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From: Eric on 28 Jul 2010 09:02
Hi all,
Here is my statistical issue:
- 10 pairs of samples (the first experienced a treatment, the second not)
- 2 sides for each sample (North and South)
- 1 measurement for each side

=> 40 measurements

I need to know if the results of the measurements are due to the side (S) , due to the treatment (T). In fact, I need to evaluate the effect of S, T and S*T.

Basically, I think it is an ANOVA with 2 factors.
What I do not know: how to form the pairs (side North of treated sample 1 should be compared to side North of the untreated one)

Thank you
Eric
From: Peter Perkins on 28 Jul 2010 11:29
On 7/28/2010 9:02 AM, Eric wrote:
> Hi all,
> Here is my statistical issue:
> - 10 pairs of samples (the first experienced a treatment, the second not)
> - 2 sides for each sample (North and South)
> - 1 measurement for each side
>
> => 40 measurements
>
> I need to know if the results of the measurements are due to the side
> (S) , due to the treatment (T). In fact, I need to evaluate the effect
> of S, T and S*T.
>
> Basically, I think it is an ANOVA with 2 factors. What I do not know:
> how to form the pairs (side North of treated sample 1 should be compared
> to side North of the untreated one)

Eric, when you say "10 pairs of samples", are they "paired" as in (by
way of analogy) a paired t-test? Or just that you have a balanced
design? Ditto "sides". You might want to think about how independent
your measurements are, and choose a model accordingly.
From: Eric on 28 Jul 2010 13:12
Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <i2pidg$sna$1(a)fred.mathworks.com>...
> On 7/28/2010 9:02 AM, Eric wrote:
> > Hi all,
> > Here is my statistical issue:
> > - 10 pairs of samples (the first experienced a treatment, the second not)
> > - 2 sides for each sample (North and South)
> > - 1 measurement for each side
> >
> > => 40 measurements
> >
> > I need to know if the results of the measurements are due to the side
> > (S) , due to the treatment (T). In fact, I need to evaluate the effect
> > of S, T and S*T.
> >
> > Basically, I think it is an ANOVA with 2 factors. What I do not know:
> > how to form the pairs (side North of treated sample 1 should be compared
> > to side North of the untreated one)
>
> Eric, when you say "10 pairs of samples", are they "paired" as in (by
> way of analogy) a paired t-test? Or just that you have a balanced
> design? Ditto "sides". You might want to think about how independent
> your measurements are, and choose a model accordingly.

Yes, they are "paired" as in a paired test. Before the experiment, I did pairs of similar samples. Thus each treated sample has a control. They are a pair.
Eric
From: Peter Perkins on 29 Jul 2010 09:22
On 7/28/2010 1:12 PM, Eric wrote:
> Yes, they are "paired" as in a paired test. Before the experiment, I did
> pairs of similar samples. Thus each treated sample has a control. They
> are a pair.

If that's the case, and if (as it sounds) your measurements at
north/south "sides" are also taken on the same "samples", then you need
to think about independence of your measurements, and perhaps consider
random effects, or consider, for example, modelling (ynorth(i) -
ysouth(i)) rather than modelling ynorth(i) and ysouth(i) as separate
measurements. By way of analogy, a paired t-test is really a one-sample
t-test on differences.

I don't know anything about your data, so the above may be completely
off base.
From: Eric on 29 Jul 2010 10:46
> If that's the case, and if (as it sounds) your measurements at
> north/south "sides" are also taken on the same "samples", then you need
> to think about independence of your measurements, and perhaps consider
> random effects, or consider, for example, modelling (ynorth(i) -
> ysouth(i)) rather than modelling ynorth(i) and ysouth(i) as separate
> measurements. By way of analogy, a paired t-test is really a one-sample
> t-test on differences.
>
> I don't know anything about your data, so the above may be completely
> off base.

Thank you Peter for your answer. I think I need to give more details. The experiment is :
- 20 plants
- Treatment : 10 experienced a treatment and 10 are the control
- I do not pool the 10 because before the experiment, I formed pairs (1 treated and 1 non treated). thus, I have 10 pairs
- Side : Hypothesis : the treatment could have an effect from side to side (North side could react differently from South (Side)
- measurements are done for each sample / each side => 40 measurements

If I put all the North side together and the South side together (regardless the pairs), there is no effect (Fisher test)
If I put all the treated together and the non-treated together (regardless the pairs), a difference is significant.

But, in these tests:
- I do not take the pairs into account
- I do not test Treatment * Side

I did an ANOVA with 2 factors to test Treatment, Side and Treatment * Side. But this ANOVA does not take the pairs into account. They put the samples together.
That is the difficulty I don't know to manage.
Is the experiment more clear ?
Eric
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