Lecture 9 - Lecture 9: 15 25 0 41 40 39 80 55 65 30 35 40...

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Lecture 9: 15 30 45 Anova: Two-Factor Without Replication Or one way with blocking 25 35 45 0 40 80 summar y Count Sum Averag e Varianc e 41 45 49 Row 1 3 90 30 225 40 50 60 Row 2 3 105 35 100 39 55 71 Row 3 3 120 40 1600 80 60 40 Row 4 3 135 45 16 55 65 75 Row 5 3 150 50 100 65 70 75 Row 6 3 165 55 256 Row 7 3 180 60 400 Row 8 3 195 65 100 Row 9 3 210 70 25 Col. 1 9 360 40 612.75 col.2 9 450 50 187.5 col. 3 9 540 60 242.75 ANOVA Source of Variation SS df MS F P-value F crit Rows 4500 8 562.5 2.341 0.070 2.591 Columns 1800 2 900 3.746 0.046 3.634 Error 3844 16 240.25 Total 10144 26 1 of 10
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For sample data: a=2, n=3 For sample data: b=3, n=3 MBA 612 – Quantitative Problem solving Notes from Lecture 9 The above data set is referenced in the following lecture. This lecture covers three main topics: Topic 1: A-priori test, as applied to one way with blocking Topic 2: Scheffé Method of Identifying differences (Post-hoc test), as applied to one way with blocking Topic 3: Two-way ANOVA 1. A-priori test A-priori test: This is a preconceived hypothesis of interest before seeing results. There are applicable to all ANOVA procedures including one way with blocking . A-priori is used to find out where significant differences are at; once it is determined from the ANOVA procedure that a significant difference does exist. We usually hunt for significant differences among the treatment means. We do not usually perform test of hypothesis hunting for significant differences among blocking means. The only test we perform on the blocked means is to determine whether or not we have blocked on a significant variable. We do that by looking at the F value associated with blocks. General Information Concerning A-Prior Tests and Post Hoc Tests Reviewed An a-priori test has a specified level of alpha assigned to that specific test. Recall that alpha is the probability of rejecting a true hypothesis. The benefit of setting alpha at a reasonable level, (other than zero) is if alpha is set reasonably high, then one has a good probability of identifying significant differences when they do exist. That is, if alpha is reasonable high, then one has
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Lecture 9 - Lecture 9: 15 25 0 41 40 39 80 55 65 30 35 40...

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