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Lec16 - Assessing the effectiveness of pairing One way to...

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Assessing the effectiveness of pairing One way to detect whether pairing was effective is to look at a scatter plot of the data: On days where the nonmutant strain has high growth, so does the mutant strain. On days where the nonmutant strain has low growth, so does the mutant strain. So on a single day the two strains are more similar to each other than either stain is to itself on two different days An upward trend indicates that pairing is effective Day Mutant Non- mutant 1 160 97 2 36 55 3 82 31 4 100 95 5 140 80 19 58 45
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Under certain conditions, electrical stimulation of a beef carcass will improve the tenderness of the meat. In this study beef carcasses were split in half, one side received current and the other side was an untreated control. Then collagen was taken from each side and the researcher measured the temperature at which the collagen shrinks -- a tender piece of meat tends to have a low collagen shrinkage temperature. Which one of these two data sets suggests that pairing was effective? 66 67 68 69 70 71 66 67 68 69 70 71 Treated side Control side 66 67 68 69 70 71 66 67 68 69 70 71 Treated side Control side A B ? Assessing the effectiveness of pairing
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Match analysis to design If the design is paired , then use a paired- sample analysis If the design is unpaired , then use an independent-sample analysis If you pair the design, but do not use a paired-sample analysis, you waste all the extra information that comes from pairing.
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Nonparametric, distribution free paired tests 1. The sign test -- simple and weak 2. Wilcoxon signed-rank test -- complicated and powerful Example: A veterinary anatomist measured the density of nerve cells at 2 sites in the intestines of 9 horses. He wanted to know whether there was a difference in nerve cell counts.
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Wilcoxon signed-rank test Step 1: State hypotheses and choose α (use α = .05) Step 4: Rank the absolute values from smallest to largest Step 5: Restore the + and - signs to the ranks to produce signed ranks Step 2: Calculate the signs and the differences Step 3: Calculate the absolute value of each difference Step 6: Calculate W + and W - W + = sum of the positive signed ranks W - = sum of the absolute values of the negative signed ranks H 0 : The sites have the same nerve cell density H A : The sites have different nerve cell densities Animal Site 1 Site II Sign d | d | Rank of | d | Signed rank 1 50.6 38.0 + 12.6 12.6 8 8 2 39.2 18.6 + 20.6 20.6 9 9 3 35.2 23.2 + 12.0 12.0 7 7 4 17.0 19.0 - -2.0 2.0 2 -2 5 11.2 6.6 + 4.6 4.6 4 4 6 14.2 16.4 - -2.2 2.2 3 -3 7 24.2 14.4 + 9.8 9.8 5 5 8 37.4 37.6 - -.2 -.2 1 -1 9 35.2 24.4 + 10.8 10.8 6 6 W + = 39 W - = 6
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Wilcoxon signed-rank test Step 6: Calculate W + and W - W + = 39 W - = 6 Step 8: W s is the larger of W + and W - W s = 39 Step 9: Compute or bracket the P -value Step 7: Check directionality if H A is directional Step 1: State hypotheses and choose α (use α = .05) Step 4: Rank the absolute values from smallest to largest Step 5: Restore the + and - signs to the ranks to produce signed ranks Step 2: Calculate the signs and the differences Step 3: Calculate the absolute value of each difference H 0 : The sites have the same nerve cell density H A : The sites have different nerve cell densities
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n = 9 W s = 39 .05 < P < .10
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