A p-value, two ways

You've seen before how there are usually two ways to get to the null distribution: through computation and through a mathematical approximation. The chi-squared goodness of fit test is no exception. The approximation distribution is again the "Chi-squared distribution" with degrees of freedom equal to the number of categories minus one.

In this exercise you'll compare these two approaches to calculate a p-value that measures the consistency of the distribution of the Iran first digits with Benford's Law. Note that the observed statistic that you created in the last exercise is saved in your work space as chi_obs_stat.

Deze oefening maakt deel uit van de cursus

Inference for Categorical Data in R

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Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Compute degrees of freedom
degrees_of_freedom <- ___ %>%
  # Pull out first_digit vector
  pull("first_digit") %>% 
  # Calculate n levels and subtract 1
  ___

# Plot both null dists
___
  # Add density layer
  ___
  # Add vertical line at obs stat
  ___ 
  # Overlay chisq approx
  stat_function(fun = dchisq, args = list(df = ___), color = "blue")

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