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Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

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Chapter 11

Tests on normality

In this chapter we present goodness-of-fit tests for the Gaussian distribution. In Section 11.1 tests based on the empirical distribution function (EDF) are treated. A good resource for this kind of test is Stephens (1986). We start with the Kolmogorov–Smirnov test. It evaluates the greatest vertical distance between the EDF and the theoretical cumulative distribution function (CDF). If both, or one parameter are estimated from the sample the distribution of the test statistic changes and the test is called the Lilliefors test on normality.

Section 11.1.1 deals with tests not based on the EDF such as the Jarque–Bera test which compares observed and expected moments of the normal distribution.

11.1 Tests based on the EDF

11.1.1 Kolmogorov–Smirnov test (Lilliefors test for normality)

Description: Tests if a sample is sampled from a normal distribution with parameter c11-math-0001 and c11-math-0002.
Assumptions:
  • Data are measured at least on an ordinal scale.
  • The sample random variables c11-math-0003 are identically, independently distributed with observations c11-math-0004 and a continuous distribution ...

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