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# chiov - Chi-square(2 Parametric vs nonparametric tests...

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Chi-square ( χ 2 ) Parametric vs. nonparametric tests Hypotheses about Frequencies Two main uses of chi-square are called goodness-of-fit and tests of independence . The goodness-of-fit test involves a single (1) independent variable. Tests of independence involve 2 or more IVs. Example of a goodness-of-fit test. Suppose we do a blind beer tasting experiment. We present 4 beers in identical glasses and allow our judges to sip away. After sampling all 4, each judge selects his/her favorite beer. We select 100 lucky participants for the study. The results are: Coors Corona Miller Sam Adams Total Frequency 15 45 30 10 100 Now if people cannot tell the difference or if they have no preference among the beers, we would expect about 25 people to choose each beer (suppose we did the study again only with all glasses of Miller and asked people to pick their favorite). There are 4 choices and 100 people: 100/4 =25. To test, we use the formula χ 2 2 = ( ) O E E where O is an observed score and E is an expected score in a cell. In our case, we expect 25 people per cell (beer).

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