Perform a chi-square test for goodness of fit.
Conduct a follow-up analysis when the results of a chi-square test are statistically significant.
Activity: Which Color M&M is the Most Common? – Part Two
For this activity, we will be using the M&M data collected yesterday. Students should have enough information and knowledge to be able to construct a 4-step significance test without much of your help at all.
Common Student Error
Students are used to the degrees of freedom formula n – 1 from one-sample t procedures. But there is a big difference here. For one-sample t procedures, n represents the sample size. For a chi-square test for goodness of fit, n represents the number of categories.
Follow Up Analysis
A follow-up analysis is only suggested if the data are statistically significant. If the data are not statistically significant, there is no reason to do further analysis.
Over the years, several free response questions have required students to perform a chi-square significance test. The follow-up analysis is not required for full credit when performing the test, but the thinking involved in the follow-up analysis may help students succeed in part (b) of the question. See 2008 #5 and 2016 #2.
We have our students add a follow up analysis sentence at the end of the conclusion for any chi-square test with statistically significant data.