Hi there,

In an incubation experiment, we want to test the extra added plastic on
soil properties. We have two factors. One is the age of plastic (a),
which has 3 levels, i.e., a0, a10, and a30; and the other one is the
applied rate (r), i.e., r0, r2, and r20. We plan to use a randomized
complete design and have 9 treatments with 3 replications for each
treatment.

The fact is r0a0, r0a10, and r0a30 are the same. They are treatments
with no added plastic. So we want to reduce those three treatments to
one. Therefore, we have 7 other than 9 treatments.

Now, we have problems performing statistical analysis. Can we use
two-way ANOVA to check the main and interaction effects of the two
factors? If yes, what's we have to pay attention to?

We really appreciate any suggestion or hint. Thanks in advance.

Best,
Jinsong

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Jinsong Zhao wrote:

Hi there,

In an incubation experiment, we want to test the extra added plastic
on soil properties. We have two factors. One is the age of plastic
(a), which has 3 levels, i.e., a0, a10, and a30; and the other one is
the applied rate (r), i.e., r0, r2, and r20. We plan to use a
randomized complete design and have 9 treatments with 3 replications
for each treatment.

The fact is r0a0, r0a10, and r0a30 are the same. They are treatments
with no added plastic. So we want to reduce those three treatments to
one. Therefore, we have 7 other than 9 treatments.

Now, we have problems performing statistical analysis. Can we use
two-way ANOVA to check the main and interaction effects of the two
factors? If yes, what's we have to pay attention to?

We really appreciate any suggestion or hint. Thanks in advance.

Best,
Jinsong

As you presumably know, ANOVA is just a special case of a linear
regression type of analysis. Your situation falls slightly outside of
that special case. My suggestion is that you look at the theory of
where ANOVA fits into its regression-type of background, in terms of regression-model structure, see what changes you need to make to that model-structure, and then proceed with fitting (and if necessary,
formal testing) of that regression model.

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On Sat, 10 Dec 2022 09:44:18 -0000 (UTC), "David Jones" <dajhawkxx@nowherel.com> wrote:

Jinsong Zhao wrote:

Hi there,

In an incubation experiment, we want to test the extra added plastic
on soil properties. We have two factors. One is the age of plastic
(a), which has 3 levels, i.e., a0, a10, and a30; and the other one is
the applied rate (r), i.e., r0, r2, and r20. We plan to use a
randomized complete design and have 9 treatments with 3 replications
for each treatment.

The fact is r0a0, r0a10, and r0a30 are the same. They are treatments
with no added plastic. So we want to reduce those three treatments to
one. Therefore, we have 7 other than 9 treatments.

Now, we have problems performing statistical analysis. Can we use
two-way ANOVA to check the main and interaction effects of the two
factors? If yes, what's we have to pay attention to?

We really appreciate any suggestion or hint. Thanks in advance.

Best,
Jinsong

As you presumably know, ANOVA is just a special case of a linear
regression type of analysis. Your situation falls slightly outside of
that special case. My suggestion is that you look at the theory of
where ANOVA fits into its regression-type of background, in terms of >regression-model structure, see what changes you need to make to that >model-structure, and then proceed with fitting (and if necessary,
formal testing) of that regression model.

Yes. Using regression is what I would try, for all the groups, coding
contrasts as needed.

Here are a couple of other thoughts.

If the factors are strong, you may get most of your useful
information from an ANOVA omitting r0 entirely, at the start. Plan
to figure out what that "baseline" means, after you plot out the rest.
If the baseline is important, perhaps that single group should
be larger than the others. Duncan's procedure for a single control
versus multiple groups recommends a larger N based on the number
of other groups -- I don't know if yours should be thought of as "6"
(with replications=3) or as "2", the number of groups in the other
contrasts (with replications = 6). I don't remember adapting Duncan's
to a two-way design before.

Age and Rate are both quantitative, which implies that a single d.f.
contrast for "linear" would be the powerful test. However, your
scaling for the regression contrasts is not linear in an obvious way,
either for (0, 2, 20) or for (0,10,30). - Often, the arbitrary-seeming
numbers have been chosen because the PI /expects/ those to be
equal-interval steps, in which case the simple (-1, 0, 1) works.

Your contrasts when including interactions will have correlations,
so the regression results that you look at for main effects should
/not/ include the interaction effects.

