Dataset mpg - Simulação - Testes de Hipóteses

# ##############################################################################
# ########################### Autonomia de Veículos ############################
# ##############################################################################

# 1. Carregamento de pacotes ---------------------------------------------------

## Carregando
if(!require("pacman")) install.packages("pacman"); library(pacman)

p_load("tidyverse", "tidymodels")

# 2. Preparação do ambiente e dos dados ----------------------------------------

## Limpa o console o ambiente
cat("\014")
rm(list = ls())

## Ajuda para o pacote 'infer'
help(package = "infer")
vignette("infer")

mpg_ <- mpg %>%
  mutate(trans = ifelse(str_detect(trans, "auto"), "auto", "manual"),
         trans = factor(trans),
         class = factor(class))

# A quilometragem/litro média é 23 ? -------------------------------------------

bootstrap_distribution <- mpg_ %>%
  specify(response = hwy) %>%
  hypothesize(null = "point",
              mu = 23) %>%
  generate(reps = 10^3,
           type = "bootstrap") %>%
  calculate(stat = "mean")

obs_mean <- mpg_ %>%
  specify(response = hwy) %>%
  calculate(stat = "mean")

visualize(bootstrap_distribution)+
  shade_p_value(obs_stat = obs_mean,
                direction = "two_sided")

bootstrap_distribution %>%
  get_p_value(obs_stat = obs_mean,
              direction = "two_sided")

# p-valor: 0.283 / não rejeitar a hipótese nula (a média é 23)

# Carros automáticos e manuais tem a mesma autonomia? --------------------------

null_distribution <- mpg_ %>%
  specify(hwy ~ trans) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 10^3, type = "permute") %>%
  calculate(stat = "diff in means",
            order = c("manual", "auto"))

obs_mean_diff <- mpg_ %>%
  specify(hwy ~ trans) %>%
  calculate(stat = "diff in means",
            order = c("manual", "auto"))

visualize(null_distribution)+
  shade_p_value(obs_stat = obs_mean_diff,
                direction = "two_sided")

null_distribution %>%
  get_p_value(obs_stat = obs_mean_diff,
              direction = "two_sided")

# p-valor: 0 / rejeitar a hipótese nula

# O tipo de transmissão influencia no gasto de combustível? --------------------

null_distribution <- mpg_ %>%
  specify(class ~ trans) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 10^4, type = "permute") %>%
  calculate(stat = "Chisq")

obs_chisq <- mpg_ %>%
  specify(class ~ trans) %>%
  calculate(stat = "Chisq")

visualize(null_distribution)+
  shade_p_value(obs_stat = obs_chisq,
                direction = "greater")

null_distribution %>%
  get_p_value(obs_stat = obs_chisq,
              direction = "greater")

# p-valor: 0 / rejeitar a hipótese nula

# 3. Plataforma de testes ------------------------------------------------------

## Função densidade
dens.fun <- function(z) with(density(null_distribution$stat), approx(x, y, z)$y)

x_start <- quantile(null_distribution$stat, probs = 0.95, names = FALSE)
x_end <- max(null_distribution$stat)

## Colorir área sob a curva de densidade (p-valor)
ggplot(null_distribution, aes(x = stat))+
  geom_density()+
  geom_area(data = data.frame(value = seq(x_start, x_end, len=100)),
            aes(x = value, y = dens.fun(value), color = NULL),
            fill = "red", alpha = 0.3)

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