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9.1 - Inference for two-way tables Hypothesis of no...

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Analysis of two-way tables Inference for two-way tables
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Inference for two-way tables Hypothesis of no association Two sampling designs and the associated models Testing for homogeneity Testing for independence The chi-square test The Chi-square distribution
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Gastric Freezing Gastric freezing was once a treatment for ulcers. Patients would swallow a deflated balloon with tubes, and a cold liquid would be pumped for an hour to cool the stomach and reduce acid production, thus relieving ulcer pain. The treatment was shown to be safe, significantly reducing ulcer pain , and so widely used for years. A randomized comparative experiment later compared the outcome of gastric freezing with that of a placebo: 28 of the 82 patients subjected to gastric freezing improved, while 30 of the 78 in the control group improved. H 0 : p gf = p placebo H a : p gf p placebo 499 . 0 025 . 0 * 231 . 0 044 . 0 78 1 82 1 637 . 0 * 363 . 0 385 . 0 341 . 0 1 1 ) ˆ 1 ( ˆ ˆ ˆ 2 1 2 1 - = - = + - = + - - = n n p p p p z 3625 . 0 78 82 30 28 ˆ = + + = pooled p
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Improvement n Treatment 28 82 34.1% Placebo 30 78 38.5% Improvement No improvement Treatment 28 54 Placebo 30 48 Expressed as a two-way table:
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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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Observed Cocaine addiction
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Comparing several populations Select independent SRSs of sizes n 1 , n 2 , . . . , n r from each of r populations,. Classify each individual in a sample according to a categorical response variable with c possible values. There are r different probability distributions, one for each population.
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