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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

Non-parametric test

Introduction, Wilcoxon rank sum test and Man-Whitney U test

Reporter: Shao-Li Han

non parametric test1
Non-Parametric Test
  • Parametric tests: certain assumptions
  • Non-parametric tests: fewer assumptions need
advantage
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
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
Sign Test
  • When to apply: conditions that single sample t-test are not met.
  • Binomial test
  • Example 1
observation
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
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
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
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
Effect Size
  • Given by the correlation coefficient
  • (M1-M2)/Standard deviation
mann whitney u test
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
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)