511_Chap4 - Alternatives to the t-Tools Stat 511 Chap 4...

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Stat 511 Chap 4 1 Alternatives to the t-Tools Stat 511 Chap 4
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Stat 511 Chap 4 2 Case Study 1: O-Ring Failures
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Stat 511 Chap 4 3 Case Study 1: O-Ring Failures observational study highly unbalanced far from normal apparently equal standard deviations – larger sample size is associated with smaller standard deviation 1 2 Count 1 2 3 4 5 10 15 Count 0 1 2 3
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Stat 511 Chap 4 4 Case Study 2: Cognitive Load randomized experiment students not randomly selected highly skewed distributions ‘censored’ data St em Leaf 21 0 20 6 19 7 18 3 17 16 15 5 14 8 13 2 12 11 10 9 8 00 7 0357 6 8 Count 1 1 1 1 1 1 1 2 4 1 St em Leaf 30 00000 29 28 27 26 5 25 24 2 23 22 8 21 20 19 18 17 7 16 1 15 0 14 6 13 09 Count 5 1 1 1 1 1 1 1 2 50 100 150 200 250 300 TIME CONVENTIONAL MODIFIED TREATMT
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Stat 511 Chap 4 5 Drastic Violations of t-test Assumptions Example -- Space Shuttle O- Ring data What assumptions are violated? normality (drastically violated) equal standard deviations? Will the log transformation help? 1 2 Count 1 2 3 4 5 10 15 Count 0 1 2 3
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Stat 511 Chap 4 6 Drastic Violations of t-test Assumptions Cognitive Load data What assumptions are violated? data are censored normality Will the log transformation help? St em Leaf 21 0 20 6 19 7 18 3 17 16 15 5 14 8 13 2 12 11 10 9 8 00 7 0357 6 8 Count 1 1 1 1 1 1 1 2 4 1 St em Leaf 30 00000 29 28 27 26 5 25 24 2 23 22 8 21 20 19 18 17 7 16 1 15 0 14 6 13 09 Count 5 1 1 1 1 1 1 1 2
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Stat 511 Chap 4 7 The Rank-Sum Test The Rank-Sum has several names Wilcoxon Rank-Sum Test Mann-Whitney U Developed in the 1940’s by Frank Wilcoxon – a chemist, not a statistician
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Stat 511 Chap 4 8 The Rank-Sum Test a nonparametric or distribution free tool no specific distributional assumptions (like normality) required tests the null hypothesis of identical population medians an implied assumption is that the populations have the same spread
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Stat 511 Chap 4 9 The Rank-Sum Test Performs nearly as well as the two-sample t- test when the data are normal and CONSIDERABLY BETTER when there are extreme outliers.
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