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Example 8 rank correlation for tied observations

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Unformatted text preview: found as shown below. Could you find any relation between and tea and coffee price. Price of tea Price of coffee Price of tea 88 90 95 70 60 75 50 Rank 3 2 1 5 6 4 7 88 120 90 134 Price of coffee 120 134 150 115 110 140 100 95 70 60 150 115 110 75 140 50 100 Rank D D2 4 3 1 5 6 2 7 1 1 0 0 0 2 0 1 1 0 0 0 4 0 2 D =6 6ΣD 2 6×6 = 1− 3 3 n −n 7 −7 36 = 1− = 1 − 0.1071 336 = 0.8929 The relation between price of tea and coffee is positive at 0.89. Based on quality the association between price of tea and price of coffee is highly positive. r = 1− Example 7: In an evaluation of answer script the following marks are awarded by the examiners. 1st 88 95 70 960 50 80 75 85 2nd 84 90 88 55 48 85 82 72 209 Do you agree the evaluation by the two examiners is fair? x R1 y R2 D 88 2 84 4 2 95 1 90 1 0 70 6 88 2 4 60 7 55 7 0 50 8 48 8 0 80 4 85 3 1 85 3 75 6 3 D2 4 0 16 0 0 1 9 30 6ΣD 2 6 × 30 = 1− 3 3 n −n 8 −8 180 = 1 − 0.357 = 0.643 = 1− 504 r = 0.643 shows fair in awarding marks in the sense that uniformity has arisen in evaluating the answer scripts between the two examiners. Example 8: Rank Correlation for tied observations. Following are the marks obtained by 10 students in a class in two tests. r = 1− Students A B C D E F G H I J Test 1 70 68 67 55 60 60 75 63 60 72 Test 2 65 65 80 60 68 58 75 63 60 70 Calculate the rank correlation coefficient between the marks of two tests. Student Test 1 R1 Test 2 R2 D D2 A 70 3 65 5.5 -2.5 6.25 B 68 4 65 5.5 -1.5 2.25 C 67 5 80 1.0 4.0 16.00 D 55 10 60 8.5 1.5 2.25 E 60 8 68 4.0 4.0 16.00 F 60 8 58 10.0 -2.0 4.00 G 75 1 75 2.0 -1.0 1.00 H 63 6 62 7.0 -1.0 1.00 I 60 8 60 8.5 0.5 0.25 J 72 2 70 3.0 -1.0 1.00 50.00 210 60 is repeated 3 times in test 1. 60,65 is repeated twice in test 2. m = 3; m = 2; m = 2 1 1 1 6[ΣD 2 + (m3 − m) + (m3 − m) + (m3 − m) 12 12 12 r = 1− 3 n −n 13 1 1 (3 − 3) + (23 − 2) + (23 − 2)] 12 12 12 = 1− 103 − 10 6[50 + 2 + 0.5 + 0.5] = 1− 990 6 × 53 672 = 1− = = 0.68 990 990 6[50 + Interpretation: There...
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