Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Statistics

11.5 Comparison of the Chi-Square Tests

Statistics11.5 Comparison of the Chi-Square Tests

You have seen the χ2 test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which χ2 test is the appropriate one to use.

  • Goodness-of-Fit: Use the goodness-of-fit test to decide whether a population with an unknown distribution fits a known distribution. In this case there will be a single qualitative survey question or a single outcome of an experiment from a single population. Goodness-of-fit is typically used to see if the population is uniform (all outcomes occur with equal frequency), the population is normal, or the population is the same as another population with a known distribution. The null and alternative hypotheses are as follows:
    H0: The population fits the given distribution.
    Ha: The population does not fit the given distribution.
  • Independence: Use the test for independence to decide whether two variables (factors) are independent or dependent. In this case there will be two qualitative survey questions or experiments and a contingency table will be constructed. The goal is to see if the two variables are unrelated/independent or related/dependent. The null and alternative hypotheses are as follows:
    H0: The two variables (factors) are independent.
    Ha: The two variables (factors) are dependent.
  • Homogeneity: Use the test for homogeneity to decide if two populations with unknown distributions have the same distribution. In this case there will be a single qualitative survey question or experiment given to two different populations. The null and alternative hypotheses are as follows:
    H0: The two populations follow the same distribution.
    Ha: The two populations have different distributions.
PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/statistics/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/statistics/pages/1-introduction
Citation information

© Apr 16, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.