Well, Once again I would like to thank you both for your time and effort in helping me out. Not only by pointing me to the method I should use, but also to explaining why this method is 'better'.
So far, I only considered the 'individuals' problem as a problem of 'values'; meaning that the differences between the individuals would be so large that the differences within the individuals would not be detected. And that was exactly what I meant by "individual variation" will "always" have effect". You cannot really discuss the exact 'values' of the samples, you can only discuss their value compared to the other values within the same subject. So I used the ranking, to indicate an 'order'. And essentially I am trying to find out if the 'same' order can always be found within one specimen. So though I agree that the average within one specimen will always be 4.5. (In fact, I have computed that, when I absentmindedly indicated that I wanted a descriptive table), I am not interested in the average value if the eight samples within one specimen, I am interested in the average value of 21 positions A. However, I never got the idea that, as Mr. Jansen pointed out, using 'individual' as an extra factor would have influences on the degrees of freedom and the way in which the sums of squares are computed. I only realised that when I read your second mail. So, I've taken the advice of Mr. Jansen, and implemented the four-way ANOVA as he suggested. Much to my surprise, I really got results I could work with. :-) I was really scared that using an ANOVA in which all three factors (Front-Back, Left-Right, and Top-Down) were taken into account would lead to very complicated results. And actually, the three-way ANOVA I performed on my ranked data (using no blocking effect for 'individual' effect) indeed did give that. So I was trying to interpret significant interaction effects like "The front-back effect differs for the left and the right side" and "The front-back effect differs for the top and down side" simultaneously. And frankly, that is far more difficult (not to mention 'explainable to others') than I thought. However, when I performed the suggested four-way ANOVA, I found that either main effects or main effects combined with only one interaction are present. This means that I can actually transform the outcome of this analysis into something that can be explained understandable. An unexpected side-effect is that hardly any left-right differences are detected, which makes my data more in agreement with the data of others, which of course is always nice to find. So, in conclusion: you both really helped me very much. You explained really clearly what I should do, what I should do not, eve after it turned out I did not give all the information needed. I must say I found it more difficult than I thought to explain the purpose of the analysis as well as the problems of your analysis in a not-too-long posting. Especially, since you have to add your thoughts as well. Thank you very very much for your effort, I hope it will help other people as well. I'm completely happy now :-) Marlies ----------------- e-mail address does exist, but is not used . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
