What's method I should use?

[Jinsong Zhao]

Hi there,

We have collect some data from an ecological experiment.

For each treatment, 4 out of 7 species are chosen, and incubated in one
unit. And then some properties, e.g., the sum of individual weights in
the unit, are measured. Totally, 35 treatments are established. For a
specific property, it varies among different treatments. It makes sense
because of the interaction between species.

To my knowledge, I could design a 2^7 factorial experiment to test the
main and interaction effect of the 7 species. This is a huge experiment
and may not be feasible. However, I don't know the design of such
experiment design or how to analyze those data.

Any hints on the name of the experimental design or the statistical
method that could be used to analyze the data? Thanks a lot in advance.

Best,
Jinsong

[Rich Ulrich]

On Fri, 9 Sep 2022 21:46:41 +0800, Jinsong Zhao <jsz...@yeah.net>
wrote:

>Hi there,
>
>We have collect some data from an ecological experiment.

I will start out by saying that this sort of 'ecological experiment'
is alien to me, including the vocabulary describing it. I had to
read this four times before it I began to translate it to my own
terms. I think that others reading this group will have the same
trouble. I offer my 'translation' to concrete terms, but the actual
details, if you provide them, might remind others of problems
that they have done or worried about.

>
>For each treatment, 4 out of 7 species are chosen, and incubated in one
>unit. And then some properties, e.g., the sum of individual weights in
>the unit, are measured. Totally, 35 treatments are established. For a
>specific property, it varies among different treatments. It makes sense
>because of the interaction between species.

Okay. An experimental unit (as I translate) is a Petri dish. Taking
4-of-7 for each dish results in a complete set of 35 dishes, one for
each unique combination. I speculate that you should do this at
least twice, so that you have Within variance to use as Error.

>
>To my knowledge, I could design a 2^7 factorial experiment to test the
>main and interaction effect of the 7 species. This is a huge experiment
>and may not be feasible. However, I don't know the design of such
>experiment design or how to analyze those data.

You can lay out a 7-way ANOVA. It certainly will be missing the
5-way, 6-way, and 7-way interactions that are absent in the data.

Testing for main effects and simple 2-way interactions is easy,
with 28 total DF. I think you need that replication to get a more
robust error term for the interaction tests. There will be 35 df
for the 3-way interactions (if I'm not screwing up); so testing
that-plus-28 DEFINITELY needs an N more than 35, and it
will be better testing with N of 70 or more.

Doing so many tests as even the 2-way interactions, without
guidance of a-priori hypotheses, certainly puts you in the position
of 'too many tests' -- the multiplicity problem. Someone might
be concerned even about the 7 main effects as being 'many'.

I have no idea how BIG you expect your effects to be. Or how
big they need to be in order to matter. So I can't say whether
you should replicate the 35-dish experiment twice or five times.
Even 10 times might be a good idea, if you are fishing among a
number of 'properties' as equal aternatives for outcome.

Hope this helps.


--
Rich Ulrich

[David Jones]

You may find what you need under the name "fractional factorial
design". This would be covered in many books on "design of
experiments". Otherwise an internet search should give you something
worthwhile.