IPS6e.PPT.Ch09

IPS6e.PPT.Ch09 - IPS Chapter 9.1 2009 W.H Freeman and...

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    Analysis of Two-Way Tables Inference for Two-Way Tables IPS Chapter 9.1 © 2009 W.H. Freeman and Company
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Objectives (IPS Chapter 9.1) Inference for two-way tables The hypothesis: no association Expected cell counts The chi-square test The chi-square test and the z test Using software
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Hypothesis: no association Again, we want to know if the differences in sample proportions are likely to have occurred just by chance due to random sampling.
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Expected cell counts Two-way tables sort the data according to two categorical variables. We want to test the hypothesis that there is no relationship between these two categorical variables ( H 0 ). To test this hypothesis, we compare actual counts from the sample data with expected counts, given the null hypothesis of no relationship. The expected count in any cell of a two-way table when H 0 is true is:
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Cocaine addiction Cocaine produces short-term feelings of physical and mental well being. To maintain the effect, the drug may have to be taken more frequently and at higher doses. After stopping use, users will feel tired, sleepy and depressed. The pleasurable high followed by unpleasant after-effects encourage repeated compulsive use, which can easily lead to dependency. Desipramine is an antidepressant affecting the brain chemicals that may become unbalanced and cause depression. It was thus tested for recovery from cocaine addiction. Treatment with desipramine was compared to a standard treatment (lithium, with strong anti-manic effects) and a placebo.
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25*26/74 ≈ 8.78 25* 0.35 16.22 25*0.65 9.14 26* 0.35 16.86 25*0.65 8.08 23* 0.35 14.92 25*0.65 Desipramine Lithium Placebo Expected relapse counts No Yes 35% 35% 35% Expected Observed Cocaine addiction
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The chi-square statistic ( χ 2 ) is a measure of how much the observed cell counts in a two-way table diverge from the expected cell counts. The formula for the χ 2 statistic is: (summed over all r * c cells in the table) χ 2 = observe d count - expected count ( 29 2 expec ted count Large values for χ 2 represent strong deviations from the expected distribution under the H 0 and provide evidence against H 0 . However, since χ 2 is a sum, how large a χ 2 is required for statistical significance will depend on the number of comparisons made. The chi-square test
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For the chi-square test, H 0 states that there is no association between the row and column variables in a two-way table. The alternative is that these variables are related. The P-value for the chi-square test is the area to the right of χ 2 under the χ 2 distribution with df (r−1) (c−1): P(χ 2 X 2 ).
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When is it safe to use a  χ  test? We can safely use the chi-square test when: The samples are simple random samples ( SRS ). All individual
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IPS6e.PPT.Ch09 - IPS Chapter 9.1 2009 W.H Freeman and...

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