Difference Between Nested and Split-Plot

[warren_s...@my-deja.com]

I cannot seem to determine what, if any, difference exists between
a split-plot design and a nested design. And, I had been taught that
there was no difference. However, Neter, Wasserman and Kutner have one
chapter on nested designs, and a second on repeated measures, where
they claim split-plot designs may be viewed as special types of repeated
measures designs, but make no mention of nested designs. Further, they
make no link between the two topics (that I can find).

From what I learned, a split-plot is a fraction of a plot (thus nested
within a plot), wherein all or a subset of the treatments were
assigned. So, maybe all split-plots are nested, but not nested designs
are split-plots?

I appreciate any clarification others may provide.

Sincerely,

Warren Schlechte

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[Paige Miller]

warren_s...@my-deja.com wrote:
>
> I cannot seem to determine what, if any, difference exists between
> a split-plot design and a nested design. And, I had been taught that
> there was no difference. However, Neter, Wasserman and Kutner have one
> chapter on nested designs, and a second on repeated measures, where
> they claim split-plot designs may be viewed as special types of repeated
> measures designs, but make no mention of nested designs. Further, they
> make no link between the two topics (that I can find).
>
> From what I learned, a split-plot is a fraction of a plot (thus nested
> within a plot), wherein all or a subset of the treatments were
> assigned. So, maybe all split-plots are nested, but not nested designs
> are split-plots?

Nested refers to the levels of the variables, and does not refer to the
experiment units. Split-plot refers to the breaking up of experimental
units, and does not refer to the levels of the variables (or said
another way, the experimental units of variable 1 are not the same as
the experimental units of variable 2).

A typical split-plot design takes an experimental unit of one variable
(e.g. a plot of land), chops it into numerous smaller pieces and each
smaller piece has a a treatment of another variable applied to it. This
"chopping" of the experimental unit does not happen with nested
variables. Split plots are not usually nested, the variables are crossed
(the opposite of nested).

A typical nested design, you have many experimental units, each used in
its entirety and the nested and non-nested variables assigned to a unit.
You may have several production lines, each producing "units", thus you
would have the units nested within production line. The units are not
crossed (unit 1 from line 1 is distinct and separate from unit 1 from
line 2), and there is no "chopping" up of the production lines as there
might be with split-plots.

In a typical nested design, you estimate variance components. In a
typical split-plot design, you estimate means or polynomial (linear,
quadratic) effects.

--
Paige Miller
Eastman Kodak Company
paige....@kodak.com
"It's nothing until I call it!" -- Bill Klem, NL Umpire

[Bruce Weaver]

On Tue, 14 Dec 1999 warren_s...@my-deja.com wrote:

> I cannot seem to determine what, if any, difference exists between
> a split-plot design and a nested design. And, I had been taught that
> there was no difference. However, Neter, Wasserman and Kutner have one
> chapter on nested designs, and a second on repeated measures, where
> they claim split-plot designs may be viewed as special types of repeated
> measures designs, but make no mention of nested designs. Further, they
> make no link between the two topics (that I can find).
>
> From what I learned, a split-plot is a fraction of a plot (thus nested
> within a plot), wherein all or a subset of the treatments were
> assigned. So, maybe all split-plots are nested, but not nested designs
> are split-plots?
>

> I appreciate any clarification others may provide.
>
> Sincerely,
>
> Warren Schlechte

Hi Warren,
Maybe a simple example will help clarify the difference. Suppose
you have a study with a treatment group (patients in this group get a
drug) and a placebo control group. You also record the dependent varible
on 2 occasions for each patient, at 1 week and 2 weeks, for example. To
illustrate:

Drug Group Placebo Group
1 week 2 weeks 1 week 2 weeks

This is a split-plot design. "Group" is the between-subjects variable, and
"time" is the with-subjects variable. Note that the 2 levels of "time"
are the same for both groups (i.e., 1 week and 2 weeks).

But now suppose it looked like this:

Drug Group Placebo Group
1 week 2 weeks 3 weeks 4 weeks

THIS is a nested design, because the levels of "time" are not the same
for the two groups. In other words, TIME IS NESTED WITHIN GROUP.

Hope this helps.
Bruce
--
Bruce Weaver
wea...@fhs.csu.mcmaster.ca
http://www.angelfire.com/wv/bwhomedir/

[Peter W Lane]

I don't think that Bruce Weaver and Paige Miller have quite given the full
story. I'll add my bit, which may help.

"Nested" can refer either to the treatment structure of a design (fixed
effects) or to the blocking structure (random effects), or to both. It means
that the main effect of one of the factors (treatment or block) has no
meaningful interpretation, and so is combined with the interaction term.

Nested treatments could be something like drug formulations nested within
drug compound. The formulations may be different for each drug so it may not
be sensible to extract the main effect of formulation. Instead, the main
effect of Compound is fitted, and then the interaction of Compound with
Formulation.

Nested blocks could be something like patients nested within centre.
Different patients are used in each centre, so the main effect of the
Patient factor has no interpretation. The random effects in the model would
then be Centre and Patient-within-Centre.

A split-plot design is an example of a design with a nested block structure.
Most examples have one treatment factor applied to "whole plots", and
another treatment applied to "sub plots", which are sub-divisions of the
whole plots. The treatment factors are usually analysed as crossed. S.e.s
for the main effect of one is estimated from the whole-plot error, and of
the other with the sub-plot error. S.e.s for the interaction is also
estimate form the sub-plot error.

You can also have a split-split-plot design, where there are sub-sub-plots
with another treatment factor. This also has nested block structure.

A split-plot design can be used as a repeated-measurement design if the
correlation between repeated time points is assumed to be particularly
simple. Specifically, each observation on a subject (whole-plot) at a
particular time (sub-plot) has the same correlation with an observation on
the same subject at any other time. This is not usually sensible, because
observations close in time tend to have larger correlations than those
separated in time. But in the particular case of just two time-points, there
is no problem.

Peter Lane
Research Statistics Unit, SmithKline Beecham peter_w_lane@sbphrd

[daegl...@gmail.com]

Perhaps you can help me understand what category my data set falls into.

I have a large sample of hardness measurements from several teeth. The data is structured like this:

2 species of monkeys
samples from several different individuals (monkey 1, monkey 2, monkey 3... etc)
samples from random post-canine teeth (i.e. molar 1, molar 2, molar 3)
within each tooth, there are several sections cut in serial sequence (i.e. cut 1, cut 2, cut 3)

Each of these serially cut sections was then sampled at least 40 times for hardness in the dentine of the teeth.

I believe I have a nested design. Species(monkey(tooth(serial cut)))
I am interested in determining which level of the hierarchy accounts for the majority of the variation.
Statistical advice badly needed. Thanks

-JDP

[Rich Ulrich]

I think you might need to describe some things more specificially.
Which of these describe main effects that can be tested?

Is "Molar1" similar across all monkeys? Or - When you say, "random
post-canine teeth", does that mean that the same teeth-locations
are not available for the several monkeys?

Does "Cut 1" potentially mean the same thing for all teeth?
- Somewhat a separate question: Is there to be an expected,
systematic relation across Cut 1, Cut 2, Cut 3?


If Yes to "similar" or "same" - By the terminology that I would use,
these would then become crossed factors. I think that would make
it "split plot", from what I gather from the Wikip article on that
topic.



--
Rich Ulrich