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Lecture 10

Political Science 3N06 2014 semester II Lecture 10a Chi square.doc

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McMaster University
Political Science
Todd Alway

Political Science 3N06 2014 Lecture 10a Chi square - What do we do when we cannot accept some of the assumptions that are required to use z-tests, t-tests, and ANOVA? - For example, cases where we know that the Population is not normal or that Population variances are not equal 2 - One possibility: χ (chi-square) - A non-parametric test – one that does not require any assumptions about the population parameters - It can be also used for nominal variables - Calculating chi-square usually starts with the construction of a bivariate table (crosstabulation) - By convention: - Columns are the categories of the independent variable - Rows are the categories of the dependent variable - Learn how to read these tables - You can follow the same 5 step model as in previous weeks, to solve for chi- square: - Step 1: Make assumptions and meet test requirements - Independent random samples - Level of measurement can be nominal - Step 2: State the H 0 - H : 0he two variables are independent - Independence in the context of the null refers to the variables we are comparing - What the null of independence means is that there is, in effect, no relationship between our independent and dependent variables - In effect, your groups are the same on the dependent variable at the population level - H : The two variables are dependent 1 - If the variables are independent, what frequency should we expect to see (f ) e in each cell of the bivariate table? 1 - Of course, what we expect to see and what we actually see are often quite different - The frequency (or number of cases) that we actually observe for each cell (0 ) isn’t likely to be exactly the same as the frequency expected under the null hypothesis - The question is whether the difference between the expected and t
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