Goodness of fit

Inference for Categorical Data in R

Andrew Bray

Assistant Professor of Statistics at Reed College

First Digit Distribution

Chi-squared distance

First Digit Distribution

Example: uniformity of party

ggplot(gss2016, aes(x = party)) +
  geom_bar() +
  geom_hline(yintercept = 149/3, color = "goldenrod", size = 2)

tab <- gss2016 %>%
     select(party) %>%
     table()
tab

Dem Ind Rep 
 43  72  34

p_uniform <- c(Dem = 1/3, Ind = 1/3, Rep = 1/3)
chisq.test(tab, p = p_uniform)$stat

X-squared 
 15.87919

Simulating the null

gss2016 %>%
  specify(response = party) %>%
  hypothesize(null = "point", p = p_uniform) %>%
  generate(reps = 1, type = "simulate")

# A tibble: 149 x 2
# Groups:   replicate [1]
   party replicate
   <fct> <fct>    
 1 I        1        
 2 D        1        
 3 I        1        
 4 I        1        
 5 D        1        
 6 R        1        
 7 I        1        
 8 R        1        
 9 D        1        
10 I        1        
# ... with 139 more rows

Simulating the null

sim_1 <- gss2016 %>%
   specify(response = party) %>%
   hypothesize(null = “point”, p = p_uniform) %>%
   generate(reps = 1, type = "simulate")

ggplot(sim_1, aes(x = party)) +
   geom_bar()

Let's practice!

Inference for Categorical Data in R