"Marlies" <[EMAIL PROTECTED]> schreef in bericht news:[EMAIL PROTECTED] > "Jos Jansen" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > > "Marlies" <[EMAIL PROTECTED]> schreef in bericht > > news:[EMAIL PROTECTED] > > > Hello statistics-group, > > > > > ---------------Explanation of problem ------------------------- > > > > > > I have a set of data, obtained from 21 biological specimen. In each > > > specimen we obtained eight samples, which are positioned like the > > > corners of a cube, meaning every sample has one unique position > > within > > > the specimen based on three 'directional' parameters: Front-Back; > > > Top_Down and Left-Right. > > > > > > I am interested in 'checking' whether or not the eight samples taken > > > from one and the same specimen can be considered equal. I started > > with > > > comparing every sample positions with all sample positions (one-way > > > ANOVA) but this gives too much information (27 pairs of positions) > > to > > > conclude anything comprehensive. > > > > > > So now we try to compare the data according to the three axes of > > > symmetry. > > > Front-Back differences > > > Top-Bottom differences > > > Left-Right differences > > > > > > I'll use the Front-Back differences as an example. > > > > > <snip> > > > > > > My idea was to use a two-way ANOVA, containing two factors: > > > 'plane' (levels: Back and Front) > > > 'position' (levels: TL, TR, DL, DR) > > > > > <snip> > > > -------------Questions ------------------------------------- > > > > > > Essentially I have four questions: > > > > > > - Is the test I prescribed (two-way ANOVA) a good way to perform > > such > > > an analysis > > > > This analysis is not valid. You should take into account the effect of > > specimen as a block effect; failing to do this results in an estimate > > of error which may be too large and has too many degrees of freedom. > > > > > - Is it 'allowable' to ignore significant influences because you > > > 'know' it is irrelevant what is means. > > > > There is nothing wrong in observing significant effects and explaining > > why you are not interested in these effects. > > > > > And if this tests is allowed > > > - Could each test between planes (Front-Back; Left-Right, Top-Down) > > be > > > regarded as an independent test (suggesting a Bonferroni-adjustment > > > per test of p/4 for each single contrast) > > > - Or should all tests be regarded as dependent, suggesting a > > > Bonferroni adjustment of p/12 for each single contrast? > > > (Personally I think I should go for the last option) > > > > The sum of squares for position effects may be decomposed and tested > > in any way you like. But the most straightforward and comprehensive > > analysis would be a decomposition according to that of a full 2^3 > > factorial with specimens as a blocking factor. Main effects > > (Front-Back; Left-Right, Top-Down) and interactions between these may > > be tested independently and no Bonferroni adjustments are required. > > The results may be presented in tables or plots of means, with > > corresponding LSD's (least significant differences) as yardsticks > > indicating their precision. > > > > Jos Jansen > > > Thank you very much for your effort for helping me out with this > question. I hope you can help me some more, but I am afraid it (once > again) is a very long posting. > > Your remark about the block-effect of the specimen pointed out that I > did indeed forgot to mention something important (*sight*). > To avoid problems with non-normality and the 'individual effect', I > ranked all my data within each biological specimen.
This, probably, introduces more problems then those you wanted to avoid. Firstly, your tests should be based then on nonparametric methods, i.c. the Friedman test. Testing contrasts in that case is not straightforward. I can not offer you any guidance in how to proceed in a theoretically sound way. As an approximation you could perform ANOVA on the ranks (as you seem to suggest). But then you will still have to account for the fact that you have ranked the data per specimen. This can be done, again, by introducing the specimen effect as a block effect in the analysis; this will correct the number of degrees of freedom for error and consequently the estimate of error. However, I am not convinced of the merits of this way of analysis, and I would suggest to analyse the original data instead of the ranks. > This, of course, means that any conclusive remarks about my data can > only be stated in terms of 'the means in the LSA-region are generally > higher than the means in the LSP-region'. But since the individual > variation will 'always' have effect, I am only interested in stating > this anyway. Differences between specimen are to be expected, but these can effectively be removed by including this effect in the analysis. But which other "individual variation" will "always" have effect? What is meant by this statement? > However, the proposed analysis, as you prescribe it, is not quite > clear for me. (This is mainly due to my inability to grasp 'short > prescriptions of statistical analysis' than to your explanation, which > was quite elaborate.) > I think what you are suggesting is to do the analysis as I proposed, > but then for every single specimen separately, leading to n=1 in every > column. > This would boil down to an three way ANOVA (factors 'individual', > 'plane' and 'position' ). > Then I should only 'worry' about the main effects of 'plane' and an > interaction effect of 'plane*position' (for the same reasons already > mentioned in my first mail). These main effects can than be analysed > further in the way I proposed in my first mail (using contrasts). > Or did I not understand you explanation at all whatsoever. (BTW, if my > proposed analysis is allowable for ranked data, I'll use that anyway. > So in that case, please don't spend time in explaining this (unless > you want to, of course). This is not what I had in mind. I suggested a 4 factor ANOVA with factors: Blocks (=Specimen) Factor A (Front vs. Back) Factor B (Left vs. Right) Factor C (Top vs. Down) and including interactions AxB, AxC, BxC and AxBxC in the model. Such an analysis is standard practice and allows testing and describing any model for the position effects. Note, that the interaction AxB measures variability of the effect of A over the levels of factor B (or reversed), and so on. The interaction AxBxC may be interpreted e.g as the difference between the levels of factor A with respect to the interaction BxC. It may be difficult to grasp the meaning of this from the words, but plots of means will be helpfull in understanding. In fact, these interactions represent the contrasts you have in mind below. You may look in standard textbooks, such as Cochran and Cox - Experimental Design - chapter on factorial experiments, for further explanation. > Furthermore, am I correct in assuming that the four comparisons are > independent because you are not (unlike post-hoc comparisons) testing > the twelve position-combinations (TL-TR; TL-DL; TL-DR; TR-DL; etc.) > against each other over the two plane-levels. But you are testing four > differences between eight samples (i.e. each sample is tested only > once). > > And if I assumed that correctly; wouldn't that mean that the idea of > splitting the 'whole' analysis up into three separate analyses > (Left-plane vs. Right- plane; Front-plane vs. Back-plane ; and > Top-plane vs. Down-plane) imply that I should indeed apply a > Bonferroni effect to accommodate that every one of the eight specimen > is compared three times in total, suggesting p/3 for every single > comparison. > I mean that position Top-Front-Left (TLF) is compared as follows: > Once in the Top-Down-analysis: TLF-DLF > Once in the Left-Right-analysis: TLF-TRF > Once in the Front-Back-analysis: TLF-TLB > > I hope I have explained myself correctly this time. Once again I would > like to apologise for my neglect of mentioning the 'individual' > factor. > My (new) questions now boil down to: > - Is the analysis as prescribed in the first e-mail allowable if the > 'blocking effect' of the individual specimens in taken into account by > performing a ranking procedure on every individual specimen. > - If so, should I then apply a Bonferroni-factor for the three > separate analyses I am performing > - If not so, then should I apply your suggestion as I tried to > interpret it? > -> And do you know any reference-example (literature or internet) > where the analysis you suggested is explained (I usually need an > example > > Thank you for reading my post and helping me out. I hope I have > clarified myself, instead of making it more muddy. Thank you for all > you help in advance, > > Marlies > > ------------------------- > e-mail adress is valid but I do not read it. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
