CRIM 320 Lecture Notes - Lecture 4: Null Hypothesis

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Lecture 4 Analysis of Categorical
Data I
-parametric versus non parametric tests
-what happens when normality cannot be assumed?
-based on characteristics of what we’re studying
-minimum entry level data
-normal distribution (known areas in curve)
when we do not have normal distribution
-very few assumptions of characteristics of pop, less powerful than parametric
how do we measure association for nominal variables?
-categories instead of mathematical numbers
-relationships between variables
-chi-square test of independence
the basic idea of chi-square
-are two variables related to one another?
-one-way chi-square is similar to one sample t test
-looking for relationship between two categorical variables
-null hypothesis – two variables are independent
-not influencing or affecting each other
-if we reject the null, we are stating that the two variables are dependent
-chi-square independence vs dependence
the logic of chi-square
-only require frequency data
-observed and expected counts
-observed: actual data collected from your sample (actual numbers in each category of
variables in dataset)
-expected counts: info we expect to have on variables if the data was independence
-reject the null if the observed counts are sufficiently different from the expected counts
**chi-square formula x2
how do we conduct a chi-square?
-1. Calculate marginal
-2. Calculate expected counts
-3. (observed – expected)2 / expected
-4. Sum across all cells
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