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Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 1C
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Candidates Judge 1 Judge 2 98 94 97 97 3. 95 98 4 90 95 89 92 6. 88 90 85 89 8 85 85 Solution: Candidates Judge 1 Judge 2 R1 R2 d. d? 1 98 94 1 4 -3 9. 97 97 0. 3 95 98 3 1 4 4 90 95 4 3 1 1 89 92 6. 88 90 7 85 89 7 7 0.5 0.25 8. -85 85 8 8 -0.5 0.25 Ed? =14.5 6(14.5) 8(82 – 1) 6Σd = 1 – = 0.83 p= 1 – n(n² – 1) Interpretation: The computed g = 0.83 indicates a "very high" positive correlation between the ranks. This means that those candidates who received high ranks from the first judge are also the candidates who received the same high ranks from the second judge. Similarly, those candidates who were ranked low by the first judge were also ranked low by the other judge. This means that the rankings of the two judges have a "very high" degree of agreement. It also implies that as to the selection of Mr. Campus Personality, the two judges have more or less the same "taste." LO
Transcribed Image Text:Candidates Judge 1 Judge 2 98 94 97 97 3. 95 98 4 90 95 89 92 6. 88 90 85 89 8 85 85 Solution: Candidates Judge 1 Judge 2 R1 R2 d. d? 1 98 94 1 4 -3 9. 97 97 0. 3 95 98 3 1 4 4 90 95 4 3 1 1 89 92 6. 88 90 7 85 89 7 7 0.5 0.25 8. -85 85 8 8 -0.5 0.25 Ed? =14.5 6(14.5) 8(82 – 1) 6Σd = 1 – = 0.83 p= 1 – n(n² – 1) Interpretation: The computed g = 0.83 indicates a "very high" positive correlation between the ranks. This means that those candidates who received high ranks from the first judge are also the candidates who received the same high ranks from the second judge. Similarly, those candidates who were ranked low by the first judge were also ranked low by the other judge. This means that the rankings of the two judges have a "very high" degree of agreement. It also implies that as to the selection of Mr. Campus Personality, the two judges have more or less the same "taste." LO
E xtension The Statistics of Ranks Spearman Rho Beauty contests are very popular not only among Filipinos but also to many people around the world. Normally, when the names of the five finalists are announced, people place their own bets on who will be the queen and the runners-up. Very often, they are happy about the results. This happens when their ranks agree with the ranks assigned by the board of judges. There might be some slight differences between the ranks assigned by the people and those by the board of judges but if overall, there is a positive correlation (or agreement) between these ranks, then everyone will be happy about the results. In this next statistical measure, we shall be concerned with correlation between ranks. Like in simple correlation, we have cases of positive correlation, zero correlation, or negative correlation. A positive rank correlation indicates that those categories that are given high ranks by one judge (or rater) are also the categories that are assigned high ranks by the other rater. Or those with low ranks in one have also low ranks in the other. A negative rank correlation is the reverse. It means that those categories who were assigned high ranks by the first rater were given low ranks by the second rater, or vice versa. The most common method used in rank correlation is the statistics developed by Spearman, where the coefficient used is symbolized by ọ (rho, Greek letter for r). To compute r, we use the formula 6Ed? p = 1 -. n(n² – 1) where d = difference between ranks n = number of categories given ranks In interpreting the computed value, we use the same qualitative interpretation as the one we use in interpreting r. Let us take this example: In a contest for Mr. Campus Personality, two judges gave their ratings to eight candidates. Transform the ratings to ranks and compute the coefficient of rank correlation. Interpret results.
Transcribed Image Text:E xtension The Statistics of Ranks Spearman Rho Beauty contests are very popular not only among Filipinos but also to many people around the world. Normally, when the names of the five finalists are announced, people place their own bets on who will be the queen and the runners-up. Very often, they are happy about the results. This happens when their ranks agree with the ranks assigned by the board of judges. There might be some slight differences between the ranks assigned by the people and those by the board of judges but if overall, there is a positive correlation (or agreement) between these ranks, then everyone will be happy about the results. In this next statistical measure, we shall be concerned with correlation between ranks. Like in simple correlation, we have cases of positive correlation, zero correlation, or negative correlation. A positive rank correlation indicates that those categories that are given high ranks by one judge (or rater) are also the categories that are assigned high ranks by the other rater. Or those with low ranks in one have also low ranks in the other. A negative rank correlation is the reverse. It means that those categories who were assigned high ranks by the first rater were given low ranks by the second rater, or vice versa. The most common method used in rank correlation is the statistics developed by Spearman, where the coefficient used is symbolized by ọ (rho, Greek letter for r). To compute r, we use the formula 6Ed? p = 1 -. n(n² – 1) where d = difference between ranks n = number of categories given ranks In interpreting the computed value, we use the same qualitative interpretation as the one we use in interpreting r. Let us take this example: In a contest for Mr. Campus Personality, two judges gave their ratings to eight candidates. Transform the ratings to ranks and compute the coefficient of rank correlation. Interpret results.
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