Less on Third Tee Moron Con, Tin Gents See Tables

Lesson #30 More on Contingency Tables

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 =

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

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

No FemaleMale Yes Sneakers No FemaleMale Yes Sneakers ObservedExpected E1E1 = =  ?

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

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

Spontaneous Abortion Alcohol Use YesNo E1E1 =

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