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Thread: paired anova for lack of a better word advice please

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    paired anova for lack of a better word advice please




    Dear All
    i am stuck at the moment between a rock and a hard place. the short of
    the story is this.
    I have 84 petri dishes each containing 4 lines of seeds (each line
    contains 4 seeds).
    these lines contain a wild type plant, and 3 knock out mutant lines.
    i have split these 84 plates into 2 groups, a high light and a low
    light.
    these two groups are then further divided into differing
    concentrations of added zinc. (7 in total, 0 , 2, 5, 15, 300, 350 and
    400 umol)
    each different concentration has 6 petri dishes as repeats.
    the plants were all harvesed and weighed as groups i.e 4 plants at a
    time.
    now i am interested in several things from a statistical point of
    view:
    A) i am interested in a significant difference between the wild type
    and the 3 different mutants (called 1a, 1b and 1c). in this case a
    paired T-Test conducted numerous times will tell me if there is a
    within concentration difference.
    B) i wish to know if there is a significant difference between
    concentrations in other words taking the concentration into account.
    my problem is that i cant do a paired t-test as plants grown on petri
    dishes in diffedrent concentrations are not paired. secondly a simple
    anova will not do as the mutant must allways be compared to the wild
    type of its own concentration. hence the for a lack of better words a
    "paired anova"
    ... any advice
    cheers
    Yoma

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    1) do you have the same number of petri dishes per treatment?
    2) are you also interested in the effect of light (I assume so, since its in your design).
    The earth is round: P<0.05

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    Dear bugman
    Thanks for the reply.
    i am interested in the effect of light yes.
    i have the following number of petri dishes:
    84 total
    42 per light treatment (2 light treatments)
    the 42 dishes per light treatment are broken worn into 7 different concentrations of zinc.
    each concentration having 6 plates.

    to answer your question yes and no, by this i mean that due to infection the occasional plate has been omitted leaving only 5 plates per concentration.
    this happens a few times in bot light treatments.

    as an update to the forum:
    i am using R (of course) and have been trying to carry out a factoral anova (after dismissing a 3 way anova).
    my data is formatted like this:
    light treatment, Zinc concentration, seed type, weight
    (high/low), (0,2,5,15,300,350,400), (wt,1a,1b,1c), average weight of seedling)
    the strange thing is that when executing the following command:
    model<-aov(weight~seed*ZN*light)
    and then
    summary.lm(model)
    i get:

    Code: 
    Call:
    aov(formula = weight ~ seed * ZN * light)
    
    Residuals:
        Min      1Q  Median      3Q     Max 
    -6.8329 -1.0244 -0.1706  0.9130 23.0957 
    
    Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
    (Intercept)         1.523122   0.698769   2.180 0.030035 *  
    seed1b              6.331149   0.988209   6.407 5.56e-10 ***
    seed1c              0.348668   0.988209   0.353 0.724459    
    seedwt              6.881466   0.988209   6.964 2.01e-11 ***
    ZN                 -0.003398   0.003028  -1.122 0.262718    
    lightlow           10.642914   0.967918  10.996  < 2e-16 ***
    seed1b:ZN          -0.017887   0.004283  -4.176 3.86e-05 ***
    seed1c:ZN          -0.001104   0.004283  -0.258 0.796784    
    seedwt:ZN          -0.018851   0.004283  -4.402 1.48e-05 ***
    seed1b:lightlow    -5.687621   1.368843  -4.155 4.22e-05 ***
    seed1c:lightlow    -2.819258   1.368843  -2.060 0.040278 *  
    seedwt:lightlow    -5.066436   1.368843  -3.701 0.000254 ***
    ZN:lightlow        -0.027007   0.004195  -6.438 4.63e-10 ***
    seed1b:ZN:lightlow  0.017588   0.005932   2.965 0.003266 ** 
    seed1c:ZN:lightlow  0.007877   0.005932   1.328 0.185211    
    seedwt:ZN:lightlow  0.015840   0.005932   2.670 0.007984 ** 
    ---
    Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 
    
