"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, 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.
Since I have done this quite some time ago, I tend to forget the
'blocking-factor' when I am thinking about 'how to analyse my data
correctly'. My apologies for that, since it is quite an important
point of view for the analysis.
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).
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.
.
.
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