1. DICE!  You are going to make your own and then we are going to test them (later) to see if they are fair!

2. Chapter 11 Chi-Squared (Categorical Data)

3. Chi-Squared  The chi-squared goodness of fit test allows us to determine whether a hypothesized distribution seems valid.  (multiple variables in a distribution – not just one)  Two types:  Chi-squared for homogeneity – tells us whether the distributions differ when there is a treatment/experiment involved.  Chi-squared for association – tells us whether the distributions differ in an observational study.

4. Chi-Squared Statistic

5. Carrying Out a Test

6.  The chi-squared test statistic compares observed minus expected COUNTS. Don’t try to perform calculations with observed minus expected proportions in each category!  The checking large sample size condition, be sure to examine the EXPECTED counts, not the observed counts.

7. When were you born?  Are births evenly distributed across the days of the week? The one-way table shows results of a random sample of 140 births from local records.  Do these data give significant evidence that local births are not equally likely on all days of the week? DaysSunMonTuesWedThursFriSat Births13232420271815

8.  State:  Plan:

9.  Do:  Conclude:

10. Follow-Up Analysis  When you reject your null hypothesis…you need to follow up by looking at individual components to see which values are the biggest contributors – or helped to push your data far enough to reject.  These components show which terms contribute most to the chi-squared statistic.

11. Homework  Pg 692 (1-9 odd, 11, 15, 19-22)  Let’s do #11 together!

12. #11