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Unformatted text preview: Chapter 13 Section 2 Inference for twoway tables Example 13.4 Treating Cocaine Addiction Chronic users of cocaine need the drug to feel pleasure. Perhaps giving them a medication that fights depression will help them stay off cocaine. A three year study compared an antidepressant called desipramine with lithium (a standard treatment for cocaine addiction) and a placebo. The subjects were 72 chronic users randomly assigned to each treatment. Here are the counts and proportions of the subjects who avoided relapse into cocaine use during the study. Group Treatment Subjects No relapse Proportion 1 Desipramine 24 14 0.583 2 Lithium 24 6 0.250 3 Placebo 24 4 0.167 The problem with multiple comparisons Test 2 1 : p p H = to see if the success rate of desipramine differs from that of lithium 3 1 : p p H = to see if desipramine differs from a placebo 3 2 : p p H = to see if lithium differs from a placebo The weakness of doing three tests is that we get three Pvalues, one for each test alone. That does not tell us how likely it is that three sample proportions are spread apart as far as these are. It may be that = 0.583 and = 0.167 are significantly different if we look at just two groups, but not significantly different if we know that they are the smallest and largest proportions in three groups. 1 p 3 p As we look at more groups, we expect the gap between the smallest and largest sample proportion to get larger. Think of comparing the tallest and the shortest person in larger and large groups of people. We cannot safely compare many parameters by doing tests or confidence intervals for two parameters at a time. Statistical methods for dealing with many comparisons with some overall measure of confidence usually have two parts: 1. An overall test to see if there is good evidence of any differences among the parameters that we want to compare. 2. A detailed followup analysis to decide which of the parameters differ and to estimate how large the differences are. Relapse NO YES Desipramine 14 10 Lithium 6 18 Placebo 4 20 3 x 2 table ( row x columns table) relationship between two categories explanatory is the treatment response is success (no relapse), failure (relapse) 6 combinations, each count occupies a cell of the table Expected Count 3 2 1 : p p p H = = not all p : a H 1 , p 2 and p 3 are equal The expected count in any cell of a twoway table when H is true is row total x column total expected count=  table total Relapse NO YES Total Desipramine 14 10 24 Lithium 6 18 24 Placebo 4 20 24 Total 24 48 72 The proportion of relapses among all 72 subject is Then the expected count for the cell for Desipramine and relapse is: Calculating the remaining cells the same way, we can compare the expected and the observed....
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This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.
 Fall '08
 O

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