In andrewpbray/infer: Tidy Statistical Inference
knitr::opts_chunk$set(fig.width = 6, fig.height = 3.5)
options(digits = 4)
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
Hypothesis tests
One numerical variable (mean)
Observed stat
( x_bar <- fli_small %>%
specify(response = dep_delay) %>%
calculate(stat = "mean") )
null_distn <- fli_small %>%
specify(response = dep_delay) %>%
hypothesize(null = "point", mu = 10) %>%
generate(reps = 1000) %>%
calculate(stat = "mean")
visualize(null_distn) +
shade_p_value(obs_stat = x_bar, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = x_bar, direction = "two_sided")
One numerical variable (standardized mean $t$)
Observed stat
( t_bar <- fli_small %>%
specify(response = dep_delay) %>%
calculate(stat = "t") )
null_distn <- fli_small %>%
specify(response = dep_delay) %>%
hypothesize(null = "point", mu = 8) %>%
generate(reps = 1000) %>%
calculate(stat = "t")
visualize(null_distn) +
shade_p_value(obs_stat = t_bar, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = t_bar, direction = "two_sided")
One numerical variable (median)
Observed stat
( x_tilde <- fli_small %>%
specify(response = dep_delay) %>%
calculate(stat = "median") )
null_distn <- fli_small %>%
specify(response = dep_delay) %>%
hypothesize(null = "point", med = -1) %>%
generate(reps = 1000) %>%
calculate(stat = "median")
visualize(null_distn) +
shade_p_value(obs_stat = x_tilde, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = x_tilde, direction = "two_sided")
One categorical (one proportion)
Observed stat
( p_hat <- fli_small %>%
specify(response = day_hour, success = "morning") %>%
calculate(stat = "prop") )
null_distn <- fli_small %>%
specify(response = day_hour, success = "morning") %>%
hypothesize(null = "point", p = .5) %>%
generate(reps = 1000) %>%
calculate(stat = "prop")
visualize(null_distn) +
shade_p_value(obs_stat = p_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = p_hat, direction = "two_sided")
Logical variables will be coerced to factors:
null_distn <- fli_small %>%
mutate(day_hour_logical = (day_hour == "morning")) %>%
specify(response = day_hour_logical, success = "TRUE") %>%
hypothesize(null = "point", p = .5) %>%
generate(reps = 1000) %>%
calculate(stat = "prop")
One categorical variable (standardized proportion $z$)
Not yet implemented.
Two categorical (2 level) variables
Observed stat
( d_hat <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
calculate(stat = "diff in props", order = c("winter", "summer")) )
null_distn <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
hypothesize(null = "independence") %>%
generate(reps = 1000) %>%
calculate(stat = "diff in props", order = c("winter", "summer"))
visualize(null_distn) +
shade_p_value(obs_stat = d_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = d_hat, direction = "two_sided")
Two categorical (2 level) variables (z)
Standardized observed stat
( z_hat <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
calculate(stat = "z", order = c("winter", "summer")) )
null_distn <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
hypothesize(null = "independence") %>%
generate(reps = 1000) %>%
calculate(stat = "z", order = c("winter", "summer"))
visualize(null_distn) +
shade_p_value(obs_stat = z_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = z_hat, direction = "two_sided")
Note the similarities in this plot and the previous one.
One categorical (>2 level) - GoF
Observed stat
Note the need to add in the hypothesized values here to compute the observed statistic.
