left_handed_FishersExactTest.Rmd

# 女性左撇子比男性左撇子多 {#lefthanded}

```{r, message=FALSE, warning=FALSE}
library(tidyverse)
library(tidybayes)
library(bayesplot)
library(rstan)
library(loo)
library(broom.mixed)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
theme_set(bayesplot::theme_default())
```






```{r}
tb <- tibble::tribble(
  ~sex,   ~left_handed, ~right_handed,
  "male",           9L,           43L,
  "female",         4L,           44L
  )

```



```{r}
steps <- seq(from = 0, to = 1, by = .01)

ggplot(data.frame(x = steps, y = dbeta(steps, shape1 = 1, shape2 = 1))) + 
  geom_line(aes(x, y)) +
  scale_x_continuous(breaks = (0:10) / 10) + 
  ylim(0, 2) +
  labs(x = "p(left-handed)", y = "density", title = "beta(1,1)")



ggplot(data.frame(x = steps, y = dbeta(steps, shape1 = 5, shape2 = 40))) + 
  geom_line(aes(x, y)) +
  scale_x_continuous(breaks = (0:10) / 10) +
  labs(x = "p(left-handed)", y = "density", title = "beta(5,40)")
```





```{r}
stan_program <- "
data {
  int<lower=1> event_1;        
  int<lower=1> event_2;        
  int<lower=1> n_1;            
  int<lower=1> n_2;            
}
parameters {
  real<lower=0,upper=1> p_1;    
  real<lower=0,upper=1> p_2;    
}
model {
  event_1 ~ binomial(n_1, p_1);
  event_2 ~ binomial(n_2, p_2);
  p_1 ~ beta(5, 40);
  p_2 ~ beta(5, 40);
}
generated quantities {
  real diff = p_1 - p_2;
}
"


stan_data <- list(
  n_1     = 52, # men
  event_1 = 9 , # left-handed men
  n_2     = 48, # women
  event_2 = 4   # left-handed women
)


stan_eq <- stan(model_code = stan_program, data = stan_data)
```


```{r}
stan_eq %>%
  tidybayes::spread_draws(diff) %>% 
  ggplot(aes(x = diff, y = 1)) +
  geom_halfeyeh() +
  geom_vline(xintercept = 0)
```