11. Chi Square University of Vermont（11。）.pdf

11. Chi Square Objectives Calculate goodness of fit Chi Square Calculate Chi Square for contingency tables Calculate effect size Save data entry time by weighting cases A Chi Square is used to analyze categorical data. It compares observed frequencies to expected or predicted frequencies. We will examine simple goodness of fit Chi Squares that involved only one variable and more complicated contingency tables that include 2 or more variables. Each type is programmed through different menu options. Let’s start with goodness of fit. Goodness of Fit Chi Square All Categories Equal Let’s begin by using a new example in Chapter 19 on the frequency with which a school yard player will “throw” Rock, Paper, Scissors. We want to test the null hypothesis that they are thrown equally often. Open RPS.sav. This file contains a string variable (Choice), a numerical variable (NumChoice = 1, 2, 3) numbering the choices, and another numerical variable named Freq, containing the frequency of each choice. We need NumChoice because SPSS does not allow you to specify a string variable as a test variable. Go to Data/Weight Cases and select Freq as the weights. Select Analyze/Nonparametric Tests/Chi Square. Select NumChoice as the Test Variable. Under Expected Values, All categories equal is the default. This is what we want since our null hypothesis is that each throw is equally likely to be chosen. Click Ok. The output follows. Chi-Square Test Frequencies As you can see, the expected values were 25 each, just