## Question 706:

1## Answer:

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The Chi-Squared test typically has two major uses. One is called the test of independence and the other is called the Goodness of Fit. In introduction statistics texts and courses and in practice, the test of independence is used more often. The test of independence, as the name suggests will determine whether two nominal (also called categorical variables) are associated with each other. If both variables are continuous (like time, money, height) you would conduct a correlation.For a Chi-Square Goodness of Fit, you would test whether your data fit a distribution, such as the Normal, Poisson or Binomial. The Null Hypothesis in the data do fit the distribution. The Alternative Hypothesis is that the data do not fit the distribution.

For the test of independence the Null Hypothesis is there is no association between variables. The alternative hypothesis is that there is an association. As an example, lets say you ask 100 men and 100 women whether they agree that Speed Dating is a good idea. You get the following data:

Women | Men | Row Total | |

Agree | 58 | 66 | 124 |

Disagree | 34 | 24 | 58 |

No Opinion | 8 | 10 | 18 |

Col Total | 100 | 100 | 200 |

You would use the Chi-Square test on the 2x3 contingency table to answer the question: Is there an association between gender and opinion of speed dating? The Null Hypothesis is that there is no association between gender and opinion and the alternative hypothesis is that there is an association (e.g. women disagree more than men).

The general formula for a Chi-Square is (Observed-Expected)

^{2}/ Expected.

In this example, the Chi-Square is 2.462 and on 2 degrees of freedom it isn't significant at p <.05. So we would NOT reject the NULL. Even though more women in this example disagree with the idea that speed dating is a good idea, it is not a large enough difference that we can be sure it isn't due to chance alone.

See the attached spreadsheet for an example of the calculations and on how to get the observed and expected values.