1. Less on Third Tee Moron Con, Tin Gents See Tables

2. Lesson #30 More on Contingency Tables

3. 1288 3147 15235 100 150 250 Lung Cancer Smokers Non-smokers Yes No A 2  2 table can also be used to do a two-sided test of two proportions RR = 6Z 0 = 3.2616

4. = 10.638 Reject H 0 if = 3.841 As before, reject H 0 Note that (Z 0 ) 2 = (3.2616) 2 = 10.638 =

5. Fisher’s Exact Test Used in a 2  2 table when at least one of the expected frequencies is less than 5 Based on the Hypergeometric distribution - used to count the number of “successes” in n trials, when the trials are not independent

6. 11 28 7 4 1832 39 11 50 No FemaleMale Yes Sneakers 14.0424.96 3.96 7.04 1832 39 11 50 No FemaleMale Yes Sneakers ObservedExpected E1E1 = 14.04 = 4.675  ?

7. In general, one variable in a contingency table can have r levels, and the other can have c levels r  c Tables The null hypothesis is still that there is no association or relationship between the variables The observed frequencies can be denoted by: OiOi i = 1, 2, 3, …, rc

8. The expected frequencies are calculated as before: The test statistic is: OiOi - E i ( ) 2 EiEi ~ under H 0 Reject H 0 if

9. Spontaneous Abortion Alcohol Use YesNo 0 1-2 3-6 7-20 21+ 6793 2068 776 456 98 33164 9099 3069 1527 287 26371 7031 2293 1071 189 10191 36955 47146 E1E1 = 7168.67

10. Compare 1-2 drinks to none Compare 3-6 drinks to none Compare 7-20 drinks to none Compare 21+ drinks to none