Quantitative Research Methods - Non-Parametric statistics

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  • Created by: Shelly23
  • Created on: 12-01-17 16:52

Rank Transformations

  • Generic way of dealing with heavily skewed or otherise difficult data
  • Assign 1 to the lowest value, 2 to the next lowest ect
  • Average score of group for same values (ties)

What are the effects?

  • Will flatten any distributions and remove gaps between outcome value ranges
  • Moves outliers closer to centre of the data
  • Hence deals with the most serious issues in non-normal data: modality, skew, outliers
  • For example identical rank scores for log-normal and transformed normal distributions 

Non-Parametric Correlation Methods

Spearman's rank

  • For non-normal but continuous data (interval and ratio)
  • Can also be used for ordinal data with many levels

Kendall's tau

  • For discrete (ie. whole numbers only) and ordinal data eg ratings on likert scale

Spearman's Rank Correlation

  • Step 1: rank transformation of the x and y variables
  • Step 2: Pearson's r correlation on the transformed variables
  • Correlation coefficent denoted by Greek letter (rho) or rs
  • rho has the ame range (-1,1) and interpretation as Pearsons r
  • rho=  (cov(rank(x),rank(y)) )/(SD(rank(x))∗SD(rank(y)))
  • where rank (x) and rank (y) denoted the rank-transformed variables x and y, respectively

Spearman's rho vs Pearson's r

  • Pearson's r assess the relationship
  • Spearman's assesses only a montonic relationship
  • Similar results if x and y ate near-normal - use Pearson
  • Different if not normal (eg. outliers) - use Spearman

Kendall's Tau Rank Correlation

  • Step 1 - rank transformation of the x and y variables
  • Step 2 - count concordant and discordant pairs

Concordant pair - ranks for both observations (x-y pairsi and j) agree (xi>xj and vi>vj or xi<xj and vi<vj)

Discordant pair - where ranks for both observations (x-y pairs i and j) differ (xi>xj and vi<vj or xi>xj and vi<vj)

  • Corelation coefficent denoted by Greek letter tau
  • Total number of pairs is n(n-1)/2 used as scaling factor
  • Tau has range (-1,1), same interpretation as r and rho
  • τ=  (number

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