[R] acutally a statistics question

[Peter Dalgaard BSA]

Jan Malte Wiener <jan.wiener at tuebingen.mpg.de> writes:

> hi,
> knowing there are a lot of statistics guru's in the R-mailing list, i
> throw in a statistics question.
> 
> i have data that i do not know how to statistically test:
> 
> subjects are repeatedly asked to make a decision (e.g. left-right ->
> coded as 0 or 1). i have 20 subjects, each subject made 8 decisions.
> 
> i now want to analyse whether my experimental manipulation induced a
> systematic bias in subjects answers. if that wasn't true i expected a
> chance level of 0.5 (50% left, 50% right).
> 
> the way i am analysing my data right now is that i calculate the mean
> of the single trials for each subject (mean of (0,1,1,1,1,0,0,1) =
> 0.625).
> now i have a vector of single subjects preferences.
> 
> assuming this distribution was normally distributed i could perform a
> one-sample t-test against a chance level (e.g. 0.5).
> obviously my data are not normally distributed -> so i guess my
> question really is: which non-parametric test does test a distribution
> against a given theoretical value (and of course-> does it exist in R)
> ?

The Wilcoxon signed-rank test.

(wilcox.test(x,mu=.5) where x is your vector of per-person means)

I wouldn't expect the distribution of individual means to be radically
different from a Normal distribution though, and in fact even in the
extreme case where all responses are either (0,...,0) or (1,...,1) --
but equally many of them under the null hypothesis -- the t-test
should have the correct distribution to quite high accuracy.
-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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