15. Chi Squared: Goodness of Fit and Contingency Tables

Recall that the \chi^{2} is essentially the distribution of sample variances s^{2} from a normal population. It has three important applications (there are others) :

  1. Hypothesis test of population variance (covered in Section 9.5).
  2. Model fitting through \chi^{2} = \mbox{SS}_{\mbox{error}} (not covered in this course).
  3. Hypothesis test of frequencies :
    a) Goodness of fit
    b) contingency tables.

Here we focus on the last application. We will use the \chi^{2} statistic to compare the measured (or observed) statistic with expected (H_{0}) frequencies. The difference of observed and expected frequencies squared represents a variance. If the difference between observed and expected frequencies is due to noise, which will have some sort of binomial distribution, then we expect the \chi^{2} statistic to be low. If the difference between observed and expected frequencies is large then there must be an effect other than noise that is causing that difference.

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Introduction to Applied Statistics for Psychology Students Copyright © 2022 by Gordon E. Sarty is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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