Mann-Whitney U and Wilcoxon signed-rank

• Mann-Whitney U

  The non-parametric version of the independent t-test

  looks at difference between two un-related samples of scores, based on difference ranks of the score

  
  

  Design - between-subjects design, comparing two different groups -> can be naturally occurring or experimental

  
  

  Assumptions - data is continuous/scale (i.e. interval or ratio), data extremely skewed (changes raw data into ranks), data is ordinal.
• MWU theory

  Scores ranked as if they’re one group but are kept separate so that total ranks for each group can be calculated

  After calculations, use critical value table

  If U <= to the table value, it is significant

  
• MWU code

  wilcox.test(DV~IV)
• Effect size

  Vargha-Delaney’s A - This measure tells us how often, on average, which condition outperforms the other

  When applied to 2 conditions, the A measure is a value between 0 and 1:

  
  

  A = 0.5, the two techniques achieve equal performance

  A < 0.5, first condition has lower values

  A > 0.5, second condition has lower values

  
  

  The closer to 0.5, the smaller the difference between techniques

  The farther from 0.5, the larger the difference
• VDA code

  VD.A(DV~COND)
• MWU write up

  need descriptives. use table one. print(table, nonnormal = TRUE). gives median and IQR

  A Mann-Whitney U test found … to be statistically significantly … in the … condition (Mdn = X.XX, IQR = X) vs. the … condition (Mdn = X.XX, IQR = X), W = XX, p = .XXX, A = .XX
• Wilcoxon signed rank

  The non-parametric version of the paired-samples t-test.

  Design - within-subjects design, comparing one group at two different time points or conditions -> can be naturally occurring or experimental

  Assumptions - skewed continuous/scale (i.e. interval or ratio) data or data is ordinal
• WSR theory


  looks at the differences between two related samples, is based on ranking the data rather than just the sign of the difference.

  the difference between the two conditions are ranked, lowest to highest.

  there are then + or - ranks, separately summed up to get a T+/- value.

  Smallest T value is used to determine significance, has to be <= to critical value on table at correct significance lvl and N.

  
• WSR code

  wilcox.test(…, …, paired=T)

  comma not tilda as there are no IV or DV.

  VD.A(…, …)

  effect size

  print(table, nonormal = TRUE)

  gives descriptives (Mdn and IQR)
• WSR write ep

  A Wilcoxon test found … to be statistically significantly … in time-point 1 (Mdn = X.XX, IQR = X) vs time-point 2 (Mdn = X.XX, IQR = X), V = X.X, p = .XXX, A = .XX

  or no significant difference
• wide vs long

  format can be wide or long.

  
  

  if long, label timepoints

  data$time<-factor(data$time,

  levels=c(1, 2),

  labels=c(“…”, “…”))

  
  

  wilcox.test(DV~time, paired=T)

  Need paired, otherwise a MWU will be ran