Goodness-Of-Fit Tests

STA6507 - Nonparametric Stats

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A simulation study: the statistical power of normality tests

We will conduct a simulation study to investigate the power of the goodness-of-fit tests:

  • Kolmogorov-Smirnov
  • Chi-squared
  • Lilliesfors
  • Shapiro-Wilk
  1. Generate samples of size \(n = {5,10,20,40,80,160,320,500,1000}\) from:
  • Chi-squared distribution with df=3
  • Student’s t-Distribution df=4
  • Exponential distribution with scale parameter of 1
  • Uniform distribution in (0,1)

  1. Apply the goodness-of-fit tests above to test normality and find the power (probability of rejecting the null hypothesis) for each of the tests.

  2. Plot the results. The sample size (x-axis) vs the power (y-axis) for each test.

  1. Comments on the results and provide recommendations for each case.