Chi-squared test statistic

Inference for Categorical Data in R

Andrew Bray

Assistant Professor of Statistics at Reed College

Comparing bar plots

Hypothesis test

null <- data %>%
  specify(var1 ~ var2) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 100, type = "permute") %>%
  calculate(stat = ?)

Choosing a statistic

observed_counts

             party
natspac       Dem Ind Rep
  TOO LITTLE    8  13   9
  ABOUT RIGHT  22  37  17
  TOO MUCH     13  22   8

expected_counts

             party
natspac        Dem  Ind  Rep
  TOO LITTLE   8.7 14.5  6.8
  ABOUT RIGHT 21.9 36.7 17.3
  TOO MUCH    12.4 20.8  9.8

Choosing a statistic

observed_counts

             party
natspac       Dem Ind Rep
  TOO LITTLE    8  13   9
  ABOUT RIGHT  22  37  17
  TOO MUCH     13  22   8

expected_counts

             party
natspac        Dem  Ind  Rep
  TOO LITTLE   8.7 14.5  6.8
  ABOUT RIGHT 21.9 36.7 17.3
  TOO MUCH    12.4 20.8  9.8

(observed_counts - expected_counts) ^ 2

             party
natspac         Dem   Ind   Rep
  TOO LITTLE  0.433 2.240 4.641
  ABOUT RIGHT 0.005 0.076 0.117
  TOO MUCH    0.349 1.492 3.284

sum((observed_counts - expected_counts) ^ 2)

12.63565

Chi-squared distance

Let's practice!

Inference for Categorical Data in R