The mean you calculate for a subject is the proportion of times that person chose "1". If you are willing to assume that the 8 decisions are repeats of the same performance (at least in the sense of being exchangeable), the number of "1"s is binomially distributed. Unless the aforementioned assumption is wildly incorrect, the proportions of the 20 Ss may be assumed to be approximately normally distributed with mean P (the population proportion) and variance P(1-P)/N. You can then apply standard tests of the hypotheses (1) that P(experimental Ss) = P(control Ss); (2) that P(experimental Ss) = 0.5; (3) that P(control Ss) = 0.5. I presume that your experimental manipulation implies two groups of 10 Ss each. This may be a little thin for the normal approximation. If that worries you, you could carry out the test assuming only that the binomial distribution applies (which entails rather more computation) and compare those results with results obtained assuming normality.
On Thu, 26 Sep 2002, Jan Malte Wiener wrote: > I have data that i do not exactly know how to statistically analyze: > > 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). Did the experimental manipulation apply to all 20 subjects, or did you have a control group that was not manipulated? > obviously my data are not normally distributed -> As remarked above, they may be be approximately normal. > so i guess my question really is: which non-parametric test does test > a distribution against a given theoretical value ? You mean, "test the mean of a distribution vs. a given value"? > Someone told me to use a 1-sample Wilcoxon signed rank test ??? Could do, I suppose; but the basic rank-sum tests don't perform well when there are lots of ties, and you only have 9 possible values (0/8 to 8/8) for each of your 20 Ss. And the "large-sample" form of the Wilcoxon assumes approximate normality anyway. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 [Old address: 184 Nashua Road, Bedford, NH 03110 (603) 471-7128] . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
