Categorical Data  2 -test Pray for a quick and painless death.

Para-what? Statistical test are divided into two types 1. Parametric: a test that compares sample data to a larger population (e.g., z, t, F). Parametric tests have stringent assumptions (e.g., sample is normally, and independently distributed). 2. Non-parametric: do not depend on a specific distribution. For that reason, they are called distribution-free, and are not

Are you nuts? Non-parametric tests do not depend on a distribution, and are easier to perform. So why not use them exclusively? 1. Parametric tests are generally robust to violations of their assumptions. 2. Parametric tests are more powerful and versatile (e.g., you can’t test for multiple variable interactions. Note: As a general rule, researchers will use parametric tests whenever possible, due to their higher power. However, when there have been gross violations of the assumptions, researchers will use non-parametric tests.

 2 Test for Single Variable Experiments Often, experiments are conducted with nominal data (e.g., product preference tests). The   (Chi-square) test is the most frequently used with nominal data.

 2 Test for Single Variable Experiments Bud’s Suds makes microbrewed beer for blue-collar drinkers. Bud’s Suds have 3 new products, but recent cut-backs mean there is only enough funding to introduce one product. So they decide to conduct an experiment. You randomly sample 150 beer drinkers, let them taste the three different products, and pick the ones they like the best Trailer TeaNASCAR NectarMountain MeadTotal 150 Frequency of drinkers picking a particular brand H 0 : No difference in preference

Computing  2 obtained 1. Determine the frequency you would expect (expected frequencies) in each cell if sampling is random from the null hypothesis population. F e = expected frequency under the null hypothesis F o = observed frequency in the sample fofo fefe 50 Trailer TeaNASCAR NectarMountain Mead Total 150

Computing  2 obtained fofo fefe 50 Trailer TeaNASCAR NectarMountain Mead Total 150

Computing  2 obtained Conclusion: Reject the null hypothesis

 2 Test for Two Variable (Two-way) Experiments Suppose the senate is trying to pass a bill to legalize medical marijuana. You are volunteering for your local senator, who asks you to take a poll. You pick a random sample of 400 voters (200 Democrats and 200 Republicans) in your district and ask them about legalization of medical marijuana. Here are the results Republican Democrat Column Margin ForAgainstRow MarginsUndecided

Computing Expected Values Republicans FOR the bill Republicans Undecided Republicans Against

Computing Expected Values Democrats FOR the bill Democrats Undecided Democrats Against

 2 Test for Two Variable (Two-way) Experiments Republican68 (80) 22 (20) 110 (100) 200 Democrat92 (80) 18 (20) 90 (100) 200 Column Margin ForAgainstRow MarginsUndecided df = (r-1)(c-1) = (2-1)(3-1) = (1)(2) = 2

Computing   Values Republicans FOR the bill Republicans Undecided Republicans Against

Computing   Values Democrats FOR the bill Democrats Undecided Democrats Against

Computing   Values Reject the Null Hypothesis. Political affiliation and attitude toward the bill are related.