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Hypothesis Testing

Jesse Cambon 02 February, 2021

References: * https://www.tidymodels.org/learn/statistics/xtabs/

library(tidymodels) # Includes the infer package
library(knitr)

# Set ggplot theme
theme_set(theme_minimal())


data(ad_data, package = "modeldata")
ad_data %>%
  count(Genotype, Class,sort=T) %>% head(5) %>% kable()
Genotype Class n
E3E3 Control 133
E3E4 Control 65
E3E4 Impaired 41
E3E3 Impaired 34
E2E3 Control 30

Chi Squared Test of Independences

ad_data %>% 
  chisq_test(Genotype ~ Class) %>%
  kable()
## Warning in stats::chisq.test(table(x), ...): Chi-squared approximation may be
## incorrect
statistic chisq_df p_value
21.57748 5 0.0006298 
observed_indep_statistic <- ad_data %>%
  specify(Genotype ~ Class) %>%
  calculate(stat = "Chisq")


# generate the null distribution using randomization
null_distribution_simulated <- ad_data %>%
  specify(Genotype ~ Class) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 500, type = "permute") %>%
  calculate(stat = "Chisq")
null_distribution_simulated %>%
  visualize() + 
  shade_p_value(observed_indep_statistic,
                direction = "greater") + theme_minimal()

ad_data %>%
  specify(Genotype ~ Class) %>%
  hypothesize(null = "independence") %>%
  visualize(method = "theoretical") + 
  shade_p_value(observed_indep_statistic,
                direction = "greater")
## Warning: Check to make sure the conditions have been met for the theoretical
## method. {infer} currently does not check these for you.


null_distribution_simulated %>%
  visualize(method = "both") + 
  shade_p_value(observed_indep_statistic,
                direction = "greater")
## Warning: Check to make sure the conditions have been met for the theoretical
## method. {infer} currently does not check these for you.