Randomized Complete Block with repeated measurements?

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

  1. Jinsong Zhao

    Jinsong Zhao Guest

    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
    #1
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  2. Jinsong Zhao

    Rich Ulrich Guest

    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
    #2
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  3. Jinsong Zhao

    Ray Koopman Guest

    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
    #3
  4. Jinsong Zhao

    Jinsong Zhao Guest

    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
    #4
  5. Jinsong Zhao

    Jinsong Zhao Guest

    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
    #5
  6. Jinsong Zhao

    Ray Koopman Guest

    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
    #6
  7. Jinsong Zhao

    Jinsong Zhao Guest

    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
    #7
  8. Jinsong Zhao

    Rich Ulrich Guest

    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
    #8
  9. Jinsong Zhao

    Ray Koopman Guest

    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.

    To answer the questions you want to ask, you need
    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
    #9
  10. Jinsong Zhao

    Jinsong Zhao Guest

    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
    #10
  11. Jinsong Zhao

    Ray Koopman Guest

    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
    #11
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