1. Chapter 13 Chi-squared hypothesis testing

2. Summary

3. The hypothesis tested by the chi-squared test is: “There is no significant difference between the observed results and what you would expect to happen.” This is called the null hypothesis. You can use your GDC to calculate two values: the chi-squared statistic and the p-value. You will be given a set of observed frequencies. You will either be given or have to work out the expected frequencies. The test will show whether or not the observed fits the expected. Test for goodness of fit

4. Goodness-of-fit test What do the numbers mean? For the data, this tells us that: So the null hypothesis is: Which really means that: Chi-squared value < critical value The variation is not significant TrueThe data is close to what we expected Chi-squared value > critical value The variation is significant FalseThe data is not close to what we expected p-value < significance level The variation is significant FalseThe data is not close to what we expected p-value > significance level The variation is not significant TrueThe data is close to what we expected

5. The hypothesis tested by the chi-squared test is: “The two variables of the data are independent.” This is called the null hypothesis, H 0. The alternative hypothesis, H 1, is: “The two variables of the data are not independent.” You can use your GDC to calculate two values: the chi-squared statistic and the p-value. You will be given a set of observed frequencies in a two-way table. You will be given or have to calculate the expected frequencies. The test shows whether or not the two variables of the bivariate data set are independent of one another. Test for independence

6. Independence test What do the numbers mean? This tells us that:So the null hypothesis is: Which really means that: Chi-squared value < critical value The data is not significantly different from expected TrueThe two variables are independent Chi-squared value > critical value The data is significantly different from expected FalseThe two variables are not independent p-value < significance level The data is significantly different from expected FalseThe two variables are not independent p-value > significance level The data is not significantly different from expected TrueThe two variables are independent

7. Expected frequencies

8. The chi-squared test for goodness of fit uses expected frequencies. What is the difference between an expected frequency and what you actually get? Should they be the same? Can they be different? If I spin a coin 10 times, I expect that 5 times I’ll get heads!