( Chisq_hat <- fli_small %>%
specify(response = origin) %>%
hypothesize(null = "point",
p = c("EWR" = .33, "JFK" = .33, "LGA" = .34)) %>%
calculate(stat = "Chisq") )
null_distn <- fli_small %>%
specify(response = origin) %>%
hypothesize(null = "point",
p = c("EWR" = .33, "JFK" = .33, "LGA" = .34)) %>%
generate(reps = 1000, type = "simulate") %>%
calculate(stat = "Chisq")
visualize(null_distn) +
shade_p_value(obs_stat = Chisq_hat, direction = "greater")
null_distn %>%
get_p_value(obs_stat = Chisq_hat, direction = "greater")
Two categorical (>2 level) variables
Observed stat
( Chisq_hat <- fli_small %>%
specify(formula = day_hour ~ origin) %>%
calculate(stat = "Chisq") )
null_distn <- fli_small %>%
specify(day_hour ~ origin) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "Chisq")
visualize(null_distn) +
shade_p_value(obs_stat = Chisq_hat, direction = "greater")
null_distn %>%
get_p_value(obs_stat = Chisq_hat, direction = "greater")
One numerical variable, one categorical (2 levels) (diff in means)
Observed stat
( d_hat <- fli_small %>%
specify(dep_delay ~ season) %>%
calculate(stat = "diff in means", order = c("summer", "winter")) )
null_distn <- fli_small %>%
specify(dep_delay ~ season) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "diff in means", order = c("summer", "winter"))
visualize(null_distn) +
shade_p_value(obs_stat = d_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = d_hat, direction = "two_sided")
One numerical variable, one categorical (2 levels) (t)
Standardized observed stat
( t_hat <- fli_small %>%
specify(dep_delay ~ season) %>%
calculate(stat = "t", order = c("summer", "winter")) )
null_distn <- fli_small %>%
specify(dep_delay ~ season) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "t", order = c("summer", "winter"))
visualize(null_distn) +
shade_p_value(obs_stat = t_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = t_hat, direction = "two_sided")
Note the similarities in this plot and the previous one.
One numerical variable, one categorical (2 levels) (diff in medians)
Observed stat
( d_hat <- fli_small %>%
specify(dep_delay ~ season) %>%
calculate(stat = "diff in medians", order = c("summer", "winter")) )
null_distn <- fli_small %>%
specify(dep_delay ~ season) %>% # alt: response = dep_delay,
# explanatory = season
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "diff in medians", order = c("summer", "winter"))
visualize(null_distn) +
shade_p_value(obs_stat = d_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = d_hat, direction = "two_sided")
One numerical, one categorical (>2 levels) - ANOVA
Observed stat
( F_hat <- fli_small %>%
specify(arr_delay ~ origin) %>%
calculate(stat = "F") )
null_distn <- fli_small %>%
specify(arr_delay ~ origin) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "F")
visualize(null_distn) +
shade_p_value(obs_stat = F_hat, direction = "greater")
null_distn %>%
get_p_value(obs_stat = F_hat, direction = "greater")
Two numerical vars - SLR
Observed stat
( slope_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "slope") )
null_distn <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "slope")
visualize(null_distn) +
shade_p_value(obs_stat = slope_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = slope_hat, direction = "two_sided")
Two numerical vars - correlation
Observed stat
( correlation_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "correlation") )
null_distn <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "correlation")
visualize(null_distn) +
shade_p_value(obs_stat = correlation_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = correlation_hat, direction = "two_sided")
Two numerical vars - SLR (t)
Not currently implemented since $t$ could refer to standardized slope or standardized correlation.
# **Standardized observed stat**
( t_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "t") )
null_distn <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
hypothesize(null = "independence") %>%
generate(reps = 1000, type = "permute") %>%
calculate(stat = "t")
visualize(null_distn) +
shade_p_value(obs_stat = t_hat, direction = "two_sided")
null_distn %>%
get_p_value(obs_stat = t_hat, direction = "two_sided")
Confidence intervals
One numerical (one mean)
Point estimate
( x_bar <- fli_small %>%
specify(response = arr_delay) %>%
calculate(stat = "mean") )
boot <- fli_small %>%
specify(response = arr_delay) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "mean")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = x_bar) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
One numerical (one mean - standardized)
Point estimate
( t_hat <- fli_small %>%
specify(response = arr_delay) %>%
calculate(stat = "t") )
boot <- fli_small %>%
specify(response = arr_delay) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "t")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
One categorical (one proportion)
Point estimate
( p_hat <- fli_small %>%
specify(response = day_hour, success = "morning") %>%
calculate(stat = "prop") )
boot <- fli_small %>%
specify(response = day_hour, success = "morning") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "prop")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = p_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
One categorical variable (standardized proportion $z$)
Not yet implemented.
