how to test treatment difference when response variable have correlation?

Discussion:

(too old to reply)

Jinsong Zhao

2020-04-29 06:24:13 UTC

Hi there,

I have set an one factor experiment with 4 level. In the experiment, I
analyzed 3 variables (V1, V2, and V3) among the 4 treatments. I am
planing to use one-way ANOVA to test the difference of each variable
among the 4 treatments, and do post hoc comparison by LSD.

However, in my experiment the 3 variables have relations like:
V1 + V2 + V3 = C
here, C (a constant) may varied among 4 treatments.

The factor we test may have effects on V1 or each of them. When V1 have
changed, then other variables may be changed accordingly. Under this
situation, I don't know if ANOVA is a suite method to do the test.

Any suggestion or reference? Thanks a lot.

Best,
Jinsong

Bruce Weaver

2020-04-29 13:42:29 UTC

Permalink

Post by Jinsong Zhao
Hi there,
I have set an one factor experiment with 4 level. In the experiment, I
analyzed 3 variables (V1, V2, and V3) among the 4 treatments. I am
planing to use one-way ANOVA to test the difference of each variable
among the 4 treatments, and do post hoc comparison by LSD.
V1 + V2 + V3 = C
here, C (a constant) may varied among 4 treatments.
The factor we test may have effects on V1 or each of them. When V1 have
changed, then other variables may be changed accordingly. Under this
situation, I don't know if ANOVA is a suite method to do the test.
Any suggestion or reference? Thanks a lot.
Best,
Jinsong

A Google search on <anova ipsative measures> turns up lots of resources that look relevant. Some of the older ones discuss use of ANOVA models, as one would expect. Some of the more recent ones suggest alternative (quite possibly better) approaches. You could also search on <compositional data analysis>.

One other thing: Fisher's LSD provides good control over the familywise alpha only when there are 3 groups. With 4 groups, you may wish to consider some other MC procedure. If you need resources concerning this point, take a look at the following:

"Statistical Methods for Psychology" by (the late) David Howell
"Serious Stats" by Thom Baguley
https://www.ncbi.nlm.nih.gov/pubmed/17128424

HTH.

Jinsong Zhao

2020-05-01 01:10:37 UTC

Permalink

Post by Bruce Weaver

Thank you very much for the searching keywords and the comments on the
selection of MC procedure.

Best,
Jinsong

Rich Ulrich

2020-04-29 18:15:27 UTC

Permalink

Those are called compositional data, or ipsative measures ...
Bruce has given you some references on that.

Post by Jinsong Zhao
here, C (a constant) may varied among 4 treatments.

... but I don't know what THAT implies, when C can vary.
Why does it vary? How does it vary? What have other people
done with similar data?

Are your scores for V1, etc., directly comparable as criteria?
Or should you be considering ratios, products, or some other
combinations?

Post by Jinsong Zhao
The factor we test may have effects on V1 or each of them. When V1 have
changed, then other variables may be changed accordingly. Under this
situation, I don't know if ANOVA is a suite method to do the test.

If you want to test the V's one at a time, ANOVA is what you have.

If you want to look at relationships, the testing might be an
application of MANOVA, which is what those "ipsative" sources
are apt to refer you to. Or you can draw up prior hypotheses
based on what you know about the V's, compute new measures
that combine a couple of the V's and test /those/ one at a time.

But "C ... varied among 4 treatments" suggests to me that
you need to be very careful and specific about what your
hypotheses are. The varying-ipsative nature of scoring
also suggests that you should pay attention to the scaling of
the measures. That is, when you are near 100% or 0% of
C, are the "intervals" stilll "equal" in terms of what you expect
from the outcome measure?

Post by Jinsong Zhao
Any suggestion or reference? Thanks a lot.

Hope this helps.

--
Rich Ulrich

Jinsong Zhao

2020-05-01 01:37:53 UTC

Permalink

Post by Rich Ulrich

Those are called compositional data, or ipsative measures ...
Bruce has given you some references on that.

Thank you and Bruce for point me to the name of my data. I don't have
the knowledge about that in my education about statistics.

Post by Rich Ulrich

Post by Jinsong Zhao
here, C (a constant) may varied among 4 treatments.

... but I don't know what THAT implies, when C can vary.
Why does it vary? How does it vary? What have other people
done with similar data?
Are your scores for V1, etc., directly comparable as criteria?
Or should you be considering ratios, products, or some other
combinations?

I should reconsider about my data. I am wrong with my previous
statement. In fact, V's have many source. Now, I am only consider it
from, e.g., soils. Thus, it may vary with different treat.

Post by Rich Ulrich

If you want to test the V's one at a time, ANOVA is what you have.

Yes, I have read many papers in my research field that apply ANOVA to
test the effects of treatment on V.

Post by Rich Ulrich
If you want to look at relationships, the testing might be an
application of MANOVA, which is what those "ipsative" sources
are apt to refer you to. Or you can draw up prior hypotheses
based on what you know about the V's, compute new measures
that combine a couple of the V's and test /those/ one at a time.
But "C ... varied among 4 treatments" suggests to me that
you need to be very careful and specific about what your
hypotheses are. The varying-ipsative nature of scoring
also suggests that you should pay attention to the scaling of
the measures. That is, when you are near 100% or 0% of
C, are the "intervals" stilll "equal" in terms of what you expect
from the outcome measure?

I am going to read some materials about this topic at first. Thank you
very much for the suggestions on the question.

Post by Rich Ulrich

Post by Jinsong Zhao
Any suggestion or reference? Thanks a lot.

Hope this helps.

That helps a lot.

Best,
Jinsong