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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

POLSCI 3N06

Todd Alway

Fall

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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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