One numerical variable, one categorical (2 levels) (diff in means)
Point estimate
( d_hat <- fli_small %>%
specify(arr_delay ~ season) %>%
calculate(stat = "diff in means", order = c("summer", "winter")) )
boot <- fli_small %>%
specify(arr_delay ~ season) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "diff in means", order = c("summer", "winter"))
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = d_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
One numerical variable, one categorical (2 levels) (t)
Standardized point estimate
( t_hat <- fli_small %>%
specify(arr_delay ~ season) %>%
calculate(stat = "t", order = c("summer", "winter")) )
boot <- fli_small %>%
specify(arr_delay ~ season) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "t", order = c("summer", "winter"))
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
Two categorical variables (diff in proportions)
Point estimate
( d_hat <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
calculate(stat = "diff in props", order = c("summer", "winter")) )
boot <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "diff in props", order = c("summer", "winter"))
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = d_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
Two categorical variables (z)
Standardized point estimate
( z_hat <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
calculate(stat = "z", order = c("summer", "winter")) )
boot <- fli_small %>%
specify(day_hour ~ season, success = "morning") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "z", order = c("summer", "winter"))
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = z_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - SLR
Point estimate
( slope_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "slope") )
boot <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "slope")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = slope_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - correlation
Point estimate
( correlation_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "correlation") )
boot <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "correlation")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se",
point_estimate = correlation_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - t
Not currently implemented since $t$ could refer to standardized slope or standardized correlation.
# **Point estimate**
( t_hat <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
calculate(stat = "t") )
boot <- fli_small %>%
specify(arr_delay ~ dep_delay) %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "t")
( percentile_ci <- get_ci(boot) )
visualize(boot) +
shade_confidence_interval(endpoints = percentile_ci)
( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) )
visualize(boot) +
shade_confidence_interval(endpoints = standard_error_ci)
andrewpbray/infer documentation built on Aug. 29, 2019, 5:57 a.m.
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knitr::opts_chunk$set(fig.width = 6, fig.height = 3.5) options(digits = 4)
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
Hypothesis tests
One numerical variable (mean)
Observed stat
( x_bar <- fli_small %>% specify(response = dep_delay) %>% calculate(stat = "mean") )
null_distn <- fli_small %>% specify(response = dep_delay) %>% hypothesize(null = "point", mu = 10) %>% generate(reps = 1000) %>% calculate(stat = "mean") visualize(null_distn) + shade_p_value(obs_stat = x_bar, direction = "two_sided") null_distn %>% get_p_value(obs_stat = x_bar, direction = "two_sided")
One numerical variable (standardized mean $t$)
Observed stat
( t_bar <- fli_small %>% specify(response = dep_delay) %>% calculate(stat = "t") )
null_distn <- fli_small %>% specify(response = dep_delay) %>% hypothesize(null = "point", mu = 8) %>% generate(reps = 1000) %>% calculate(stat = "t") visualize(null_distn) + shade_p_value(obs_stat = t_bar, direction = "two_sided") null_distn %>% get_p_value(obs_stat = t_bar, direction = "two_sided")
One numerical variable (median)
Observed stat
( x_tilde <- fli_small %>% specify(response = dep_delay) %>% calculate(stat = "median") )
null_distn <- fli_small %>% specify(response = dep_delay) %>% hypothesize(null = "point", med = -1) %>% generate(reps = 1000) %>% calculate(stat = "median") visualize(null_distn) + shade_p_value(obs_stat = x_tilde, direction = "two_sided") null_distn %>% get_p_value(obs_stat = x_tilde, direction = "two_sided")
One categorical (one proportion)
Observed stat
( p_hat <- fli_small %>% specify(response = day_hour, success = "morning") %>% calculate(stat = "prop") )
null_distn <- fli_small %>% specify(response = day_hour, success = "morning") %>% hypothesize(null = "point", p = .5) %>% generate(reps = 1000) %>% calculate(stat = "prop") visualize(null_distn) + shade_p_value(obs_stat = p_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = p_hat, direction = "two_sided")
Logical variables will be coerced to factors:
null_distn <- fli_small %>% mutate(day_hour_logical = (day_hour == "morning")) %>% specify(response = day_hour_logical, success = "TRUE") %>% hypothesize(null = "point", p = .5) %>% generate(reps = 1000) %>% calculate(stat = "prop")
One categorical variable (standardized proportion $z$)
Not yet implemented.
