Chap15-Chi-Squared-Tests

Chap15-Chi-Squared-Tests - 1 Chap 15: Chi-Squared Tests 2...

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1 CHAPTER 15: CHI-SQUARED TESTS Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 15: Chi-Squared Tests b Topics of Chapter 15 b 1. Chi-Squared Goodness-of-Fit Test b 2. Chi-Squared Tests of a Contingency Table . How z sts and Chi uared Tests relate 2 b 3. How z-Tests and Chi-Squared Tests relate b 4. Chi-Squared Test for Normality Chap 15: Chi-Squared Tests b Chi-Squared Goodness-of-Fit Test b The ANOVA technique asks the following question: s Assuming that all populations have the same mean -- how likely is the observed variation between treatments? 3 b The Chi-Squared Goodness-of-Fit test does something similar: it compares some observed outcome with some expected outcome and judges how likely the observed outcome is. s We start explaining it with an example. b 1. Chi-Squared Goodness-of-Fit Test b Example (p582-4): s Say, the market shares of company A, B, and “others” are before some advertisement campaign 45%, 40% and 15%. 4 Chap 15: Chi-Squared Tests s Company A then conducts an aggressive campaign. s To find the effectiveness of the campaign, a survey after- wards asked 200 random consumers for their preference: s Results: s I use Brand A : 102 s I use Brand B: 82 s I use some other brand: 16
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b 1. Chi-Squared Goodness-of-Fit Test b Step 1: Write down hypotheses: 5 Chap 15: Chi-Squared Tests b 1. Chi-Squared Goodness-of-Fit Test b Step 1: Write down hypotheses: 6 Chap 15: Chi-Squared Tests b Step 2: Write down the results in a table. s Intuitively, how could we measure whether the market shares have changed? What would we expect if H 0 was true? 200*45%=90 200*40%=80 200*15%=30 b 1. Chi-Squared Goodness-of-Fit Test b Step 3: Compute the χ 2 statistic… s which measures the difference between the expected and the observed value (scaled by the expected value). 7 Chap 15: Chi-Squared Tests b 1. Chi-Squared Goodness-of-Fit Test b Step 3: Compute the χ 2 statistic… s which measures the difference between the expected and the observed value (scaled by the expected value). 8 Chap 15: Chi-Squared Tests χ 2 = 8.18
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b 1. Chi-Squared Goodness-of-Fit Test b Step 4: Rejection Region & Conclusion s Find rejection region: 9 Chap 15: Chi-Squared Tests s Conclude: s How to do this with Excel? b 1. Chi-Squared Goodness-of-Fit Test b Using Excel: 10 Chap 15: Chi-Squared Tests That’s it! Yes, it is really that easy! b 1. Chi-Squared Goodness-of-Fit Test b Another example. b Suppose: s We only had 2 categories, company A and company B. 11 Chap 15: Chi-Squared Tests s Before campaign: 55% versus 45% market share. s After campaign, survey of 200 people with results: s use Brand A: 124 s use Brand B: 76 b Practice: Solve!
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This note was uploaded on 03/26/2012 for the course STAT 1100 taught by Professor Chiappetta during the Spring '08 term at Pittsburgh.

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Chap15-Chi-Squared-Tests - 1 Chap 15: Chi-Squared Tests 2...

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