Statistics and Data Analysis

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Part 24: Hypothesis Tests 24-1/33 Statistics and Data Analysis Professor William Greene Stern School of Business IOMS Department Department of Economics.

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Statistics and Data Analysis Professor William Greene Stern School of Business IOMS Department Department of Economics

Statistics and Data Analysis Part 15 – Hypothesis Tests: Part 3

A Test of Independence In the credit card example, are Own/Rent and Accept/Reject independent? Hypothesis: Prob(Ownership) and Prob(Acceptance) are independent Formal hypothesis, based only on the laws of probability: Prob(Own,Accept) = Prob(Own)Prob(Accept) (and likewise for the other three possibilities. Rejection region: Joint frequencies that do not look like the products of the marginal frequencies.

A Contingency Table Analysis

Independence Test Step 2: Expected proportions assuming independence: If the factors are independent, then the joint proportions should equal the product of the marginal proportions. Hypothetical (Actual) [Rent,Reject] 0.54404 x 0.21906 = 0.11918 (.13724) [Rent,Accept] 0.54404 x 0.78094 = 0.42486 (.40680) [Own,Reject] 0.45596 x 0.21906 = 0.09988 (.08182) [Own,Accept] 0.45596 x 0.78094 = 0.35606 (.37414)

Comparing Actual to Expected

When is Chi Squared Large? For a 2x2 table, the critical chi squared value for α = 0.05 is 3.84. (Not a coincidence, 3.84 = 1.962) Our 103.33 is large, so the hypothesis of independence between the acceptance decision and the own/rent status is rejected.

Computing the Critical Value For an R by C Table, D.F. = (R-1)(C-1) CalcProbability Distributions  Chi-square The value reported is 3.84146.

Analyzing Default Do renters default more often (at a different rate) than owners? To investigate, we study the cardholders (only) We have the raw observations in the data set. DEFAULT OWNRENT 0 1 All 0 4854 615 5469 46.23 5.86 52.09 1 4649 381 5030 44.28 3.63 47.91 All 9503 996 10499 90.51 9.49 100.00

Hypothesis Test

In my sample of 210 travelers between Sydney and Melbourne, it appears that there is a relationship between income and the decision whether to fly or not. Do the data suggest that the mode choice and income are independent?

Treatment Effects in Clinical Trials Does Phenogyrabluthefentanoel (Zorgrab) work? Investigate: Carry out a clinical trial. N+0 = “The placebo effect” N+T – N+0 = “The treatment effect” Is N+T > N+0 (significantly)? Placebo Drug Treatment No Effect N00 N0T Positive Effect N+0 N+T

Confounding Effects

What About Confounding Effects? Normal Weight Obese Nonsmoker Smoker Age and Sex are usually relevant as well. How can all these factors be accounted for at the same time?