observed_stat_examples.R
In infer: Tidy Statistical Inference

## ----include=FALSE------------------------------------------------------------
knitr::opts_chunk$set(fig.width = 6, fig.height = 4.5, 
                      message = FALSE, warning = FALSE) 
options(digits = 4)

## ----load-packages, echo = FALSE----------------------------------------------
library(dplyr)
library(infer)

## ----load-gss-----------------------------------------------------------------
# load in the dataset
data(gss)

# take a look at its structure
dplyr::glimpse(gss)

## -----------------------------------------------------------------------------
x_bar <- gss %>%
  specify(response = hours) %>%
  calculate(stat = "mean")

## -----------------------------------------------------------------------------
x_bar <- gss %>%
  observe(response = hours, stat = "mean")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = hours) %>%
  hypothesize(null = "point", mu = 40) %>%
  generate(reps = 1000) %>%
  calculate(stat = "mean")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = x_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = x_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
t_bar <- gss %>%
  specify(response = hours) %>%
  hypothesize(null = "point", mu = 40) %>%
  calculate(stat = "t")

## -----------------------------------------------------------------------------
t_bar <- gss %>%
  observe(response = hours, null = "point", mu = 40, stat = "t")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = hours) %>%
  hypothesize(null = "point", mu = 40) %>%
  generate(reps = 1000) %>%
  calculate(stat = "t")

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
  specify(response = hours)  %>%
  assume("t")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = t_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = t_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist, method = "both") +
  shade_p_value(obs_stat = t_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = t_bar, direction = "two-sided")

## -----------------------------------------------------------------------------
gss %>%
  t_test(response = hours, mu = 40)

## -----------------------------------------------------------------------------
x_tilde <- gss %>%
  specify(response = age) %>%
  calculate(stat = "median")

## -----------------------------------------------------------------------------
x_tilde <- gss %>%
  observe(response = age, stat = "median")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = age) %>%
  hypothesize(null = "point", med = 40) %>% 
  generate(reps = 1000) %>% 
  calculate(stat = "median")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = x_tilde, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = x_tilde, direction = "two-sided")

## -----------------------------------------------------------------------------
set.seed(1)

gss_paired <- gss %>%
   mutate(
      hours_previous = hours + 5 - rpois(nrow(.), 4.8),
      diff = hours - hours_previous
   )

gss_paired %>%
   select(hours, hours_previous, diff)

## -----------------------------------------------------------------------------
x_tilde <- gss_paired %>%
  specify(response = diff) %>%
  calculate(stat = "mean")

## -----------------------------------------------------------------------------
x_tilde <- gss_paired %>%
  observe(response = diff, stat = "mean")

## -----------------------------------------------------------------------------
null_dist <- gss_paired %>%
  specify(response = diff) %>%
  hypothesize(null = "paired independence") %>% 
  generate(reps = 1000, type = "permute") %>% 
  calculate(stat = "mean")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = x_tilde, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = x_tilde, direction = "two-sided")

## -----------------------------------------------------------------------------
p_hat <- gss %>%
  specify(response = sex, success = "female") %>%
  calculate(stat = "prop")

## -----------------------------------------------------------------------------
p_hat <- gss %>%
  observe(response = sex, success = "female", stat = "prop")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = sex, success = "female") %>%
  hypothesize(null = "point", p = .5) %>%
  generate(reps = 1000) %>%
  calculate(stat = "prop")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = p_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = p_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  dplyr::mutate(is_female = (sex == "female")) %>%
  specify(response = is_female, success = "TRUE") %>%
  hypothesize(null = "point", p = .5) %>%
  generate(reps = 1000) %>%
  calculate(stat = "prop")

## -----------------------------------------------------------------------------
p_hat <- gss %>%
  specify(response = sex, success = "female") %>%
  hypothesize(null = "point", p = .5) %>%
  calculate(stat = "z")

## -----------------------------------------------------------------------------
p_hat <- gss %>%
  observe(response = sex, success = "female", null = "point", p = .5, stat = "z")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = sex, success = "female") %>%
  hypothesize(null = "point", p = .5) %>%
  generate(reps = 1000, type = "draw") %>%
  calculate(stat = "z")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = p_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = p_hat, direction = "two-sided")

## ----prop_test_1_grp----------------------------------------------------------
prop_test(gss,
          college ~ NULL,
          p = .2)

