# Lec13 - How to do a(nondirectional Wilcoxon-Mann-Whitney...

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How to do a (nondirectional) Wilcoxon-Mann-Whitney Test The Wilcoxon-Mann-Whitney test statistic is denoted U s and measures the degree of shift or separation between the two samples. Large values of U s indicate that the two samples are separated We use the U critical values in Table 6. 1 2 3 5 7 10 13 10 11 15 16 17 20 2 3 7 13 15 16 1 5 10 11 17 20 A B ? Which pair of samples appear more separated ?

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How to do a (nondirectional) Wilcoxon-Mann-Whitney Test Example : Soil respiration Step 1: State hypotheses and choose α H 0 : The gap and growth areas do not differ with respect to soil respiration H A (nondirectional): The distribution of soil respiration rates tends to be higher in one of the two populations α = .05 Step 2: Arrange the observations in increasing order
How to do a (nondirectional) Wilcoxon-Mann-Whitney Test Step 1: State hypotheses and choose α Step 2: Arrange the observations in increasing order The K 2 count: For each observation in sample 2, we count the number of observations in sample 1 that are smaller. Count 1/2 for each tied observation. Check the counts: check that K 1 + K 2 = n 1 n 2 K 1 + K 2 = 49.5+6.5 = 56.0 n 1 n 2 = 7 · 8 = 56 Step 3: Determine two counts, K 1 and K 2 and check your counts The K 1 count: For each observation in sample 1, we count the number of observations in sample 2 that are smaller. Count 1/2 for each tied observation.

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How to do a (nondirectional) Wilcoxon-Mann-Whitney Test Step 1: State hypotheses and choose α Step 2: Arrange the observations in increasing order Step 3: Determine two counts, K 1 and K 2 and check your counts U s =49.5 Step 5: Determine the P -value computationally or by bracketing in Table 6 n equal to the larger sample size and n ´ equal to the smaller sample size Step 4: The test statistic U s is the larger of K 1 and K 2 n = 8 n’ = 7
U s =49.5 n = 8 n’ = 7 U s =49.5 The P -value is between .01 and .02 Thus P < .05 and we reject H 0

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If U s is exactly equal to a critical value, then the P -value is less than the column heading An important technicality U s =46 For example, if U s = 46, then .02 < P -value < .05 U s =55 if U s = 55, then P -value < .001 U s =47 if U s = 47, then .02 < P -value < .05
How to do a (directional) Wilcoxon-Mann-Whitney Test Step 1: State hypotheses and choose α Step 2: Arrange the observations in increasing order Step 3: Determine two counts, K 1 and K 2 and check your counts Step 4: The test statistic U s is the larger of K 1 and K 2 Step 5: Determine the P -value computationally or by bracketing in Table 6 n equal to the larger sample size and n ´ equal to the smaller sample size Step 3.5: Check directionality Check whether the data deviate from H 0 in the direction specified by H A by comparing K 1 to K 2 . (a) If not, the P -value is greater than .50 (b) If so, proceed to step 4 For directional tests, use the one-tail probabilities

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Example In a pharmacological study, researchers measured the concentration of the brain chemical dopamine in six rats exposed to toluene and six control rats. The concentrations in the striatum region of the brain were: Dopamine (ng/g) Toluene Control 3,420 1,820 2,314 1,843 1,911 1,397 2,464 1,803 2,781 2,539 2,803 1,990
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Lec13 - How to do a(nondirectional Wilcoxon-Mann-Whitney...

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