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# Untitled

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1. library(magrittr)
2.
3.
4. # Function Declaration ----------------------------------------------------
5.
6. type_1_errors <- function(n_coeff, alpha, n_samples = 100000) {
7.   # Resampling approach to Type I Error estimation
8.   #
9.   # Args:
10.   #   n_coeff (int): Number of coefficients in model.
11.   #   alpha (dbl): Confidence level to accept alternative hypothesis.
12.   #   n_samples (int): Number of iterations to build sampling distribution.
13.   #     Defaults to 100,000.
14.
15.   p <- 1- alpha
16.   samples <- rbinom(n_samples, n_coeff, p)
17.   outcome_probs <-samples %>%
18.     table() %>%
19.     prop.table()
20.
21.   expected_value <- sum(as.double(names(outcome_probs)) * outcome_probs)  # weighted average of outcomes
22.
23.   list(
24.     n_coeff = n_coeff,
25.     alpha = alpha,
26.     outcomes = outcome_probs,
27.     percent_outcome = outcome_probs * 100,
28.     expected_errors = expected_value,
29.     raw = samples
30.     )
31. }
32.
33.
34. # Example -----------------------------------------------------------------
35.
36. n_coeff <- 63
37. alpha <- 0.95
38. error <- type_1_errors(n_coeff, alpha)
39.
40. print(paste0('model with ', n_coeff, ' coefficients ...'))
41. print(paste0('expected type I errors with alpha=', error\$alpha, ': ', error\$expected_errors))
42. print('error distribution (%):')
43. print(error\$percent_outcome)
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