    Residual standard error: 3.247 on 308 degrees of freedom
    Multiple R-squared: 0.7129,     Adjusted R-squared: 0.6989 
    F-statistic: 50.98 on 15 and 308 DF,  p-value: < 2.2e-16
    no mention of 1a or high light!
    i cannot work out why unless i am using the wrong test!
    many thanks
    --yoma

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    You're probably missing those because R needs to make the model full rank. The same issue is discussed in this thread and there's a link to a lecture in one of my posts toward the end of that if you want to read more about this.

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    As for seed weight, is this the final weight? were ALL the initial weights the same / did you weigh them initially?
    The earth is round: P<0.05

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    yes seed weight is the final weight.
    all plants were planted and harvested at the same time.
    they were not weighed before planting as they were planted as seeds.
    cheers
    Yoma

    @Dason
    thanks i will look into that later.
    it has been buggin me for a while.
    just had a look over it and it is the case that some of my petri dishes had to be ommited due to infection. as a result in some concentration levels there are 5 repeats not 6.
    is this what would be causing the problem?
    thanks
    yoma
    Last edited by yoma819; 08-10-2010 at 07:31 AM. Reason: addition

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    update:
    the only problem i am having now is just that the 1a and the high light keeps dissapearing.
    does anyone know how i can stop this?

    here is my output
    Code: 
    > summary.lm(model)
    
    Call:
    aov(formula = weight ~ seed * zinc * light)
    
    Residuals:
          Min        1Q    Median        3Q       Max 
    -10.13153  -0.43882  -0.04083   0.43031  19.72397 
    
    Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
    (Intercept)                 1.9142     1.1485   1.667 0.096748 .  
    seed1b                      9.3119     1.6242   5.733 2.65e-08 ***
    seed1c                      0.3044     1.6242   0.187 0.851457    
    seedwt                      9.3004     1.6242   5.726 2.75e-08 ***
    zinczn15                   -0.8852     1.7035  -0.520 0.603759    
    zinczn2                     0.1953     1.6242   0.120 0.904392    
    zinczn300                  -1.6146     1.6242  -0.994 0.321088    
    zinczn350                  -1.5657     1.6242  -0.964 0.335932    
    zinczn400                  -1.5602     1.7035  -0.916 0.360563    
    zinczn5                    -1.1087     1.7035  -0.651 0.515722    
    lightlow                    8.8017     1.6242   5.419 1.34e-07 ***
    seed1b:zinczn15            -7.7509     2.4091  -3.217 0.001453 ** 
    seed1c:zinczn15            -0.2004     2.4091  -0.083 0.933752    
    seedwt:zinczn15            -8.4839     2.4091  -3.522 0.000504 ***
    seed1b:zinczn2              0.5831     2.2970   0.254 0.799814    
    seed1c:zinczn2             -0.4285     2.2970  -0.187 0.852166    
    seedwt:zinczn2              2.0857     2.2970   0.908 0.364689    
    seed1b:zinczn300           -9.1323     2.2970  -3.976 9.03e-05 ***
    seed1c:zinczn300           -0.2374     2.2970  -0.103 0.917774    
    seedwt:zinczn300           -8.6908     2.2970  -3.784 0.000191 ***
    seed1b:zinczn350           -9.2132     2.2970  -4.011 7.85e-05 ***
    seed1c:zinczn350           -0.3704     2.2970  -0.161 0.872009    
    seedwt:zinczn350           -8.9306     2.2970  -3.888 0.000128 ***
    seed1b:zinczn400           -9.2692     2.4091  -3.848 0.000149 ***
    seed1c:zinczn400           -0.4113     2.4091  -0.171 0.864575    
    seedwt:zinczn400           -9.2729     2.4091  -3.849 0.000148 ***
    seed1b:zinczn5             -6.4224     2.4091  -2.666 0.008146 ** 
    seed1c:zinczn5              0.8729     2.4091   0.362 0.717392    
    seedwt:zinczn5             -5.1349     2.4091  -2.131 0.033961 *  
    seed1b:lightlow            -9.3817     2.2970  -4.084 5.84e-05 ***
    seed1c:lightlow            -1.8265     2.2970  -0.795 0.427212    
    seedwt:lightlow            -8.0725     2.2970  -3.514 0.000517 ***
    zinczn15:lightlow           1.1885     2.3537   0.505 0.614012    
    zinczn2:lightlow            2.0043     2.2970   0.873 0.383675    
    zinczn300:lightlow         -7.6043     2.2970  -3.311 0.001059 ** 
    zinczn350:lightlow         -7.5731     2.3537  -3.218 0.001452 ** 
    zinczn400:lightlow         -7.9828     2.3133  -3.451 0.000649 ***
    zinczn5:lightlow            4.1310     2.3537   1.755 0.080384 .  
    seed1b:zinczn15:lightlow    9.6429     3.3287   2.897 0.004079 ** 
    seed1c:zinczn15:lightlow    0.7586     3.3287   0.228 0.819889    
    seedwt:zinczn15:lightlow   12.8477     3.3287   3.860 0.000142 ***
    seed1b:zinczn2:lightlow    -0.8990     3.2484  -0.277 0.782177    
    seed1c:zinczn2:lightlow    -1.3732     3.2484  -0.423 0.672836    
    seedwt:zinczn2:lightlow    -2.6843     3.2484  -0.826 0.409349    
    seed1b:zinczn300:lightlow   9.7844     3.2484   3.012 0.002843 ** 
    seed1c:zinczn300:lightlow   1.9351     3.2484   0.596 0.551870    
    seedwt:zinczn300:lightlow   8.7914     3.2484   2.706 0.007240 ** 
    seed1b:zinczn350:lightlow   9.4691     3.3287   2.845 0.004788 ** 
    seed1c:zinczn350:lightlow   1.5498     3.3287   0.466 0.641878    
    seedwt:zinczn350:lightlow   8.0641     3.3287   2.423 0.016072 *  
    seed1b:zinczn400:lightlow  10.0394     3.2716   3.069 0.002370 ** 
    seed1c:zinczn400:lightlow   1.8637     3.2716   0.570 0.569378    
    seedwt:zinczn400:lightlow   8.5554     3.2716   2.615 0.009426 ** 
    seed1b:zinczn5:lightlow     7.7549     3.3287   2.330 0.020564 *  
    seed1c:zinczn5:lightlow    -3.3832     3.3287  -1.016 0.310368    
    seedwt:zinczn5:lightlow     3.7101     3.3287   1.115 0.266030    
    ---
    Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 
    
    Residual standard error: 2.813 on 268 degrees of freedom
    Multiple R-squared: 0.8124,     Adjusted R-squared: 0.774 
    F-statistic: 21.11 on 55 and 268 DF,  p-value: < 2.2e-16 
    
    >
    any comments would be appreciated

    it was generated by:
    Code: 
     model<-aov(weight~seed*zinc*light)
    thanks again
    Yoma

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    i am probably just thinking aloud to myself but...
    levels of signisicance are determined by the control i.e the wild type.
    so surely i need to construct 3 anova models and lay them on top of each other?
    one to test for significance between weed type and growth (base of wild type)
    another to test that significance against zinc
    and a last one to test both against light level.
    does this sound plausable to anyone?
    --yoma

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    Quote Originally Posted by yoma819 View Post
    update:
    the only problem i am having now is just that the 1a and the high light keeps dissapearing.
    does anyone know how i can stop this?
    I already mentioned that it's trying to make the model full rank. If you want to learn more about what it's doing and why you can follow the link in my previous post. Notice that you're missing more than just 1a and high_light. You're missing any interaction term where those would be involved. I would suggest learning a little bit about what it's doing. Read lecture 7 found here for more info.

