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Non-parametric test for repeated measures and post-hoc single comparisons in R?

6 messages · Tal Galili, Peter Dalgaard, saschaview at gmail.com +1 more

Original
saschaview at gmail.com
# 
Some attribute x from 17 individuals was recorded repeatedly on 6 time 
points using a Likert scale with 7 distractors. Which statistical 
test(s) can I apply to check whether the changes along the 6 time points 
were significant?

set.seed( 123 )
x <- matrix( sample( 1:7, 17*6, repl=T ),
   nrow = 17, byrow = TRUE,
   dimnames = list(1:17, paste( 'T', 1:6, sep='' ))
)

I found the Friedman test and the Quade test for testing the overall 
hypothesis.

friedman.test( x )
quade.test( x )

However, the R help files, my text books (Bortz, Lienert and Boehnke, 
2008; K?hler, Schachtel and Voleske, 2007; both German), and the 
Wikipedia texts differ in what they propose as requirements for the 
tests. R says that data need to be unreplicated. I read 'unreplicated' 
as 'not-repeated', but is that right? If so, the example, in contrast, 
in friedman.test() appears to use indeed repeated measures. Yet, 
Wikipedia says the contrary that is to say the test is good especially 
if data represents repeated measures. The text books say either (in the 
same paragraph, which is very confusing). What is right?

In addition, what would be an appropriate test for post-hoc single 
comparisons for the indication which column differs from others 
significantly?

Bortz, Lienert, Boehnke (2008). Verteilungsfreie Methoden in der 
Biostatistik. Berlin: Springer
K?hler, Schachtel, Voleske (2007). Biostatistik: Eine Einf?hrung f?r 
Biologen und Agrarwissenschaftler. Berlin: Springer
saschaview at gmail.com
#
On 19.02.12 19:31, Tal Galili wrote:

            

      
      
      
    

        
Thank you, Tal! As you already mentioned, your interesting post supports 
Friedman being indeed the right test for my problem, but it does not 
explain why and what my mis-interpretation of unreplicated versus 
unrepeated is.

However, your code may help to run post-hoc single comparisons.

Yet, I may take the chance to clarify that my problem is that Wikipedia, 
text books, and the R help say different things -- at least to my 
understanding.

Anyway, you helped, thank you!

  
  


  


      

    

    

      
      

        


  

        

      Peter Dalgaard
    

    

      
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Repeated measures means that you have multiple measurements on the same individual. Usually, the same person measured at different time points. So if you have N individuals and T times, then you can place your observations in an N*T layout. 

In this layout, you can have 1 observation per cell or R > 1 observations. In the former case, the design is referred to as unreplicated.  Got it?

-pd

        
On Feb 19, 2012, at 19:25 , saschaview at gmail.com wrote:

        

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      saschaview at gmail.com
    

    

      
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Thanks, I got it! (And I think I should have googled what "replicated" 
means!) However, then Bortz, Lienert, Boehnke are imprecise, if not 
wrong: "Der Friedman-Test setzt voraus, dass die N Individuen 
wechselseitig unabh?ngig sind, dass also nicht etwa ein und dasselbe 
Individuum zweimal oder mehrmals im Untersuchungsplan auftritt" (p. 
271). Which I (hope to) translate: The Friedman test requires the N 
individuals to be reciprocally independent, which means that one 
individual cannot occur twice or more times in the research design.

*S*

        
On 19.02.12 22:04, peter dalgaard wrote:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Meyners, Michael
    

    

      
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No, the authors are correct: the individuals (i.e. the 17 individuals) you have need to be independent (i.e. no correlation between them, let alone any individual running through your temporal experiment more than once, as indicated in the citation), while the *observations* are of course dependent as they are within the same subject (individual -- they have the same subject effect). Think of Friedman as a non-parametric 2-way ANOVA with one of the factors being subject; observations of the same subject are dependent, but once you include the subject effect, the errors are assumed to be independent (which implies that subjects need to be independent and should, e.g., not work on the assessment together).
The imprecision is in your interpretation of individuals vs. observations. 
HTH, Michael