Statistical Inference

The Catfish Data

p <- 37/50
q <- 1-p

Coin Flipping & Sample Sizes

coin <- c("Heads","Tails")

Take a random sample (e.g., flip it!)

sample( coin, size=10, replace=TRUE )

 [1] "Heads" "Heads" "Tails" "Tails" "Tails" "Tails" "Tails" "Tails" "Heads"
[10] "Tails"

Heads

Heads

Tails

Tails

Tails

Tails

Tails

Tails

Heads

Tails

Sample Sizes

N <- c( 10, 20, 50, 100, 250, 500 )

df <- data.frame( N = rep(N, each=20),
                  Catfish = NA )

flip_coins <- function( n ) {
  outcome <- sample(coin,size=n,replace=TRUE)
  return( sum( outcome == "Heads" ) )
}

df$Catfish = sapply( df$N,  
                     flip_coins, 
                     simplify=TRUE )

head( df )

library( ggplot2 )
df$N <- as.factor( df$N ) 
ggplot( df, aes(N, Catfish, fill=N)) + 
  geom_violin() +
  theme_minimal( base_size = 16 ) + 
  theme( legend.position = "none")