"Kasper Hornbaek" <[EMAIL PROTECTED]> schreef in bericht news:[EMAIL PROTECTED] > Hi, > > I have a question on how to analyse an exprimental design. > > We had three treatments (C, T, M) of which only two could be > administred to each subject. The subjects receieved those treatments > in two weeks following each other (W1, W2). I total there were six > experimental groups, each defined by a treatment combination, i.e. > > grp w1 w2 > 1 C T > 2 C M > 3 T C > 4 T M > 5 M C > 6 M T > > We are interested in comparing the effects of treatments, e.g. C vs M. > Right now I am considering a repeated measures analysis, with week and > grp as factors. However, I cannot figure out how to compose the > contrasts that would answer our questions. > > Any hints? Is there some other, conceptually easier approach I could > take? Any litterature on this?
This experimental design is a balanced incomplete block design, with subjects being the blocks . A description of the analysis can be found in any standard book on experimental design and the analysis can probably best be performed by standard software for this type of design. There are two possibilities: intrablock analysis, and analysis with 'recovery of interblock information'. The latter is, in fact, a mixed model analysis. For this special case one could equivalently proceed according to the following lines (I suppose that treatment combinations have been randomly assigned to subjects). Calculate differences and sums per subject. The intrablock analysis can be performed by regression of the differences using 2 contrast vectors for treatments differences (a third would be redundant), and 3 contrast vectors for sequence effects (one for each treatment combination). The interblock analysis can be performed similarly by regression analysis of the sums. The estimates from intra- and interblock analysis may eventually be combined, using the inverse of estmated variances as weights; this may be not worthwile, since the interblock estimates probably are much less precise than the intrablock estimates. This analysis covers all aspects that have been touched in posts by Jim Clark and Donald Burrill. Jos Jansen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
