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Non-parametric test. Introduction, Wilcoxon rank sum test and Man-Whitney U test Reporter: Shao-Li Han. Non-Parametric Test. Parametric tests: certain assumptions Non-parametric tests: fewer assumptions need . Advantage. Few or no assumption Reduce the effect of the outlies

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## Non-parametric test

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**Non-parametric test**Introduction, Wilcoxon rank sum test and Man-Whitney U test Reporter: Shao-Li Han**Non-Parametric Test**• Parametric tests: certain assumptions • Non-parametric tests: fewer assumptions need**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**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!!**Sign Test**• When to apply: conditions that single sample t-test are not met. • Binomial test • Example 1**Observation**• Use less number • One tail or 2 tails =>excel function, =binomdistprovided 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!**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 x0> y0 and x0<y0 is just the same • They have the same medians. W left tail statistc • Example 2 Nominal data: Ex. Marriage status: single, marriage, devoiced, widow… Ordinal data: Ex. The academic performance: A, B, C, D and E**Different sample size**• A bit more care is required • W represents the left tail static; W’ for right tail statictic • Using reverse ranking • Example**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**Effect Size**• Given by the correlation coefficient • (M1-M2)/Standard deviation**Mann-Whitney U Test**• Alternative form of Wilcoxon rank-Sum test • No matter which sample is bigger!! • Mann-Whitney Tables • Observed value of U < Ucrit -> Reject the hypothesis • Mathematic processing …ex. U1+U2=n1*n2… • Examples…**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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