Chi-Square Test for Goodness of Fit Day 2
Chapter 11 - Day 2 - Lesson 11.1
Learning Targets
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State and check the Random, 10%, and Large Counts conditions for performing a chi-square test for goodness of fit.
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Perform a chi-square test for goodness of fit.
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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
Activity:
Answer Key:
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.
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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.