intransitivity_proportions.R

library(tidyverse)

## testing overall incidence of intransitivity

# number of intransitive fish in each experiment per the results
intransitive <- c(9, 6, 6)

# total number of fish in each experiment
total <- c(10, 11, 23) + intransitive

# test whether, across all experiments, there are more intransitive fish than expected by chance
binom.test(x = sum(intransitive), n = sum(total), p = 0.25)
# result: 
# Exact binomial test
# 
# data:  sum(intransitive) and sum(total)
# number of successes = 21, number of trials = 65, p-value = 0.1964
# alternative hypothesis: true probability of success is not equal to 0.25
# 95 percent confidence interval:
#   0.2123276 0.4505496
# sample estimates:
#   probability of success 
# 0.3230769 


# we can do a proportion test to see whether the proportion of intransitive fish
# is different across the three experiments
prop.test(intransitive, total) # p = 0.147, not significant

# if we were to do post-hoc test with Bonferonni-Holm correction, we would do it like this:
pairwise.prop.test(intransitive, total, p.adjust.method = "holm")


## resampling individual females across experiments

# define a vector with 21 intransitive females, 44 transitive
females <- c(rep("intransitive", 21), rep("transitive", 44))


resample_intransitive <- function(x, reps = 1000, seed = 1234){
  
  # set the seed for reproducability
  set.seed(seed)
  
  # define a tibble to store the results
  df <- tibble::tibble(
    experiment_1 = vector(mode = "integer", length = reps),
    experiment_2 = vector(mode = "integer", length = reps),
    experiment_3 = vector(mode = "integer", length = reps),
    replicate = vector(mode = "integer", length = reps)
  )
  
  for(i in 1:reps){
    df$replicate[i] <- i
    
    # resample
    # this randomly reshuffles the placement of the intransitive females
    y <- sample(x, replace = FALSE)
    
    # experiment 1, n = 19
    # get the number of intransitive females in the first experiment
    num_1 = sum(y[1:19] == "intransitive")
    
    # experiment 2, n = 17
    num_2 = sum(y[20:36] == "intransitive")
    
    # experiment 3, n = 29
    num_3 = sum(y[37:length(y)] == "intransitive")
    
    # run a binomial test and extract the p-value for the proportion of intransitive females
    df$experiment_1[i] <- broom::tidy(binom.test(x = num_1, n = 19, p = 0.25)) %>% dplyr::pull("p.value")
    df$experiment_2[i] <- broom::tidy(binom.test(x = num_2, n = 17, p = 0.25))%>% dplyr::pull("p.value")
    df$experiment_3[i] <- broom::tidy(binom.test(x = num_3, n = 29, p = 0.25))%>% dplyr::pull("p.value")
    
  }
  
  df
  
}


resample_intransitive(females) %>% 
  rowwise() %>%
  mutate(at_least_one_test_sig = if_else(any(experiment_1 <= 0.05,
                                             experiment_2 <= 0.05, 
                                             experiment_3 <= 0.05), TRUE, FALSE)) %>%
  group_by(at_least_one_test_sig) %>%
  count

# # A tibble: 2 x 2
# # Groups:   at_least_one_test_sig [2]
# at_least_one_test_sig     n
# <lgl>                 <int>
#   1 FALSE                   785
# 2 TRUE                    215