511_Chap5 - Comparisons Among Several Samples Stat 511 Chap...

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Stat 511 Chap 5 1 Comparisons Among Several Samples Stat 511 Chap 5
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Stat 511 Chap 5 2 Purpose of this chapter In the previous chapters we compared two groups In chapter 5 we compare 3 or more groups. Concepts are similar, but there are things to take advantage of, new questions to ask, and some new things to worry about. The usual procedure for making inferences when 3 or more groups are being compared is called Analysis of Variance (ANOVA) – but our author initially avoids the name so that you won t think ANOVA is something like Levene s test
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Stat 511 Chap 5 3 What we mean!! ANOVA ANalysis Of VAriance A better way to think of it Analysis of Means relative to Variances
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Stat 511 Chap 5 4 Case 5.1 Diet vs Longevity randomized experiment mice not randomly selected? 6 treatment groups 2 groups can t fully answer the research questions box plots are very useful 10 20 30 40 50 LIFETIME aNP bN/N85 clopro dN/R50 eR/R50 fN/R40 DIETa
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Stat 511 Chap 5 5 Display 5.3 Page 116 In addition to question – Does diet make a difference, there are several specific questions we would like to answer. We could answer these questions with ordinary 2-sample t-tools, but this chapter describes an improved method that takes advantage of all of the data
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Stat 511 Chap 5 6 Case 5.2 Spock Trial Jury selection is in three steps Clerk of Court selects 300 potential jurors at random Before a trial, a venire of 30 jurors chosen at random Final jury chosen by lawyers, not at random
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Stat 511 Chap 5 7 The Data 5 10 15 20 25 30 35 40 45 50 PERCENT A B C D E F SPOCK'S JUDGE
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Stat 511 Chap 5 8 Two Important Questions Does Spock s judge have fewer women in his venire s than the other judges? Yes! Do the other six judges differ in their % women? Probably not. What is the scope of inference? Two-sample t-tools aren t appropriate for answering these questions
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Stat 511 Chap 5 9 General Approach same as for two-sample problems graphical exploration of data (often with side- by-side box plots) identification and examination of outliers consideration of transformations application of appropriate inferential techniques
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Stat 511 Chap 5 10 Comparing Any Two Means With two treatment groups we almost always are making inferences about: μ 2 μ 1 But if we have 5 treatments, the research question might require inferences about μ 3 μ 2 or μ 1 μ 4 or even something exotic like μ 1 – (1/4)( μ 2 + μ 3 + μ 4 + μ 5 )
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11 Multiple Comparison Problem Suppose we have 10 treatment groups, and the research question is whether any of the possible 2-mean comparisons (pairwise differences) are real? How many pairwise differences are
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511_Chap5 - Comparisons Among Several Samples Stat 511 Chap...

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