Chi Squared - Tutorial Pearson's Chi-square Test for...

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Tutorial: Pearson's Chi-square Test for Independence Ling 300, Fall 2008 What is the Chi-square test for? The Chi-square test is intended to test how likely it is that an observed distribution is due to chance. It is also called a "goodness of fit" statistic, because it measures how well the observed distribution of data fits with the distribution that is expected if the variables are independent. A Chi-square test is designed to analyze categorical data. That means that the data has been counted and divided into categories. It will not work with parametric or continuous data (such as height in inches). For example, if you want to test whether attending class influences how students perform on an exam, using test scores (from 0-100) as data would not be appropriate for a Chi-square test. However, arranging students into the categories "Pass" and "Fail" would. Additionally, the data in a Chi-square grid should not be in the form of percentages, or anything other than frequency (count) data. Thus, by dividing a class of 54 into groups according to whether they attended class and whether they passed the exam, you might construct a data set like this: Pass Fail Attended 25 6 Skipped 8 15 IMPORTANT : Be very careful when constructing your categories! A Chi-square test can tell you information based on how you divide up the data. However, it cannot tell you whether the categories you constructed are meaningful. For example, if you are working with data on groups of people, you can divide them into age groups (18-25, 26-40, 41-60...) or income level, but the Chi-square test will treat the divisions between those categories exactly the same as the divisions between male and female, or alive and dead! It's up to you to assess whether your categories make sense, and whether the difference (for example) between age 25 and age 26 is enough to make the categories 18-25 and 26-40 meaningful. This does not mean that categories based on age are a bad idea, but only that you need to be aware of the control you have over organizing data of that sort. Another way to describe the Chi-square test is that it tests the null hypothesis that the variables are independent. The test compares the observed data to a model that distributes the data according to the expectation that the variables are independent. Wherever the observed data doesn't fit the model, the likelihood that the variables are dependent becomes stronger, thus proving the null hypothesis incorrect!
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The following table would represent a possible input to the Chi-square test, using 2 variables to divide the data: gender and party affiliation. 2x2 grids like this one are often the basic example for the Chi-square test, but in actuality any size grid would work as well: 3x3, 4x2, etc. Democrat Republican Male 20 30 Female 30 20 This shows the basic 2x2 grid. However, this is actually incomplete, in a sense; generally, the data table should include "marginal" information giving the total counts for each column and row, as well as for the whole data set: Democrat Republican Total Male 20 30 50 Female 30 20 50 Total 50
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