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Chapter 11

# Chapter 11 - Review Quantitative Data Analyses so far One...

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Review: Quantitative Data Analyses so far

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σ 2 =? p = ? µ = ? σ known σ not known One population tests µ 1 = µ 2 2 populations test
Quantitative Bivariate Data What about Qualitative Data?

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Chapter 11 Applications of Chi Square
Chi-Square Statistic Qualitative Data Have Observed numbers = Counts Ex: The number of men vs. women that smoke or don’t smoke Three Types of Chi Square Tests 1) 2) 3

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All 3 tests use same statistic equation Different equation (from Chapter 5) but same Table 8 O = Observed Number E = Expected Number 1 tailed tests: interest is the right tail = big χ 2 * values What does a small χ 2 * value mean?
- = E E O 2 2 ) ( * χ 0 0

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Chi Square Tests 1) Goodness of Fit Tests Book calls multinomial experiments 2) Tests of Independence 3) Tests of Homogeneity (treatment effects) Qualitative Data (observed #s) 1 qualitative variable 2 qualitative variables
Goodness of Fit Tests Flashback: Do data fit binomial distribution? Key Points: You have a single list of observed numbers in categories Question drives hypotheses H o : H a : Hypotheses often verbal statements

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Do car crashes occur on different days with the same frequency? Sample from Maryland in May 2004 Example Test the claim that accidents occur with equal frequency Use α = 0.05 What is the expected # for each square given the question ? Day Sun Mon Tue Wed Thur Fri Sat # Fatalities 31 20 20 22 22 29 36
1 . State your question (ID population) Are fatal auto accidents equally likely on all days in Maryland? 2. State your H o and H a (define symbols)

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Calculate test statistic need to calculate expected values expected #s based on null hypothesis here: accidents equally likely on all days so: take the total # of accidents and divide by 7 to get the expected # for each day =180 ∕ 7 = 25.7 -Chi Square tests do have 1 Assumption:
Day Sun Mon Tue Wed Thu Fri Sat # fatalities Observed 31 20 20 22 22 29 36 # fatalities Expected 25.7 25.7 25.7 25.7 25.7 25.7 25.7 - = E E O 2 2 ) ( * χ

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- = E E O 2 2 ) ( * χ

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