Two categorical (2 level) variables
Observed stat
( d_hat <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% calculate(stat = "diff in props", order = c("winter", "summer")) )
null_distn <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% hypothesize(null = "independence") %>% generate(reps = 1000) %>% calculate(stat = "diff in props", order = c("winter", "summer")) visualize(null_distn) + shade_p_value(obs_stat = d_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = d_hat, direction = "two_sided")
Two categorical (2 level) variables (z)
Standardized observed stat
( z_hat <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% calculate(stat = "z", order = c("winter", "summer")) )
null_distn <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% hypothesize(null = "independence") %>% generate(reps = 1000) %>% calculate(stat = "z", order = c("winter", "summer")) visualize(null_distn) + shade_p_value(obs_stat = z_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = z_hat, direction = "two_sided")
Note the similarities in this plot and the previous one.
One categorical (>2 level) - GoF
Observed stat
Note the need to add in the hypothesized values here to compute the observed statistic.
( Chisq_hat <- fli_small %>% specify(response = origin) %>% hypothesize(null = "point", p = c("EWR" = .33, "JFK" = .33, "LGA" = .34)) %>% calculate(stat = "Chisq") )
null_distn <- fli_small %>% specify(response = origin) %>% hypothesize(null = "point", p = c("EWR" = .33, "JFK" = .33, "LGA" = .34)) %>% generate(reps = 1000, type = "simulate") %>% calculate(stat = "Chisq") visualize(null_distn) + shade_p_value(obs_stat = Chisq_hat, direction = "greater") null_distn %>% get_p_value(obs_stat = Chisq_hat, direction = "greater")
Two categorical (>2 level) variables
Observed stat
( Chisq_hat <- fli_small %>% specify(formula = day_hour ~ origin) %>% calculate(stat = "Chisq") )
null_distn <- fli_small %>% specify(day_hour ~ origin) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "Chisq") visualize(null_distn) + shade_p_value(obs_stat = Chisq_hat, direction = "greater") null_distn %>% get_p_value(obs_stat = Chisq_hat, direction = "greater")
One numerical variable, one categorical (2 levels) (diff in means)
Observed stat
( d_hat <- fli_small %>% specify(dep_delay ~ season) %>% calculate(stat = "diff in means", order = c("summer", "winter")) )
null_distn <- fli_small %>% specify(dep_delay ~ season) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "diff in means", order = c("summer", "winter")) visualize(null_distn) + shade_p_value(obs_stat = d_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = d_hat, direction = "two_sided")
One numerical variable, one categorical (2 levels) (t)
Standardized observed stat
( t_hat <- fli_small %>% specify(dep_delay ~ season) %>% calculate(stat = "t", order = c("summer", "winter")) )
null_distn <- fli_small %>% specify(dep_delay ~ season) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "t", order = c("summer", "winter")) visualize(null_distn) + shade_p_value(obs_stat = t_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = t_hat, direction = "two_sided")
Note the similarities in this plot and the previous one.
One numerical variable, one categorical (2 levels) (diff in medians)
Observed stat
( d_hat <- fli_small %>% specify(dep_delay ~ season) %>% calculate(stat = "diff in medians", order = c("summer", "winter")) )
null_distn <- fli_small %>% specify(dep_delay ~ season) %>% # alt: response = dep_delay, # explanatory = season hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "diff in medians", order = c("summer", "winter")) visualize(null_distn) + shade_p_value(obs_stat = d_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = d_hat, direction = "two_sided")
One numerical, one categorical (>2 levels) - ANOVA
Observed stat
( F_hat <- fli_small %>% specify(arr_delay ~ origin) %>% calculate(stat = "F") )
null_distn <- fli_small %>% specify(arr_delay ~ origin) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "F") visualize(null_distn) + shade_p_value(obs_stat = F_hat, direction = "greater") null_distn %>% get_p_value(obs_stat = F_hat, direction = "greater")
Two numerical vars - SLR
Observed stat
( slope_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "slope") )
null_distn <- fli_small %>% specify(arr_delay ~ dep_delay) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "slope") visualize(null_distn) + shade_p_value(obs_stat = slope_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = slope_hat, direction = "two_sided")
Two numerical vars - correlation
Observed stat
( correlation_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "correlation") )
null_distn <- fli_small %>% specify(arr_delay ~ dep_delay) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "correlation") visualize(null_distn) + shade_p_value(obs_stat = correlation_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = correlation_hat, direction = "two_sided")
Two numerical vars - SLR (t)
Not currently implemented since $t$ could refer to standardized slope or standardized correlation.
