16. Mann-Whitney U-Test Used to compare two samples from two populations Assumptions: The two samples are independent and random The value measured is a continuous variable The measurement scale used is at least ordinal If they differ, the distributions of the two populations will differ only with respect to the central location
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19. Mann-Whitney U-Test (continued) Mann-Whitney U-Statistics where: n 1 and n 2 are the two sample sizes R 1 and R 2 = sum of ranks for samples 1 and 2
20. Mann-Whitney U-Test (continued) Claim: Median class size for Math is larger than the median class size for English A random sample of 9 Math and 9 English classes is selected (samples do not have to be of equal size) Rank the combined values and then split them back into the separate samples
24. Mann-Whitney U-Test H 0 : Median M ≤ Median E H A : Median M > Median E Claim: Median class size for Math is larger than the median class size for English Note: U 1 + U 2 = n 1 n 2 (continued) Math: English:
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33. Large Sample Example Since z = -2.80 < -1.645, we reject H 0 Reject H 0 = .05 Do not reject H 0 0 (continued)