prob_of_winning.r

#' I had a quick chat with Nikos earlier today, 
#' and I need to generate the same analysis Nikos described for three separate data sets 
#' (they're all attached and include variables labelled task2score and task3score respectively).
#' In the end what I'm trying to calculate is the probability a subject's task 3 score is 
#' strictly lower than a randomly selected task 2 score from the same experiment. 
#' Each file contains only the observations I need to include in the analysis.


#packages
library(readr)
library(dplyr)
library(ggplot2)


# load data
ADM_Lab <- read_csv("~/Downloads/ADM_Lab.csv")
Matters <- read_csv("~/Downloads/Matters.csv")
ADM_MTurk <- read_csv("~/Downloads/ADM_MTurk.csv")

possible_task3_score <- unique(
  c(ADM_Lab$task3score,
    Matters$task3score,
    ADM_MTurk$task3score)
) %>% 
  sort

# does not take into account tie break rule
CDF_data = bind_rows(
  {
    tibble(
      task_3_score = possible_task3_score,
    ) %>% 
      left_join(
        ADM_Lab %>% 
          group_by(task2score) %>% 
          tally() %>% 
          select(task_3_score=task2score, n=nn, everything()) 
      ) %>% 
      mutate(
        group = 'ADM_Lab',
        n = ifelse(is.na(n), 0, n)
      )
  },
  {
    tibble(
      task_3_score = possible_task3_score,
    ) %>% 
      left_join(
        Matters %>% 
          group_by(task2score) %>% 
          tally() %>% 
          select(task_3_score=task2score, everything()) 
      ) %>% 
      mutate(
        group = 'Matters',
        n = ifelse(is.na(n), 0, n)
      )
  },
  {
    tibble(
      task_3_score = possible_task3_score,
    ) %>% 
      left_join(
        ADM_MTurk %>% 
          group_by(task2score) %>% 
          tally() %>% 
          select(task_3_score=task2score, everything()) 
      ) %>% 
      mutate(
        group = 'ADM_MTurk',
        n = ifelse(is.na(n), 0, n)
      )
  }
) %>% 
  group_by(group) %>% 
    mutate(
      scores_below = cumsum(n) - n,
      probability_of_winning_stricklyLess = scores_below / sum(n)
    )


# plotting


CDF_data %>% 
  ggplot(
    aes(
      y = probability_of_winning_stricklyLess,
      x = task_3_score,
      group = group,
      color = group
    )
  ) +
  geom_line() +
  labs(
    x = "Number of successful tasks in part 3",
    y = "Probability of winning tournament"
  ) +
  scale_y_continuous(labels = scales::percent)