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  specify(college ~ sex, success = "no degree") %>%
  calculate(stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  observe(college ~ sex, success = "no degree", 
          stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(college ~ sex, success = "no degree") %>%
  hypothesize(null = "independence") %>% 
  generate(reps = 1000) %>% 
  calculate(stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
r_hat <- gss %>% 
  specify(college ~ sex, success = "no degree") %>%
  calculate(stat = "ratio of props", order = c("female", "male"))

## -----------------------------------------------------------------------------
r_hat <- gss %>% 
  observe(college ~ sex, success = "no degree",
          stat = "ratio of props", order = c("female", "male"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(college ~ sex, success = "no degree") %>%
  hypothesize(null = "independence") %>% 
  generate(reps = 1000) %>% 
  calculate(stat = "ratio of props", order = c("female", "male"))

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = r_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = r_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
or_hat <- gss %>% 
  specify(college ~ sex, success = "no degree") %>%
  calculate(stat = "odds ratio", order = c("female", "male"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(college ~ sex, success = "no degree") %>%
  hypothesize(null = "independence") %>% 
  generate(reps = 1000) %>% 
  calculate(stat = "odds ratio", order = c("female", "male"))

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = or_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = or_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
z_hat <- gss %>% 
  specify(college ~ sex, success = "no degree") %>%
  hypothesize(null = "independence") %>%
  calculate(stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
z_hat <- gss %>% 
  observe(college ~ sex, success = "no degree",
          stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(college ~ sex, success = "no degree") %>%
  hypothesize(null = "independence") %>% 
  generate(reps = 1000) %>% 
  calculate(stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
  specify(college ~ sex, success = "no degree") %>%
  assume("z")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = z_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = z_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist, method = "both") +
  shade_p_value(obs_stat = z_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = z_hat, direction = "two-sided")

## ----prop_test_2_grp----------------------------------------------------------
prop_test(gss, 
          college ~ sex,  
          order = c("female", "male"))

## -----------------------------------------------------------------------------
Chisq_hat <- gss %>%
  specify(response = finrela) %>%
  hypothesize(null = "point",
              p = c("far below average" = 1/6,
                    "below average" = 1/6,
                    "average" = 1/6,
                    "above average" = 1/6,
                    "far above average" = 1/6,
                    "DK" = 1/6)) %>%
  calculate(stat = "Chisq")

## -----------------------------------------------------------------------------
Chisq_hat <- gss %>%
  observe(response = finrela,
          null = "point",
          p = c("far below average" = 1/6,
                "below average" = 1/6,
                "average" = 1/6,
                "above average" = 1/6,
                "far above average" = 1/6,
                "DK" = 1/6),
          stat = "Chisq")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(response = finrela) %>%
  hypothesize(null = "point",
              p = c("far below average" = 1/6,
                    "below average" = 1/6,
                    "average" = 1/6,
                    "above average" = 1/6,
                    "far above average" = 1/6,
                    "DK" = 1/6)) %>%
  generate(reps = 1000, type = "draw") %>%
  calculate(stat = "Chisq")

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
  specify(response = finrela) %>%
  assume("Chisq")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist_theory, method = "both") +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
chisq_test(gss, 
           response = finrela,
           p = c("far below average" = 1/6,
                 "below average" = 1/6,
                 "average" = 1/6,
                 "above average" = 1/6,
                 "far above average" = 1/6,
                 "DK" = 1/6))

## -----------------------------------------------------------------------------
Chisq_hat <- gss %>%
  specify(formula = finrela ~ sex) %>% 
  hypothesize(null = "independence") %>%
  calculate(stat = "Chisq")

## -----------------------------------------------------------------------------
Chisq_hat <- gss %>%
  observe(formula = finrela ~ sex, stat = "Chisq")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(finrela ~ sex) %>%
  hypothesize(null = "independence") %>% 
  generate(reps = 1000, type = "permute") %>% 
  calculate(stat = "Chisq")

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
  specify(finrela ~ sex) %>%
  assume(distribution = "Chisq")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist, method = "both") +
  shade_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = Chisq_hat, direction = "greater")

## -----------------------------------------------------------------------------
gss %>%
  chisq_test(formula = finrela ~ sex)

