lecture_12 - Three-way Contingency Tables Lecture 12 ILRST...

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        Three-way Contingency Tables Lecture 12 ILRST 212
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    Marginal versus Conditional  Independence Example:                                               Response Clinic     Treatment             Success     Failure  1                  A                     18            12                      B                     12             8  2                  A                      2              8                      B                      8             32 Total              A                     20            20                      B                     20            40
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    Marginal versus Conditional  Independence It is seen that given clinic, response and treatment are  conditionally independent.  When we ignore clinic, the odds of a success is twice as  high for treatment A as treatment B.
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    Marginal versus Conditional  Independence If we ignore treatment , we see that the odds of success in  clinic 1 is 6 times the odds of success in clinic 2. Also , ignoring success, we see the odds of treatment A in  clinic 1 is 6 times the odds of treatment A in clinic 2. Clinic 1 tends to use treatment A more often, and clinic 1  also tends to have more successes.
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    Marginal versus Conditional  Independence Combining both the results, we can conclude that patients  who attend clinic 1 tend to be younger than those who go to  clinic 2, perhaps they have a better success rate than  subjects in clinic 2 regardless of the treatment received. Hence it is misleading to study only the marginal table,  concluding that successes are more likely with treatment A  than with treatment B.
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        Homogenous Association There is homogenous X-Y association in a 2*2*K table  when  θ xy(1) =  θ xy(2) =  θ xy(3) = ………………………………… θ xy(k)
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