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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 box2 Topics of Chapter 15 box5 1. Chi-Squared Goodness-of-Fit Test box5 2. Chi-Squared Tests of a Contingency Table box5 3. How z-Tests and Chi-Squared Tests relate 2 box5 4. Chi-Squared Test for Normality Chap 15: Chi-Squared Tests box2 Chi-Squared Goodness-of-Fit Test box5 The ANOVA technique asks the following question: square6 Assuming that all populations have the same mean -- how likely is the observed variation between treatments? 3 box5 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. square6 We start explaining it with an example. box2 1. Chi-Squared Goodness-of-Fit Test box5 Example (p582-4): square6 Say, the market shares of company A, B, and “others” are before some advertisement campaign 45%, 40% and 15%. Company A then conducts an aggressive campaign. 4 Chap 15: Chi-Squared Tests square6 square6 To find the effectiveness of the campaign, a survey after- wards asked 200 random consumers for their preference: square6 Results: square6 I use Brand A : 102 square6 I use Brand B: 82 square6 I use some other brand: 16

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box2 1. Chi-Squared Goodness-of-Fit Test box5 Step 1: Write down hypotheses: 5 Chap 15: Chi-Squared Tests box2 1. Chi-Squared Goodness-of-Fit Test box5 Step 1: Write down hypotheses: 6 Chap 15: Chi-Squared Tests box5 Step 2: Write down the results in a table. square6 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 box2 1. Chi-Squared Goodness-of-Fit Test box5 Step 3: Compute the χ 2 statistic… square6 which measures the difference between the expected and the observed value (scaled by the expected value). 7 Chap 15: Chi-Squared Tests box2 1. Chi-Squared Goodness-of-Fit Test box5 Step 3: Compute the χ 2 statistic… square6 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
box2 1. Chi-Squared Goodness-of-Fit Test box5 Step 4: Rejection Region & Conclusion square6 Find rejection region: 9 Chap 15: Chi-Squared Tests square6 Conclude: square6 How to do this with Excel? box2 1. Chi-Squared Goodness-of-Fit Test box5 Using Excel: 10 Chap 15: Chi-Squared Tests That’s it! Yes, it is really that easy! box2 1. Chi-Squared Goodness-of-Fit Test box5 Another example. box5 Suppose: square6 We only had 2 categories, company A and company B. 11 Chap 15: Chi-Squared Tests square6 Before campaign: 55% versus 45% market share. square6 After campaign, survey of 200 people with results: square6 use Brand A: 124 square6 use Brand B: 76 box5 Practice: Solve!

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

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