demos.Rmd

---
title: "R Notebook"
output: html_notebook
---



```{r}
library(tidyverse)
library(palmerpenguins)
library(boot)
```


```{r}
penguins_df <- penguins
penguins_df
```
```{r}
bootstrap_penguin_test <- function(measurement, interval){
  func_stat <- function(data, i) {
    stat <- data[i, ] %>%
      summarize(boot_stat = mean({{measurement}}, na.rm = TRUE)) %>%
      pull(boot_stat) 
    
    return(stat)
  }
  
  adelie_ci <- penguins_df %>%
    filter(species == "Adelie") %>%
    boot(statistic = func_stat, R = 1000, sim = "ordinary") %>%
    boot.ci(conf = interval, type = "bca")
  
  chinstrap_b_ci <- penguins_df %>%
    filter(species == "Chinstrap") %>%
    boot(statistic = func_stat, R = 1000, sim = "ordinary") %>%
    boot.ci(conf = interval, type = "bca")
  
  gentoo_b_ci <- penguins_df %>%
    filter(species == "Gentoo") %>%
    boot(statistic = func_stat, R = 1000, sim = "ordinary") %>%
    boot.ci(conf = interval, type = "bca")
  
  ci_plot <- rbind(adelie_ci$bca, chinstrap_b_ci$bca, gentoo_b_ci$bca) %>% 
    cbind(c("Adelie", "Chinstrap", "Gentoo")) %>%
    as_tibble() %>%
    ggplot() +
      geom_errorbarh(aes(y = V6, xmin = V4, xmax = V5)) + 
      theme(axis.text.x = element_text(angle = 45, vjust = 1, hjust=1)) +
      ylab("Species") + 
      ggtitle(paste0("Confidence Interval (", interval, ") of Penguin Size"))
  
  return(ci_plot)
}
```

```{r}
bootstrap_penguin_test(
  measurement = `flipper_length_mm`, 
  interval = 0.95
)
```

# Hypothesis Test Example 1:

Is there a difference in flipper size between chinstrap and gentoo penguins?

H_null: There is no difference in flipper size between chinstrap and gentoo penguins
- mean_flipper_size_chinstrap == mean_flipper_size_gentoo
H_alternative: There is a difference in flipper size between chinstrap and gentoo penguins
- mean_flipper_size_chinstrap != mean_flipper_size_gentoo

Have enough evidence at the 5 percent significant level to reject the null hypothesis and conclude that there is a difference in mean flipper size between chinstrap and gentoo penguins.

## Assumptions

### QQ Plot

```{r}
penguins_df %>%
  drop_na() %>%
  filter(species == "Gentoo") %>%
  ggplot() +
    stat_qq(aes(sample = flipper_length_mm, color = sex)) +
    stat_qq_line(aes(sample = flipper_length_mm, color = sex))
```

### Shapiro Wilk Test

```{r}
penguins_df %>%
  drop_na() %>%
  filter(species == "Gentoo", sex == "male") %>%
  pull(flipper_length_mm) %>%
  shapiro.test()
```

```{r}
penguins_df %>%
  drop_na() %>%
  filter(species == "Gentoo", sex == "female") %>%
  pull(flipper_length_mm) %>%
  shapiro.test()
```
## t test
```{r}
male_flippers <- penguins_df %>%
  filter(species == "Gentoo", sex == "male") %>%
  pull(flipper_length_mm)

female_flippers <- penguins_df %>%
  filter(species == "Gentoo", sex == "female") %>%
  pull(flipper_length_mm)

t.test(male_flippers, female_flippers, alternative = "two.sided")
```

```{r}
wilcox.test(male_flippers, female_flippers, alternative = "two.sided")
```