Bootstrapping and Confidence Intervals

Based on Chapter 8 of ModernDive. Code for Quiz 12.

Load the R packages we will use.

library(tidyverse)
library(moderndive) #install before loading
library(infer) #install before loading
library(fivethirtyeight) #install before loading

What is the average age of members that have served in congress?

set.seed(123)
congress_age_100 <- congress_age  %>% 
  rep_sample_n(size=100)

Construct the confidence interval

1. Use specify to indicate the variable from congress_age_100 that you are interested in

congress_age_100  %>% 
  specify(response = age)
Response: age (numeric)
# A tibble: 100 x 1
     age
   <dbl>
 1  53.1
 2  54.9
 3  65.3
 4  60.1
 5  43.8
 6  57.9
 7  55.3
 8  46  
 9  42.1
10  37  
# ... with 90 more rows

2. generate 1000 replicates of your sample of 100

congress_age_100  %>% 
  specify(response = age)  %>% 
  generate(reps = 1000, type= "bootstrap")
Response: age (numeric)
# A tibble: 100,000 x 2
# Groups:   replicate [1,000]
   replicate   age
       <int> <dbl>
 1         1  42.1
 2         1  71.2
 3         1  45.6
 4         1  39.6
 5         1  56.8
 6         1  71.6
 7         1  60.5
 8         1  56.4
 9         1  43.3
10         1  53.1
# ... with 99,990 more rows

The output has 100,000 rows

3. calculate the mean for each replicate

bootstrap_distribution_mean_age  <- congress_age_100  %>% 
  specify(response = age)  %>% 
  generate(reps = 1000, type = "bootstrap")  %>% 
  calculate(stat = "mean")

bootstrap_distribution_mean_age
Response: age (numeric)
# A tibble: 1,000 x 2
   replicate  stat
       <int> <dbl>
 1         1  53.6
 2         2  53.2
 3         3  52.8
 4         4  51.5
 5         5  53.0
 6         6  54.2
 7         7  52.0
 8         8  52.8
 9         9  53.8
10        10  52.4
# ... with 990 more rows

The bootstrap_distribution_mean_age has 1000 means

4. visualize the bootstrap distribution

visualize(bootstrap_distribution_mean_age) 

Calculate the 95% confidence interval using the percentile method

congress_ci_percentile  <- bootstrap_distribution_mean_age %>% 
  get_confidence_interval(type = "percentile", level = 0.95)

congress_ci_percentile
# A tibble: 1 x 2
  lower_ci upper_ci
     <dbl>    <dbl>
1     51.5     55.2
obs_mean_age  <-  congress_age_100  %>% 
  specify(response = age)  %>% 
  calculate(stat = "mean")  %>% 
  pull()

obs_mean_age
[1] 53.36
visualize(bootstrap_distribution_mean_age) +
  shade_confidence_interval(endpoints = congress_ci_percentile) + 
  geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1 )

pop_mean_age  <- congress_age  %>% 
  summarize(pop_mean= mean(age))  %>% pull()

pop_mean_age
[1] 53.31373
visualize(bootstrap_distribution_mean_age) +
  shade_confidence_interval(endpoints = congress_ci_percentile) + 
   geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1) +
   geom_vline(xintercept = pop_mean_age, color = "purple", size = 3)

Save the previous plot to preview.png and add to the yaml chunk at the top

ggsave(filename = "preview.png", 
       path = here::here("_posts", "2022-04-21-bootstrapping"))