Quantitative Research Methods - Non-Parametric statistics
- Created by: Shelly23
- Created on: 12-01-17 16:52
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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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