• Treatment of mice with new medical treatment
• Efron and Tibshirani - Modern fathers of statistics

x = c(94, 197, 16, 38, 99, 141, 23) # T group
y = c(52, 104, 146, 10, 51, 30, 40, 27, 46) # C group

library(vecsets)
P = 1000 #  number of total permutations
d = rep(0, P) # repeat 0s P times ('place holder')
for(i in 1:P){
  # new T group permutation
  x_new = sample(x = c(x, y), size = 7, replace = F) 
  # rest of the data - C group
  y_new = vsetdiff(c(x,y), x_new) 
  # new stats
  d[i] = mean(x_new) - mean(y_new) 
}

# logical condition that shows True or False
larger_than_observed_difference <- d >= mean(x) - mean(y) 
# get count of permutations that gave stats larger than observed stats
count = length(d[larger_than_observed_difference]) 
count

## [1] 149

# calculate p-value 
p_value = count/P 
p_value

## [1] 0.149

library(vecsets)
P = 1000 #  number of total permutations
d = rep(0, P) # repeat 0s P times ('place holder')
for(i in 1:P){
  # new T group permutation
  x_new = sample(x = c(x, y), size = 7, replace = F) 
  # rest of the data - C group
  y_new = vsetdiff(c(x,y), x_new) 
  # new stats
  d[i] = median(x_new) - median(y_new) 
}

# count of permutations that gave stats larger than observed stats
count = length(d[d >= median(x) - median(y)])
count

## [1] 170

# calculate p-value 
p_value = count/P 
p_value

## [1] 0.17