Chi-Square Tests for Goodness of Fit
Day 141 - Lesson 10.2
Check conditions for a test about the distribution of a categorical variable.
Calculate the P-value for a test about the distribution of a categorical variable.
Use the four-step process to perform a chi-square test for goodness of fit.
Activity: Which color M&M is the most common? Part 2.
Yesterday students were introduced to the chi-square test statistic and how to calculate it by hand. Today we are going to expand that into a full significance test using yesterday’s M&M data. To do that we need to add in conditions and calculating the P-value. The conditions are Random and Large Counts. The large counts condition is different than the one we use for proportions: the expected counts must be greater than 5. We already calculated the test statistic yesterday but we didn’t find the P-value using table C. To use table C we need the degrees of freedom, df = n – 1, where n is the number of categories.
As students are working through the activity you should add in any explanation they need. The expected counts and degrees of freedom are explained in the activity but extra help might still be needed. After students work through the first page, the second page compiles all the work in a four-step format. This might feel a little repetitive but it is important to model to students what you will be expecting to see for work. When students are working, they will probably draw a normal curve for the picture. Make sure to catch this and point out why this is no longer correct. You should discuss how a Chi-Square test statistic cannot be less than 0 which is why the picture is different. We also wanted to draw attention to how this is different from the previous four-step problems so highlight that at the end.