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  specify(age ~ college) %>% 
  calculate(stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  observe(age ~ college,
          stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(age ~ college) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>%
  calculate(stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
t_hat <- gss %>% 
  specify(age ~ college) %>% 
  hypothesize(null = "independence") %>%
  calculate(stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
t_hat <- gss %>% 
  observe(age ~ college,
          stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(age ~ college) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>%
  calculate(stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
  specify(age ~ college) %>%
  assume("t")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = t_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = t_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
visualize(null_dist, method = "both") +
  shade_p_value(obs_stat = t_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = t_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  specify(age ~ college) %>% 
  calculate(stat = "diff in medians", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  observe(age ~ college,
          stat = "diff in medians", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(age ~ college) %>% # alt: response = age, explanatory = season
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>%
  calculate(stat = "diff in medians", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = d_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
F_hat <- gss %>% 
  specify(age ~ partyid) %>%
  calculate(stat = "F")

## -----------------------------------------------------------------------------
F_hat <- gss %>% 
  observe(age ~ partyid, stat = "F")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
   specify(age ~ partyid) %>%
   hypothesize(null = "independence") %>%
   generate(reps = 1000, type = "permute") %>%
   calculate(stat = "F")

## -----------------------------------------------------------------------------
null_dist_theory <- gss %>%
   specify(age ~ partyid) %>%
   hypothesize(null = "independence") %>%
   assume(distribution = "F")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = F_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist_theory) +
  shade_p_value(obs_stat = F_hat, direction = "greater")

## -----------------------------------------------------------------------------
visualize(null_dist, method = "both") +
  shade_p_value(obs_stat = F_hat, direction = "greater")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = F_hat, direction = "greater")

## -----------------------------------------------------------------------------
slope_hat <- gss %>% 
  specify(hours ~ age) %>% 
  calculate(stat = "slope")

## -----------------------------------------------------------------------------
slope_hat <- gss %>% 
  observe(hours ~ age, stat = "slope")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
   specify(hours ~ age) %>% 
   hypothesize(null = "independence") %>%
   generate(reps = 1000, type = "permute") %>%
   calculate(stat = "slope")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = slope_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = slope_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
correlation_hat <- gss %>% 
  specify(hours ~ age) %>% 
  calculate(stat = "correlation")

## -----------------------------------------------------------------------------
correlation_hat <- gss %>% 
  observe(hours ~ age, stat = "correlation")

## -----------------------------------------------------------------------------
null_dist <- gss %>%
   specify(hours ~ age) %>% 
   hypothesize(null = "independence") %>%
   generate(reps = 1000, type = "permute") %>%
   calculate(stat = "correlation")

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = correlation_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = correlation_hat, direction = "two-sided")

## -----------------------------------------------------------------------------
obs_fit <- gss %>%
  specify(hours ~ age + college) %>%
  fit()

## -----------------------------------------------------------------------------
null_dist <- gss %>%
  specify(hours ~ age + college) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>%
  fit()

## -----------------------------------------------------------------------------
null_dist2 <- gss %>%
  specify(hours ~ age + college) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute", variables = c(age, college)) %>%
  fit()

## -----------------------------------------------------------------------------
visualize(null_dist) +
  shade_p_value(obs_stat = obs_fit, direction = "two-sided")

## -----------------------------------------------------------------------------
null_dist %>%
  get_p_value(obs_stat = obs_fit, direction = "two-sided")

## -----------------------------------------------------------------------------
x_bar <- gss %>% 
  specify(response = hours) %>%
  calculate(stat = "mean")

## -----------------------------------------------------------------------------
x_bar <- gss %>% 
  observe(response = hours, stat = "mean")

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(response = hours) %>%
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "mean")

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- get_ci(boot_dist, type = "se", point_estimate = x_bar)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
sampling_dist <- gss %>%
   specify(response = hours) %>%
   assume(distribution = "t")

## -----------------------------------------------------------------------------
theor_ci <- get_ci(sampling_dist, point_estimate = x_bar)

theor_ci

visualize(sampling_dist) +
  shade_confidence_interval(endpoints = theor_ci)

## -----------------------------------------------------------------------------
t_hat <- gss %>% 
  specify(response = hours) %>%
  hypothesize(null = "point", mu = 40) %>%
  calculate(stat = "t")

## -----------------------------------------------------------------------------
t_hat <- gss %>% 
  observe(response = hours,
          null = "point", mu = 40,
          stat = "t")

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(response = hours) %>%
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "t")

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = t_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
p_hat <- gss %>% 
   specify(response = sex, success = "female") %>%
   calculate(stat = "prop")

## -----------------------------------------------------------------------------
p_hat <- gss %>% 
   observe(response = sex, success = "female", stat = "prop")

