Let's expand from scenarios involving binomial variables, as we investigated in Part I, to scenarios involving multinomial variables. Political affiliation is a multinomial variable with three possible values: D, R, and I. How would we go about assessing whether a community is evenly split between the three, with 33.3% in each category? You have a random sample of 90 community members with 40 D, 30 R, and 20 I. If the null hypothesis is true, we expect about 30, 30, and 30 sample members in each of the three political affiliation categories. The word “about” needs to be more exact: would 35, 30, 25 be close enough? 37, 30, 23? 40, 30, 20?

We need to (re)invent a sample statistic that reflects how far the actual observed counts are from our expected counts. If we sum up the differences between the ...

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