Goodnesss Of Fit

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    Amol Kulkarni

    As we all know there are different test for Goodness Of Fit viz:-Anderson Darling,Kolmogorov Smirnov,Ryan Joiner,Chi-Square etc
    I would like to know whether Chi-Square test is meant only Discrete Distributions or Continous distributions also.Also is there any restriction on sample size for Chi-Square test.



    there is no restriction on sample size as long as no more than 20% of your “cells” have an expected value of less than 5. This is a warning you get when you use SAS JMP (not sure for other software).



    Goodness of Fit, Tests for Homogeneity, and Test for Indepenced are all forms of Chi Square testing. As in all cases your value is based on the sample size being relative and representative. So to answer your question Yes you attempt to make your sample size meet these criteria.
    I cannot give you a number as that would presume I knew what you were sampling. As stated in the presvious response you need at least five, but more is always better.



    The Chi-square tests can be used for continuous distributions, but they are not as powerful as other available tests, such as Shapiro-Wilks test for normal distributions and Anderson-Darling tests for many other continuous distributions.
    Quote from “Goodness-of-Fit Techniques” by D’Agostino and Stephens:
    “Chi-squared tests are generally less powerful than EDF (empirical distribution function) tests and special-purpose tests of fit.” Thought they acknowldge that these tests do have a place due to their flexibility and ease-of-use, and are “the most practical tests of fit in many situations.”
    Specifically for normal distribution testing, they say “the Kolmogorov-Smirnov test is only a historical curiosity. It should never be used.” and “when a complete sample is available the chi-square tests should not be used. It does not have good power when compared to the above tests [Shapiro-Wilk, D’Agostino-Pearson, Anderson-Darling].”

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