Randomized Complete Block with repeated measurements?

Discussion in 'Scientific Statistics Math' started by Jinsong Zhao, Nov 24, 2011.

1. Jinsong ZhaoGuest

Hi there,

We are going to carry out a incubation experiment with duration about 30
days. We will measure specific indicator at day 1, 3, 5, 10, 20 and 30.

Because of limitation of space, the experiment can not be replicated. We
are going to do the same experiment three times one after another.

It seems to be a design of randomized Complete Block with repeated
measurements. I am not sure about whether it is statistical reasonable.

Any suggestions will be really appreciated. Thanks in advance.

Regards,
Jinsong

Jinsong Zhao, Nov 24, 2011

2. Rich UlrichGuest

That is a Repeated Measurement with intervals that are nominally
unequal. Can they be treated as Equal?
So you have a repeated measure design with N=3.
What Block? What is Randomized?

Rich Ulrich, Nov 25, 2011

3. Ray KoopmanGuest

I agree with Rich's comments and questions. Also,
what is the research question? What do you hope to show?

Ray Koopman, Nov 25, 2011
4. Jinsong ZhaoGuest

Thanks a lot for the reply.

The time for measurement is set by preliminary experiment. They should
be unequal. Dose repeated measurement design require equal intervals?
What is N?
We want to do the incubation experiment with 3 replications, however, we
don't have enough space for the 3 replications. Thus the experiment is
carried out one after another. The 3 replications now became 3 blocks.
In each block, the incubation experiment is running in a randomized way.

Regards,
Jinsong

Jinsong Zhao, Nov 25, 2011
5. Jinsong ZhaoGuest

Thanks.

The research questions is the variation of CO2 or other greenhouse under
different conditions, e.g., water content, temperature. The CO2 and
other indicators will be measured at different time through the experiment.

We hope to know whether water content, temperature or their interaction
have effects on the emission of CO2. The variation with time also be
considered.

Regards,
Jinsong

Jinsong Zhao, Nov 25, 2011
6. Ray KoopmanGuest

The design you described is a 3 x 6 simple-repeated-measures design:
3 replications of a sequence of measurements of a single variable
made at 6 specific time points. It is at best capable of giving you
a little information about relations among the 6 time-point means.
Where do water content and temperature enter the picture?

Ray Koopman, Nov 25, 2011
7. Jinsong ZhaoGuest

Thanks a lot. The experiment can be described by the following design matrx:

Subject Water Temperature Time
1 1 1 1
1 1 1 3
1 1 1 5
1 1 1 10
1 1 1 20
1 1 1 30
2 2 1 1
2 2 1 3
2 2 1 5
2 2 1 10
2 2 1 20
2 2 1 30
3 1 2 1
3 1 2 3
3 1 2 5
3 1 2 10
3 1 2 20
3 1 2 30
4 1 2 1
4 1 2 3
4 1 2 5
4 1 2 10
4 1 2 20
4 1 2 30

The above one is a typical repeated measurement design. In previous
post, we hope to replicate the experiment 3 times one by one. Thus,
there will be 3 blocks, each for one experiment.

Regards,
Jinsong

Jinsong Zhao, Nov 25, 2011
8. Rich UlrichGuest

A contrast with one degree of freedom, like "linear trend", gives
far superior power for detecting a linear trend -- if that is what is
interest, and what is present. The easy-to-state equal-interval for
time is equal-days, but that is usually not good for an experiment
with a zero time-point. I expect that your "preliminary experiemt"
does give you (approximately) equal intervals for changes in your
outcome, so that is good.

If plants are incubating, you may have a scaling problem from
the size: When plants are tiny, the CO2 effects must be smaller
at the start, compared to later. Measuring "CO2 per plant weight" --
or per leaf area, or whatever makes biological sense -- might be a
useful way to standardize outcomes. Using logarithms is sometimes
useful when the outcome relates to exponential growth, but that
might not be as useful as some aspect of size, here.
N is sample size. Three is small.
Okay. Agriculture may use the term Block this way, though I would
simply call these replications. If they are Blocks, then your N is 1
for each block .

What is randomized? Subjects are usually randomized in a
"randomized experiment." This is a description that you need
to be more specific about, because I think this generic term
has some specific implications that are not met.

Rich Ulrich, Nov 25, 2011
9. Ray KoopmanGuest

The design you need is usually laid out like this,
where each 'y' denotes an observation.

........Time.........

Water Temp Subj 1 3 5 10 20 30

1 1 1 y y y y y y
. . . . . . .
. . . . . . .
. . . . . . .
n y y y y y y

1 2 n+1 y y y y y y
. . . . . . .
. . . . . . .
. . . . . . .
2n y y y y y y

2 1 2n+1 y y y y y y
. . . . . . .
. . . . . . .
. . . . . . .
3n y y y y y y

2 2 3n+1 y y y y y y
. . . . . . .
. . . . . . .
. . . . . . .
4n y y y y y y

This is a mixed 2-between, 1-within design.
The between-subjects factors are Water and Temp.
The within-subject (i.e., repeated-measures) factor is Time.
Equivalently, you can say that Water, Temp, and Time are crossed;
Subjects are crossed with Time and nested in Water x Temp.

multiple subjects in each of the 4 Water x Temp cells.
You don't need the same number of subjects in each cell,
but the analysis will be stronger if the number is the same.

Ray Koopman, Nov 25, 2011
10. Jinsong ZhaoGuest

Yes, the design is what I hope to describe. However, the number of
subject in each treatment (Water x Temp) is only one (n = 1 in your
layout), for the space limitation.

I will replicate the above design 3 times one after another. The final
design may like:

........Time.........
block Water Temp Subj 1 3 5 10 20 30
1 1 1 1 y y y y y y
1 1 2 2 y y y y y y
1 2 1 3 y y y y y y
1 2 2 4 y y y y y y

2 1 1 5 y y y y y y
2 1 2 6 y y y y y y
2 2 1 7 y y y y y y
2 2 2 8 y y y y y y

3 1 1 9 y y y y y y
3 1 2 10 y y y y y y
3 2 1 11 y y y y y y
3 2 2 12 y y y y y y

In the experiments, the Subj and block have almost same initial
conditions, is it possible to treat the block as replication?

Thanks again.

Regards,
Jinsong

Jinsong Zhao, Nov 28, 2011
11. Ray KoopmanGuest

Analyze the data as a 4-way factorial design:
Block x Water x Temp x Time, with 1 observation per cell.

Treat Block as a random factor. Then the error term for testing
any effect not involving Block is its interaction with Block.

Effects involving Block can not be tested.

Ray Koopman, Nov 28, 2011