# **Standardized observed stat** ( t_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "t") )
null_distn <- fli_small %>% specify(arr_delay ~ dep_delay) %>% hypothesize(null = "independence") %>% generate(reps = 1000, type = "permute") %>% calculate(stat = "t") visualize(null_distn) + shade_p_value(obs_stat = t_hat, direction = "two_sided") null_distn %>% get_p_value(obs_stat = t_hat, direction = "two_sided")
Confidence intervals
One numerical (one mean)
Point estimate
( x_bar <- fli_small %>% specify(response = arr_delay) %>% calculate(stat = "mean") )
boot <- fli_small %>% specify(response = arr_delay) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "mean") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = x_bar) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
One numerical (one mean - standardized)
Point estimate
( t_hat <- fli_small %>% specify(response = arr_delay) %>% calculate(stat = "t") )
boot <- fli_small %>% specify(response = arr_delay) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "t") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
One categorical (one proportion)
Point estimate
( p_hat <- fli_small %>% specify(response = day_hour, success = "morning") %>% calculate(stat = "prop") )
boot <- fli_small %>% specify(response = day_hour, success = "morning") %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "prop") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = p_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
One categorical variable (standardized proportion $z$)
Not yet implemented.
One numerical variable, one categorical (2 levels) (diff in means)
Point estimate
( d_hat <- fli_small %>% specify(arr_delay ~ season) %>% calculate(stat = "diff in means", order = c("summer", "winter")) )
boot <- fli_small %>% specify(arr_delay ~ season) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "diff in means", order = c("summer", "winter")) ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = d_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
One numerical variable, one categorical (2 levels) (t)
Standardized point estimate
( t_hat <- fli_small %>% specify(arr_delay ~ season) %>% calculate(stat = "t", order = c("summer", "winter")) )
boot <- fli_small %>% specify(arr_delay ~ season) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "t", order = c("summer", "winter")) ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
Two categorical variables (diff in proportions)
Point estimate
( d_hat <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% calculate(stat = "diff in props", order = c("summer", "winter")) )
boot <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "diff in props", order = c("summer", "winter")) ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = d_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
Two categorical variables (z)
Standardized point estimate
( z_hat <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% calculate(stat = "z", order = c("summer", "winter")) )
boot <- fli_small %>% specify(day_hour ~ season, success = "morning") %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "z", order = c("summer", "winter")) ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = z_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - SLR
Point estimate
( slope_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "slope") )
boot <- fli_small %>% specify(arr_delay ~ dep_delay) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "slope") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = slope_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - correlation
Point estimate
( correlation_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "correlation") )
boot <- fli_small %>% specify(arr_delay ~ dep_delay) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "correlation") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = correlation_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
Two numerical vars - t
Not currently implemented since $t$ could refer to standardized slope or standardized correlation.
# **Point estimate** ( t_hat <- fli_small %>% specify(arr_delay ~ dep_delay) %>% calculate(stat = "t") )
boot <- fli_small %>% specify(arr_delay ~ dep_delay) %>% generate(reps = 1000, type = "bootstrap") %>% calculate(stat = "t") ( percentile_ci <- get_ci(boot) ) visualize(boot) + shade_confidence_interval(endpoints = percentile_ci) ( standard_error_ci <- get_ci(boot, type = "se", point_estimate = t_hat) ) visualize(boot) + shade_confidence_interval(endpoints = standard_error_ci)
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