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Suppose that we have 30 plants (that are the same exact plants). Suppose that we choose 15 out of a sample of 30 plants and we seeded them with a drag. We then want to test whether this drag has an effect of making them grow faster. So we have 15 plants with a drag, and 15 plants with no drag. Let's suppose that the weather conditions are the same and they are at the same exact place-location. Are they paired or unpaired? Before I ask this question I searched it and by definition:

Paired samples mean that we take a sample (let's say a plant) and we see how it grows, then we put the drag to the EXACT same plant and see whether it makes any difference. According to this definition, I would use UNpaired samples since I am choosing two different groups of plants and not the same plant each time. BUT, concerning the fact that all these 30 plants are the same (they are the same object) can I still use a paired t-test? Thank you, I hope my question makes sense.

I read many examples with animals or humans. Of course if we have humans or animals then of course the answer is very simple, since every animal or human being is different. Subsequently if I use two different groups of human for example, the samples could be unpaired. But when I use objects like plants or clouds or trees or something like that. Does it make any sense to consider them as different, avoiding the fact that we are talking about the same object.

NobodyNada
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van boeren
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  • When you take measurement on the same plants the growth rates could be correlated. So often you take paired differences. However you have not made it clear what the measurement of growth is. So it is not clear that a t test should apply. To be realistic there could be confounding variables such as location of the plant and amount of sunlight that could be included and then you might want to do some form of analysis of variance. – Michael R. Chernick Apr 18 '17 at 22:52
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    yes but in my example I use 15 plants with drag, and 15 plants with no drag. So you say that because the plants are the same (the type of the plant) we should still consider this comparison as paired right? Let's suppose that the weather conditions are the same and they are at the same exact place-location. @MichaelChernick – van boeren Apr 18 '17 at 22:57
  • Why was the question edited like this? – Michael R. Chernick Apr 18 '17 at 23:29
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No, it is not paired. Paired and un-paired depend on the randomization used to apply the treatment. So to justify the use of the paired t-test, you would have had to select 15 pairs of plants - presumably on some grounds of common similarity. For each pair, you would toss a coin and randomly assign a drag to one member of the pair. In the end, you would have 15 with drags and 15 without, but the randomization would be different than in the study you describe.

The idea of doing a paired test is to reduce the plant to plant variation by randomizing across similar plants.

In an unpaired study with a treatment applied randomly to 15 of 30 subjects, there are $\binom{30}{15}$ possible samples. But with a paired experiment, there are $2^{15}$. The sample spaces are different, so the model is different.

Placidia
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  • Therefore, if we know that they just simply choose 15 out of a sample of 30, then it means that it is unpaired because we do not know that the randomization was a 50-50 result. So in my example we consider them as unpaired since we do not know how they have been chosen. Right? – van boeren Apr 18 '17 at 23:11
  • In any study with paired subjects, the authors should report the basis upon which pairing was made. That's how you would know. – Placidia Apr 18 '17 at 23:14