Re: ANOVA or battery of t-tests, how to identify subgroups that differ from average across subgroups.

On Sep 28, 7:04 pm, ge...@xxxxxxxxx wrote:
Hello,

I have toxicity measurements for objects which belong to 9
categories (various species of plants)(n=6,6,7,8,5,9,7,2,8). I would
like to know if there is some difference between objects of a category
and the rest of the data. I am not really interested in comparison
category A vs category B but rather to comparison category A vs
pooled(categories B,C,D....) - I would like to have a conclusion like
species of categories X, Y are resistant, species of category Z
issensitive.

What I was experimenting with:
1. simply t-tests for all combinations "objects of category X" vs.
"pooled objects of all other categories". After bonferroni to correct
for 9 t-tests, no results are significant.
2. anova - here I get significant difference but I don t know how to
show which are those categories that are different. I infered that you
can use contrasts for various comparisons but in examples I found in
books and over internet comparison vs rest of dataset is not used
(moreover it would require one-more contrast to have all category vs.
rest comparisons). I found tukey test in R, but it contrasts
individual categories with each other not category vs. average...

what is the right way of doing such things? is the category with just
2 members and problem and should be removed?

Please help. Thank you
(I used free R software during my tries; I would welcome a
recommendation of some free/cheap statistics software, that is not
command based).

My data(logarithmed):
values<-c(656.5, 668.5, 598, 689.5, 769, 717.5, 615, 713.5, 625, 641,
718.5, 686, 740.5, 641, 701, 697, 604.5, 668.5, 650.5, 489, 721.5,
660.5, 658.5, 643, 752, 695, 686, 645, 655, 686.5, 603, 707.5,
677.5, 627, 697.5, 637.5, 716.5, 675, 650, 736, 659, 678, 684,
618, 581, 584.5, 674.5, 735, 632, 676, 718.5, 680, 726.5, 723.5,
628, 572, 646, 691)

categories<-c(9, 9, 4, 9, 1, 9, 3, 8, 4, 3, 3, 3, 5, 4, 4, 1, 3, 7, 5,
3, 6, 6, 6, 1, 1, 6, 1, 5, 4, 4, 4, 4, 7, 7, 7, 7, 7, 8, 5, 9, 2,
2, 2, 6, 6, 6, 7, 9, 2, 2, 5, 3, 1, 9, 2, 6, 6, 9)

Those values are surprisingly large for logs. Have they been scaled?
Here are the means and standard deviations, along with the data.

cat n mean s.d. sorted data
1 6 712.250 46.3052 643,686,697,726.5,752,769
2 6 659.500 24.3454 628,632,659,676,678,684
3 7 633.429 75.5681 489,604.5,615,641,680,686,718.5
4 8 652.125 42.8409 598,603,625,641,655,686.5,701,707.5
5 5 680.900 45.0935 645,650,650.5,718.5,740.5
6 9 637.444 52.5312 572,581,584.5,618,646,658.5,660.5,695,721.5
7 7 671.286 31.3340 627,637.5,668.5,674.5,677.5,697.5,716.5
8 2 694.250 27.2236 675,713.5
9 8 702.188 30.2772 656.5,668.5,689.5,691,717.5,723.5,735,736

The first value in category 3 looks suspiciously low.
If that value is dropped then the mean rises to 657.500
and the standard deviation drops to 44.5578.

When you compare one mean to the pool of the others, do you want to
use the pool of the means (i.e., the unweighted mean of the other
means) or the pool of the data (which would weight each mean by the
corresponding n)?
.

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