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Non-parametric test Introduction, Wilcoxon rank sum test and Man-Whitney U test Reporter: Shao-Li Han

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Non-Parametric Test Parametric tests: certain assumptions Non-parametric tests: fewer assumptions need

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Advantage Few or no assumption Reduce the effect of the outlies Even for ordinal and sometimes even nominal data Nominal data: Ex. Marriage status: single, marriage, devoiced, widow… Ordinal data: Ex. The academic performance: A, B, C, D and E

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Statistic Character No estimate of variance No confidence interval Fewer measures of effect size Chi-Square test of independence is one of non-parametric statitics Median, instead of the mean Not as powerful as parametric alternatives!!

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Sign Test When to apply: conditions that single sample t-test are not met. Binomial test Example 1

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Observation Use less number One tail or 2 tails =>excel function, =binomdist provided one tail probablity Not for ranked-signs, for example 1, there should be different influence in “50” and “25” on the result, although the signs of the two value are all “1”. Wilcoxon’s ranked-sign test!

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Wilcoxon Rank Sum Test for Independent Samples 2 independent samples are drawn from populations with an ordinal distribution. H0: the observations come from the same population. The probability when x 0 > y 0 and x 0

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Different sample size A bit more care is required W represents the left tail static; W’ for right tail statictic Using reverse ranking Example

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If 2 samples are sufficiently large Sample size > 10 or greater than 20 Wilcoxon table W statistic is approximately normal N(μ,σ) Example 3

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Effect Size Given by the correlation coefficient (M1-M2)/Standard deviation

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Mann-Whitney U Test Alternative form of Wilcoxon rank-Sum test No matter which sample is bigger!! Mann-Whitney TablesTables Observed value of U Reject the hypothesis Mathematic processing …ex. U1+U2=n1*n2… Examples…

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Example ADHD vs non-ADHD children Academic performance, A, B, C among students from a given grade 1 elementary school. By using Wilcoxon rank sum test or Mann-Whitney U test Sample size > 20 (in excel file)

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