Hello statistics-group,
Basically, my main question is whether or not I am statistically
allowed to do a hypothesis-testing as described below.
However, if you have a great idea for doing it completely different,
yet no too complicated to explain a statistics-'beginner', feel free
to comment.
I hope I wrote it down in an comprehensive way, not too long, not too
short and not using any words that might give the wrong impression. I
will be using SPSS for my analysis, though I do not think it should
matter for my question.
Thank you for reading it
Marlies
---------------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.
---------------- Example of proposed analysis
-------------------------------
Data can be written down as follows:
| Front | Back | Total
------------------------------------------------------------
Top_Left | mu_TLF | mu_TLB | mu_TL*
Top_Right | mu_TRF | mu_TRB | mu_TR*
Down_Left | mu_DLF | mu_DLB | mu_DL*
Down_Right | mu_DRF | mu_DRB | mu_DR*
-------------------------------------------------------------
Total | mu_*F | mu_*B | mu_**
With:
mu_TLF = the average (N=21) value of all Top-Left specimens in the
Front-plane.
Initially I'm only interested in the question:
H0: mu_*F = mu_*B
"Is there a difference in the average value of the Front and Back
data?"
However, if the H0 should be rejected (i.e. there is a difference in
the average value of the Front and Back planes), then I am interested
in four contrasts:
H0: mu_TLF = mu_TLB
H0: mu_TRF = mu_TRB
H0: mu_DLF = mu_DLB
H0: mu_DRF = mu_DRB
"Is there a difference in the mean of Front- and Back data in the
TL-region?"
"Is there a difference in the mean of Front- and Back data in the
TR-region?"
"Is there a difference in the mean of Front- and Back data in the
DL-region?"
"Is there a difference in the mean of Front- and Back data in the
DR-region?"
My idea was to use a two-way ANOVA, containing two factors:
'plane' (levels: Back and Front)
'position' (levels: TL, TR, DL, DR)
* A significant effect for main factor 'plane' would indicate that a
difference exists between the Front- and Back planes for all regions.
No further analysis necessary.
* A significant effect for main factor 'plane' and/or a significant
effect for the interaction factor 'plane*position' would indicate that
a difference exists between the Front- and Back planes, but not for
all regions.
A follow-up analysis is performed for each of the four contrasts,
using \lmatrix (in SPSS)
* A significant main effect for 'position' will be ignored, because it
indicates that the four positions within one of the planes differ.
This effect will however be analysed with one of the other two-way
ANOVA analyses.
-------------Questions -------------------------------------
Essentially I have four questions:
- Is the test I prescribed (two-way ANOVA) a good way to perform such
an analysis
- Is it 'allowable' to ignore significant influences because you
'know' it is irrelevant what is means.
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)
.
.
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