In andrewpbray/infer: Tidy Statistical Inference

knitr::opts_chunk$set(fig.width = 8, fig.height = 3) 

Note: The type argument in generate() is automatically filled based on the entries for specify() and hypothesize(). It can be removed throughout the examples that follow. It is left in to reiterate the type of generation process being performed.

Data preparation

library(nycflights13)
library(dplyr)
library(ggplot2)
library(stringr)
library(infer)
set.seed(2017)
fli_small <- flights %>% 
  na.omit() %>% 
  sample_n(size = 500) %>% 
  mutate(season = case_when(
    month %in% c(10:12, 1:3) ~ "winter",
    month %in% c(4:9) ~ "summer"
  )) %>% 
  mutate(day_hour = case_when(
    between(hour, 1, 12) ~ "morning",
    between(hour, 13, 24) ~ "not morning"
  )) %>% 
  select(arr_delay, dep_delay, season, 
         day_hour, origin, carrier)

• Two numeric - arr_delay, dep_delay
• Two categories
  • season ("winter", "summer"),
  • day_hour ("morning", "not morning")
• Three categories - origin ("EWR", "JFK", "LGA")
• Sixteen categories - carrier

---

One numerical variable, one categorical (2 levels)

Calculate observed statistic

The recommended approach is to use specify() %>% calculate():

obs_chisq <- fli_small %>%
  specify(origin ~ season) %>% # alt: response = origin, explanatory = season
  calculate(stat = "Chisq")

The observed $\chi^2$ statistic is r obs_chisq.

Or using chisq_test in infer

obs_chisq <- fli_small %>% 
  chisq_test(formula = origin ~ season) %>% 
  dplyr::select(statistic)

Again, the observed $\chi^2$ statistic is r obs_chisq.

Or using another shortcut function in infer:

obs_chisq <- fli_small %>% 
  chisq_stat(formula = origin ~ season)

Lastly, the observed $\chi^2$ statistic is r obs_chisq.

Randomization approach to $\chi^2$-statistic

chisq_null_perm <- fli_small %>%
  specify(origin ~ season) %>% # alt: response = origin, explanatory = season
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>%
  calculate(stat = "Chisq")

visualize(chisq_null_perm) +
  shade_p_value(obs_stat = obs_chisq, direction = "greater")

Calculate the randomization-based $p$-value

chisq_null_perm %>% 
  get_p_value(obs_stat = obs_chisq, direction = "greater")

Theoretical distribution

chisq_null_theor <- fli_small %>%
  specify(origin ~ season) %>% 
  hypothesize(null = "independence") %>%
  # generate() ## Not used for theoretical
  calculate(stat = "Chisq")

visualize(chisq_null_theor, method = "theoretical") +
  shade_p_value(obs_stat = obs_chisq, direction = "right")

Overlay appropriate $\chi^2$ distribution on top of permuted statistics

visualize(chisq_null_perm, method = "both") +
  shade_p_value(obs_stat = obs_chisq, direction = "right")

Compute theoretical p-value

fli_small %>% 
  chisq_test(formula = origin ~ season) %>% 
  dplyr::pull(p_value)

andrewpbray/infer documentation built on Aug. 29, 2019, 5:57 a.m.