Overview
On this page, we discuss the Chi-Square distribution and how it can be used in a “Pearson’s Chi-Squared Hypothesis Test”, testing either for Goodness of fit (“one-way table”) or Independence (“two-way table”).
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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Understand that a random variable measuring relative squares of differences between observed and expected counts has a probability distribution which is approximated by a “Chi-Squared Distribution” \(\chi^2\) for a specific value of the “degrees of freedom” (df).
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Be able to determine \(P\)-values for a \(\chi^2\) distribution, by using a table of critical \(\chi^2\) values or software.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Use a One-Way Table Test (also called Goodness of Fit Test) of observed (count) data \(\mathcal{O}_i\) against expected counts \(E_i\) given by a hypothesized probability distribution (for example uniform or binomial).
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Use a Two-Way Table (also called contingency table) of observed count data for two categorical variables to perform a (Chi-Square) Test of Independence.
To prepare for class
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Watch the following video (5min, by jbstatistics) which introduces the Chi-Square (\(\chi^2\)) Distribution:
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Watch the following video (5min, by jbstatistics) which explains how to find \(P\)-values for a Chi-Square (\(\chi^2\)) Distribution, either using a table of critical \(\chi^2\) values or using software:
After class
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Watch the following video (9min, by jbstatistics) which shows an example of performing a 1-way table test or Goodness of Fit Test using the \(\chi^2\) distribution, by comparing the data against a hypothesized discrete distribution:
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Watch the first half of the following video (8min, by jbstatistics) which shows an example of performing a Goodness of Fit Test against a Binomial distribution:
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Watch the following video (10min, by jbstatistics) which shows how to perform a Test for Independence of two categorical variables using a \(\chi^2\) distribution:
