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Thread: Best design for this experiment?

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    Best design for this experiment?




    Hello all.
    I am having some trouble with my experiment and would be the best way to analyze the data.
    I have 4 different chemicals each at one different concentrations and I want to assess their effects on yield and I would like to know if there are interactions between all possible combinations of chemicals; AB, AC, AD, BC, BD, CD, ABC, ABD, ACD, BCD, ABCD. Thank you!

    Chemicals: A,B,C and D
    1 level for each (one concentration) chemical
    Response: yield

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    Re: Best design for this experiment?

    Any ideas for how you would analyze this? It always helps to know what you're thinking first. Sample sizes? How was yield measured? In general, just give us more details...inquiring minds want to know!

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    Re: Best design for this experiment?

    I am thinking factorial design. 10 replicates for each treatment combination (11) = 110 . Yield was measured in Kg/hectare. My confusions starts with the factorial design, which it is "x" number of factors each with "y" levels on a independent variable, but I only have 1 factor with 4 levels (4 different chemicals), but I want to assess interactions of all 4 chemicals and possible combinations...

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    Re: Best design for this experiment?

    hah! JP i now wonder if you like to play WoW...enquiring minds want to know! that's something some of the characters say in it.

    Sorry Daelve - I tried to answer your question and then realised I was too ignorant...I'll leave it for the experts.

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    Re: Best design for this experiment?

    WoW....some of the characters say that? You must have meant to ask whether I quote the primary tagline from the National Enquirer TV commercials from the 1980s. Eat that, WoW chumps. No WoW for me. Not a single game on my computer...I can't handle video games, oddly.

    daelve, I'm being a bit daft tonight. Clarify this for me:
    - 4 chemicals (A,B,C,D)
    - For each chemical, are they multiple concentrations? For instance, for chemical A, are they two or three concentrations?

    Just wanted to get this right. If there are multiple concentrations for each chemical, this is a HUGE experiment. Perhaps I'm wrong.

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    Re: Best design for this experiment?

    lol! i have my answer. i shall now bow out of this thread which I rudely interrupted.

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    Re: Best design for this experiment?

    jpkelley, just one concentration for each chemical.

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    Re: Best design for this experiment?

    So, just to get this right...you have something like the following example:

    chemical A = 20% Coca-Cola
    chemical B = 80% alcohol
    chemical C = 10% orange juice
    chemical D = 40% milk

    You then have 10 replicates each of A mixed with B (treatment AB), 10 replicates of B mixed with C (treatment BC), etc.

    If this is the case, it seems like this is a really simple model where treatment is the single variable in your model. Run post-hoc tests to test for differences between treatments after correcting for multiple comparisons.

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    Re: Best design for this experiment?

    so this is not a factorial design, because I only have one factor?

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    Re: Best design for this experiment?

    Not in the traditional sense, no. Not sure about the terminology...if you absolutely wanted to give it a name, maybe a "combinatorial experiment"???? This is one of those points where people who are well-versed in formal experimental design can chime in, because I know not the terminology.

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    Re: Best design for this experiment?

    Thank you jpkelley!

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    Re: Best design for this experiment?

    I don't know... my gut is telling me something is not quite right. (And if Malcolm Gladwell is right then this should be a cause for at least some concern!) On the one hand, yes, you can view these treatments as simply being 4 levels of a single factor, and the analysis is quite straightforward. But in the OP you mention that you want to look at combinations of different chemicals, and this single-factor type of design is not intended for answering that kind of question. Another way to look at this -- one that is admittedly quite a bit more complicated but which would allow you to look at combinations in at least a rudimentary way -- is to view each chemical is being a separate binary factor (e.g., the "chemical A" factor would have the 2 levels "present" or "absent"). This would give you the combinations that you alluded to in the OP and allow you to answer questions like: Which chemical seems to increase yield the most on average (simple effects)? Does the degree to which chemical A is helpful depend on whether chemical B is also present (two-way interactions)? Does the degree to which the effectiveness of A depends on B, itself depend on whether chemical C is present (three-way interactions)? Etc.

    Now, it's not clear to me that this is really what you want to do here. It seems to me that if you were really interested in looking at these combinatorial questions, you would also want to incorporate different concentrations of each chemical, which you didn't do (this would be the nightmare experiment that jpkelley hinted at...). But it is at least closer to what you initially said in the OP, whatever that is worth. I guess you'll have to decide for yourself if these are the kind of questions you want to ask or if you're really just interested in the more simple single-factor questions (which seem perfectly reasonable to me).
    “In God we trust. All others must bring data.”
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    Re: Best design for this experiment?

    I like Jake's approach much better, though I haven't thought about how the model would be set up. You're describing something like this, Jake?

    Code: 
       treatment_combo replicate treat_A treat_B treat_C treat_D     yield
    1               AB         1       1       1       0       0 0.9290775
    2               AB         2       1       1       0       0 0.7034794
    3               AC         1       1       0       1       0 0.5725186
    4               AC         2       1       0       1       0 0.6479030
    5               AD         1       1       0       0       1 0.9648538
    6               AD         2       1       0       0       1 0.8338965
    7               BC         1       0       1       1       0 0.8964288
    8               BC         2       0       1       1       0 0.9651693
    9               BD         1       0       1       0       1 0.6827829
    10              BD         2       0       1       0       1 0.9963998
    11              CD         1       0       0       1       1 0.9897916
    12              CD         2       0       0       1       1 0.7905199
    13             ABC         1       1       1       1       0 0.5592225
    14             ABC         2       1       1       1       0 0.5494699
    15             ABD         1       1       1       0       1 0.8485482
    16             ABD         2       1       1       0       1 0.9366433
    17             ACD         1       1       0       1       1 0.7725443
    18             ACD         2       1       0       1       1 0.7741910
    19             BCD         1       0       1       1       1 0.9421293
    20             BCD         2       0       1       1       1 0.4625564
    21            ABCD         1       1       1       1       1 0.5543312
    22            ABCD         2       1       1       1       1 0.8735392
    I agree that this is the only way to say something about the independent of effect of A, B, C, and D. It might also allow you to isolate the effects of AxB, though I haven't thought about the issues that might arise from specifying all reasonable interactions (likely not good).

    If you wanted to just know about combinations (i.e. compound efficacy...I'm imagining this is something about fertilizer), then a single factor might be the simplest. But, as Jake rightly points out, that won't tell you much and definitely won't give you much insight about future direction (i.e. new and optimal combinations of chemicals).

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    Re: Best design for this experiment?

    Yeah I think so. I didn't look too closely at your coding scheme (dummy coding makes my head hurt...) but I think we're on the same page. I'm not entirely convinced that this is the way the experiment ought to in fact be conducted, but it's at least an option which the OP can take or leave...
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    Re: Best design for this experiment?


    The chemicals are pollutants that can co-occur, thus possible synergistic or antagonistic effects on yield could be present. That is why I want to assess possible combinations of all 4 pollutants. Also, I want to see the effects of several concentrations for each pollutant.

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