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    Quote Originally Posted by Dason View Post
    I already mentioned that it's trying to make the model full rank. If you want to learn more about what it's doing and why you can follow the link in my previous post. Notice that you're missing more than just 1a and high_light. You're missing any interaction term where those would be involved. I would suggest learning a little bit about what it's doing. Read lecture 7 found here for more info.
    yes i understand this now, thanks for the link.
    as you can probably imagine to newcomers it just looks as if data is dissapearing.
    what do you think of my previous post about multiple amova models?
    cheers
    yoma

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    Well you can always do a post-hoc test to do those individual tests so I don't see the point in doing multiple ANOVAs.

    Also: It might look like terms are disappearing but it does this for a reason. It might be that it's confusing for a newcomer but that almost might be a good thing because if you don't understand whats going on you're probably not going to interpret things correctly anyways. Note that I'm not saying they do this to confuse people. It really is a good system if you know what's going on. SAS does a similar type of thing to make the model full rank but it drops the last parameter instead of the first parameter. There are other ways to get a full rank model. It's also possible to just not have a full rank model at all (a parameter for everything) but then the individual parameters aren't estimable and then you have to use contrasts to answer any of your questions and really that's more of a pain than just understanding a full rank model in the first place.

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    Hi Yoma

    just a quick follow up. I hope you get this sorted because it sounds like a cool GH experiment!

    I just wanted to add that even though you are usuing seeds in this project, it would have been a good idea to have intial weight in your model as a co-variate. I have conducted similar studies on salt marsh plant seed and even moss spores (we used diameter as a proxy for weight) and in each case, the relative growth measurements were strongly related to initial weight inidcating an imbalance of resources or "fitness" from the outset.

    Food for thought. Thats all.
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    Smile

    Dear all especially Bugman

    i am so very close now.
    i have found out how to overlay models as i have been helped by a friend.
    tell me what you think of this:

    Code: 
    
    assuming a table is loaded and attached and that R knows that light and zinc are factors
    
    
    > model1<-glm(y~1)
    > model1<-glm(y~zinc) 
    > anova(modela,modelb,test="Chi")
    Analysis of Deviance Table
    
    Model 1: y ~ 1
    Model 2: y ~ zinc
      Resid. Df Resid. Dev Df Deviance P(>|Chi|)    
    1       323    11308.8                          
    2       317     6665.6  6   4643.2 < 2.2e-16 ***
    ---
    Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 
    > model3<-glm(y~zinc+light)
    > anova(mode1b,model3,test="Chi")
    Error in anova(mode1b, model3, test = "Chi") : object 'mode1b' not found
    > anova(modelb,model3,test="Chi")
    Analysis of Deviance Table
    
    Model 1: y ~ zinc
    Model 2: y ~ zinc + light
      Resid. Df Resid. Dev Df Deviance P(>|Chi|)    
    1       317     6665.6                          
    2       316     4878.9  1   1786.7 < 2.2e-16 ***
    ---
    Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
    what does everyone think?
    yet again thank you to everyone who had a look at this post and especially those that contributed!
    --yoma

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    i really am jumping between the fire and the frying pan haha
    i cn now compare models but i can only compare models that i am not interested in.
    i think my key to success lies in answering this question:
    how do i conduct multiple paired t tests between:
    wt and 1a
    wt and 1b
    wt and 1c
    just between seeds on the same zinc levels!
    so basically it would be all wild type weights on zinc level 0 paired with all 1a weights on zinc level 0 and so on for wt:1b and wt:1c and then for every zinc concentration.
    that would really eventually solve my problem as i could then use an anova model to test for significance between each T-test.

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    If you wanted to do this run the ANOVA and use the package "multcomp" for planned comparisons.

    But what about your light factor?
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