--
Rich Ulrich

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On 2022/12/11 4:40, Rich Ulrich wrote:

On Sat, 10 Dec 2022 09:44:18 -0000 (UTC), "David Jones" <dajhawkxx@nowherel.com> wrote:

Jinsong Zhao wrote:

Hi there,

In an incubation experiment, we want to test the extra added plastic
on soil properties. We have two factors. One is the age of plastic
(a), which has 3 levels, i.e., a0, a10, and a30; and the other one is
the applied rate (r), i.e., r0, r2, and r20. We plan to use a
randomized complete design and have 9 treatments with 3 replications
for each treatment.

The fact is r0a0, r0a10, and r0a30 are the same. They are treatments
with no added plastic. So we want to reduce those three treatments to
one. Therefore, we have 7 other than 9 treatments.

Now, we have problems performing statistical analysis. Can we use
two-way ANOVA to check the main and interaction effects of the two
factors? If yes, what's we have to pay attention to?

We really appreciate any suggestion or hint. Thanks in advance.

Best,
Jinsong

As you presumably know, ANOVA is just a special case of a linear
regression type of analysis. Your situation falls slightly outside of
that special case. My suggestion is that you look at the theory of
where ANOVA fits into its regression-type of background, in terms of
regression-model structure, see what changes you need to make to that
model-structure, and then proceed with fitting (and if necessary,
formal testing) of that regression model.

Yes. Using regression is what I would try, for all the groups, coding contrasts as needed.

Here are a couple of other thoughts.

If the factors are strong, you may get most of your useful
information from an ANOVA omitting r0 entirely, at the start. Plan
to figure out what that "baseline" means, after you plot out the rest.
If the baseline is important, perhaps that single group should
be larger than the others. Duncan's procedure for a single control
versus multiple groups recommends a larger N based on the number
of other groups -- I don't know if yours should be thought of as "6"
(with replications=3) or as "2", the number of groups in the other
contrasts (with replications = 6). I don't remember adapting Duncan's
to a two-way design before.

Age and Rate are both quantitative, which implies that a single d.f.
contrast for "linear" would be the powerful test. However, your
scaling for the regression contrasts is not linear in an obvious way,
either for (0, 2, 20) or for (0,10,30). - Often, the arbitrary-seeming numbers have been chosen because the PI /expects/ those to be
equal-interval steps, in which case the simple (-1, 0, 1) works.

Your contrasts when including interactions will have correlations,
so the regression results that you look at for main effects should
/not/ include the interaction effects.

Thanks a lot for the reply and instructions. I do not understand well
about coding contrasts. My knowledge of statistics, which I only learned introductory statistics during my college, is very limited. If you could
point me to some textbooks about this kind of statistical analysis, I
would really appreciate it.

Best,
Jinsong

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On Sun, 11 Dec 2022 21:48:27 +0800, Jinsong Zhao <jszhao@yeah.net>
wrote:

(me)

< snip stuff >

Your contrasts when including interactions will have correlations,
so the regression results that you look at for main effects should
/not/ include the interaction effects.

Thanks a lot for the reply and instructions. I do not understand well
about coding contrasts. My knowledge of statistics, which I only learned >introductory statistics during my college, is very limited. If you could >point me to some textbooks about this kind of statistical analysis, I
would really appreciate it.

Okay, you have had one intro course in statistics. Did you take a
lot of math, including matrix theory? I did. Basic calculus
certainly helped me understand distributions and tests. In my
first job, as a computer programmer, I was mentored by a
statistician -- but I was able to help HIM with, for instance,
canonical correlation and factor analysis, which are 'merely'
particular manipulations of matrices. (And regression is one
simple case of canonical correlation.)

The intro-to-stats that I took in psychology was the most worthless
course of my career, for content. However, it partly prepared me for consulting with psychologists who know no math.

I don't have any idea how much you know. It would be
malpractice of a sort to point you at a text and say, Good Luck.

There are SO MANY ways to go wrong.

Maybe read up first, in some intro-to-regression book in your
area. After you have read enough to understand the language,
hire a consultant for /few/ hours of consulting. Let them design
and run the analyses, and interpret them.

Ask questions; float your ideas, and see how close you came;
ask THEM for what texts they recommend.

Having worked as a statistical consultant, I can say that the
time-consuming part of the task is often "cleaning up the data."
Missing values? Out of range values? - What do you want to do?
You should be able to clean the data, and quickly show them
you have done that step. Plots and graphs of bivariate
distributions are good for providing assurance that there are
no hidden problems.

- Professors at universities are apt to be willing to moonlight.
Someone who has published relevant research would be best.
A theorist who has never dealt with real data might be terrible.

(I'm recalling a fine theorist who made several fine posts here,
back during the Bush administration. Reef_fish Bob was
autistic-spectrum: bad at context, and hostile to people as
a reflex.)

--
Rich Ulrich

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