Week3BMTB2304 - ADM2304 Wilcoxon Test or Type II Error Dr Suren Phansalker Twenty adults in a random sample were asked to rate politicians in

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ADM2304 Wilcoxon Test & β or Type II Error Dr. Suren Phansalker Twenty adults in a random sample were asked to rate politicians in general, on a scale of 1 to 100. A median score of 50 would indicate that people thought that politicians were OK. Numbers significantly above 50 would indicate that they were thought of as being commendable and numbers significantly below 50 would indicate they were deplorable. Here are the results of the ratings. Data Display Opinion 49 27 39 75 59 67 22 61 58 60 72 62 49 48 19 32 60 80 55 68 Test the hypothesis that: k k 0 :5 A HM d d = 0 0 Here the distribution is reasonably symmetrical but is not known to be normal. As such, testing the Population Median is more appropriate than testing the Population Mean. MTB > boxp c1 Boxplot of Opinion 80 70 60 50 40 30 20 Opinion Boxplot of Opinion Diagram#1 1
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Data Display Row Opinion Median Difference:di Abs(di) Rank R+ R- 1 49 50 -1 1 1.5 17.0 1.5 2 27 50 -23 23 16.0 6.0 16.0 3 39 50 -11 11 9.5 12.0 9.5 4 75 50 25 25 17.0 9.5 18.0 5 59 50 9 9 6.0 5.0 1.5 6 67 50 17 17 12.0 7.5 3.0 7 22 50 -28 28 18.0 15.0 20.0 8 61 50 11 11 9.5 11.0 13.5 9 58 50 8 8 5.0 7.5 10 60 50 10 10 7.5 19.0 11 72 50 22 22 15.0 4.0 12 62 50 12 12 11.0 13.5 13 49 50 -1 1 1.5 14 48 50 -2 2 3.0 15 19 50 -31 31 20.0 16 32 50 -18 18 13.5 17 60 50 10 10 7.5 18 80 50 30 30 19.0 19 55 50 5 5 4.0 20 68 50 18 18 13.5 MTB > print k1-k7 Data Display K1 20.0000 K2 105.000 K3 26.7862 K4 127.000 K5 83.0000 K6 127.000 K7 0.821319 Here: K1 = n = 20 K2 = (1 )2 0 ( 2 0 1 ) 105 44 T nn μ ++ == = K3 = ( 1)(2 1) 20(20 1)(2*20 1) 17220 26.7862 24 24 24 T n σ + + = = K4 = 127 R + = K5 = 83 R = K6 = max( , ) max(127,83) 127 TR R +− ∑∑ = Please note that MiniTab uses the Max Value and the Text Book uses the Min Value. Technically, there is no difference; in effect, only the signs change. 62 7 3 127.0 105.0 0.8213 26.7862 T Calc T KK T Kz K = = = 2
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[ 0.8213]*(2) Calc pV a l PZ z =>= = 2 {0.5 – A(0.8213)} = 2 { 0.5 – 0.2946} = 0.4108 See the graph below.
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This note was uploaded on 01/10/2012 for the course TEFLER 2304 taught by Professor Phansalker during the Winter '11 term at University of Ottawa.

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Week3BMTB2304 - ADM2304 Wilcoxon Test or Type II Error Dr Suren Phansalker Twenty adults in a random sample were asked to rate politicians in

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