mm9 - Chapter 9 Analysis of Two-Way Tables Two-way (i.e....

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Unformatted text preview: Chapter 9 Analysis of Two-Way Tables Two-way (i.e. contingency) tables: to classify & analyze categorical data: Binomial counts: success vs. failure Proportions: binomial count divided by total sample size Well later see that inference via two-way tables is an alternativewith advantages & disadvantagesto the z-test for comparing two sample proportions: . prtest hsci, by(white) An advantage of two-way tables is that they can examine more than two variables. A disadvantage of two-way tables is that they can only do two-sided hypothesis tests. Heres a two-way table: . tab hsci white, cell Nonwhite White Total not hsci50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% Nonwhite White Total not hsci 50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% The row variable : hsci vs. not hsci. The column variable : white vs. nonwhite. Nonwhite White Total not hsci 50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% Cells : each combination of values for the two variables (50, 103, 5, 42). Nonwhite White Total not hsci50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% J oint distributions : Each cells percentage of the total sample (50/200=.250; 103/200=.515; 5/200=.025; 42/200=.210). Nonwhite White Total not hsci50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% The marginal frequencies : the row totals (153, 47) & the column totals (55, 145). Nonwhite White Total not hsci50 103 153 25.0% 51.5% 76.5% hsci 5 42 47 2.5% 21.0% 23.5% Total 55 145 200 27.5% 72.5% 100.0% The marginal distributions : each row total/sample total (76.5%, 23.5%). Each column total/sample total (27.5%, 72.5%). Here are the same data displayed as column conditional probabilities : . tab hsci white, col nofreq nonwhite white Total no 90.91% 71.03% 76.5% yes 9.09% 28.97% 23.5% Total 100.0% 100.% 100.00% The conditional distributions (i.e conditional probabilities) : Columndivide each column cell count by its column total count. Here are the same data displayed as row conditional probabilities...
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This note was uploaded on 07/11/2011 for the course SYA 6305 taught by Professor Tardanico during the Fall '08 term at FIU.

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mm9 - Chapter 9 Analysis of Two-Way Tables Two-way (i.e....

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