Chapter 11 - Chapter 11: Goodness of Fit and Contingency...

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Chapter 11: Goodness of Fit and Contingency Analysis Chapter 11: Two types of tests 1. Goodness-of-fit Actual frequency distribution tested against an expected frequency distribution E.g., test that sample data has a normal distribution 2. Contingency Analysis Frequency distributions between two variables are compared with one another E.g., test that there is a relationship between two variables based on their distributions
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Chapter 11: Goodness of Fit and Contingency Analysis 1. Kolmogorov-Smirnov Goodness-of-Fit Test. 2. Chi-Square Goodness-of-Fit Test. Chapter 11: Three actual tests will be examined. 3. Chi-Square Contingency Analysis.
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Chapter 11: Goodness of Fit and Contingency Analysis Test #1: Kolmogorov-Smirnov (K- S) “Goodness -of- Fit” Recall : assumption of parametric tests requires that samples are drawn from a normally distributed population. Q : Is there some way we can test to see if our samples are normally distributed (i.e., so we know if applying a parametric test is appropriate)? A : Yes, we use the K-S test. The K-S test for Normality : compares the cumulative relative frequencies (CRF) of observed sample data with that of a perfect normal distribution. Recall that CRF can be shown as an OGIVE . If the two OGIVEs “match”, the sample distribution can be considered normal
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Chapter 11: Goodness of Fit and Contingency Analysis Test #1: Kolmogorov-Smirnov (K- S) “Goodness -of- Fit” p.32: Ogive (Cumulative Frequency) p. 157: examples of observed and expected (normal) ogives Q. becomes: does the CRF match that of a normal distribution?
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Chapter 11: Goodness of Fit and Contingency Analysis Structure of hypothesis tests : H o : Observed CRF = Expected CRF (i.e., the population from which the sample is drawn is normally distributed). H A : Observed CRF ≠ Expected CRF (i.e., the population from which the sample is drawn is not normally distributed). Test #1: Kolmogorov-Smirnov (K- S) “Goodness -of- Fit” CRF: Cumulative relative frequency. Test Statistic = D statistic, using the D-distribution: D = maximum |CRF o – CRF e | o=observed; e = expected
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Chapter 11: Goodness of Fit and Contingency Analysis Test #1: Kolmogorov-Smirnov (K- S) “Goodness -of- Fit” Step 1: Find the CRF for the observed and expected (normal) distributions.
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Chapter 11 - Chapter 11: Goodness of Fit and Contingency...

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