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
 specify(response = sex, success = "female") %>%
 generate(reps = 1000, type = "bootstrap") %>%
 calculate(stat = "prop")

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = p_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
sampling_dist <- gss %>%
   specify(response = sex, success = "female") %>%
   assume(distribution = "z")

## -----------------------------------------------------------------------------
theor_ci <- get_ci(sampling_dist, point_estimate = p_hat)

theor_ci

visualize(sampling_dist) +
  shade_confidence_interval(endpoints = theor_ci)

## -----------------------------------------------------------------------------
d_hat <- gss %>%
  specify(hours ~ college) %>%
  calculate(stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
d_hat <- gss %>%
  observe(hours ~ college,
          stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(hours ~ college) %>%
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "diff in means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = d_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
sampling_dist <- gss %>%
   specify(hours ~ college) %>%
   assume(distribution = "t")

## -----------------------------------------------------------------------------
theor_ci <- get_ci(sampling_dist, point_estimate = d_hat)

theor_ci

visualize(sampling_dist) +
  shade_confidence_interval(endpoints = theor_ci)

## -----------------------------------------------------------------------------
d_hat <- gss %>%
  specify(hours ~ college) %>%
  calculate(stat = "ratio of means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
d_hat <- gss %>%
  observe(hours ~ college,
          stat = "ratio of means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(hours ~ college) %>%
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "ratio of means", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = d_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
t_hat <- gss %>%
  specify(hours ~ college) %>%
  calculate(stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
t_hat <- gss %>%
  observe(hours ~ college,
          stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(hours ~ college) %>%
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "t", order = c("degree", "no degree"))

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = t_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  specify(college ~ sex, success = "degree") %>%
  calculate(stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
d_hat <- gss %>% 
  observe(college ~ sex, success = "degree",
          stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
  specify(college ~ sex, success = "degree") %>%
  generate(reps = 1000, type = "bootstrap") %>% 
  calculate(stat = "diff in props", order = c("female", "male"))

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = d_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
sampling_dist <- gss %>% 
  specify(college ~ sex, success = "degree") %>%
   assume(distribution = "z")

## -----------------------------------------------------------------------------
theor_ci <- get_ci(sampling_dist, point_estimate = d_hat)

theor_ci

visualize(sampling_dist) +
  shade_confidence_interval(endpoints = theor_ci)

## -----------------------------------------------------------------------------
z_hat <- gss %>% 
  specify(college ~ sex, success = "degree") %>%
  calculate(stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
z_hat <- gss %>% 
  observe(college ~ sex, success = "degree",
          stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
  specify(college ~ sex, success = "degree") %>%
  generate(reps = 1000, type = "bootstrap") %>% 
  calculate(stat = "z", order = c("female", "male"))

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = z_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
slope_hat <- gss %>% 
  specify(hours ~ age) %>%
  calculate(stat = "slope")

## -----------------------------------------------------------------------------
slope_hat <- gss %>% 
  observe(hours ~ age, stat = "slope")

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(hours ~ age) %>% 
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "slope")

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = slope_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
correlation_hat <- gss %>% 
  specify(hours ~ age) %>%
  calculate(stat = "correlation")

## -----------------------------------------------------------------------------
correlation_hat <- gss %>% 
  observe(hours ~ age, stat = "correlation")

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
   specify(hours ~ age) %>% 
   generate(reps = 1000, type = "bootstrap") %>%
   calculate(stat = "correlation")

## -----------------------------------------------------------------------------
percentile_ci <- get_ci(boot_dist)

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = percentile_ci)

## -----------------------------------------------------------------------------
standard_error_ci <- boot_dist %>%
  get_ci(type = "se", point_estimate = correlation_hat)

visualize(boot_dist) +
  shade_confidence_interval(endpoints = standard_error_ci)

## -----------------------------------------------------------------------------
obs_fit <- gss %>%
  specify(hours ~ age + college) %>%
  fit()

## -----------------------------------------------------------------------------
boot_dist <- gss %>%
  specify(hours ~ age + college) %>%
  generate(reps = 1000, type = "bootstrap") %>%
  fit()

## -----------------------------------------------------------------------------
conf_ints <- 
  get_confidence_interval(
    boot_dist, 
    level = .95, 
    point_estimate = obs_fit
  )

## -----------------------------------------------------------------------------
visualize(boot_dist) +
  shade_confidence_interval(endpoints = conf_ints)