55 2.73 3.55 3.65 ...
##  $ Expense   : num [1:100] 48.9 72.1 85.2 56.6 64.6 63 40.8 65.4 37.3 63 ...
##  $ Income    : num [1:100] 1.61 2.07 2.84 1.55 2.32 2.1 1.69 2.18 1.71 2.1 ...
##  $ Gas       : num [1:100] 27.4 24.2 22.3 23.1 27.3 ...
##  $ Course    : chr [1:100] "Face-to-Face" "Virtual" "Face-to-Face" "Virtual" ...
##  $ Law       : chr [1:100] "Agree" "Agree" "Agree" "Agree" ...
##  $ Economic  : chr [1:100] "Regular" "Good" "Regular" "Bad" ...
##  $ Race      : chr [1:100] "Ethnic" "Ethnic" "Ethnic" "Ethnic" ...

str(Muestra2)

## tibble [29 × 8] (S3: tbl_df/tbl/data.frame)
##  $ Definitive: num [1:29] 4 3.55 2.73 3.55 3.65 ...
##  $ Expense   : num [1:29] 48.9 72.1 85.2 56.6 64.6 63 40.8 65.4 37.3 63 ...
##  $ Income    : num [1:29] 1.61 2.07 2.84 1.55 2.32 2.1 1.69 2.18 1.71 2.1 ...
##  $ Gas       : num [1:29] 27.4 24.2 22.3 23.1 27.3 ...
##  $ Course    : chr [1:29] "Face-to-Face" "Virtual" "Face-to-Face" "Virtual" ...
##  $ Law       : chr [1:29] "Agree" "Agree" "Agree" "Agree" ...
##  $ Economic  : chr [1:29] "Regular" "Good" "Regular" "Bad" ...
##  $ Race      : chr [1:29] "Ethnic" "Ethnic" "Ethnic" "Ethnic" ...

Aclarando dudas

1. Nuestras bases de datos (Muestra1, Muestra2) contienen entre 100 a 26 objetos de 800 totales, apenas de ello solo uso 8 variables las cuales seleccionare Expenses e Income como cuantitativas y como binarias solo se usara Course y Economic

Variables dentro de nuestras bases de datos: Definitive

1. Expense

2. Income

3. Gas

4. Course

5. Law

6. Economic

7. Race

Mi razon de escoger aquellas 4 variantes que porque mi compañero (ahora retiro la materia) acepto conmigo hacer esas 4 variables, con ese punto en mente realizare la actividad con aquellas variantes.

Intervalos de confianza