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I want to describe the relationship between pairs of continuous variables. I know this is commonly done just by looking at a scatterplot, but I think this is not appropriate for my problem, because (1) my sample size is small (15), (2) I have a to do 28 comparisons, and (3) my goal is to have some certainty when describing a relationship, and make just a visual evaluation seems to me that is easy to make mistakes.

I am doing a research the relationship of soft and hard tissue in humans and simply stated my question is How is the relationship between soft and hard tissue? is it linear, exponential, etc? I appreciate if you could recommend me a test or a way to provide confident results on this matter

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    $\begingroup$ You should look at scatter plots regardless of whether you wish to proceed further and regardless of sample size. You are more likely to make mistakes if you don't have a good feel for your data. That said, "the relationship between soft tissue and hard tissue" is not likely to be clear even to people in your field. Are you e.g. measuring amounts of hard and soft issue? comparing hard and soft tissue on other variables? What you're seeking here is unclear. $\endgroup$ – Nick Cox Apr 6 '18 at 11:46
  • $\begingroup$ There is no way to get around the problem of a sample size that is too small. $\endgroup$ – Michael R. Chernick Apr 6 '18 at 13:55
  • $\begingroup$ Thank to all, Nick, when I say that I'm going to study the relationship between soft tissue and hard tissue, I mean specifically to variables as muscle mass, fiber length and other muscular variables with bone proportions (simple linear measurements, eg: the breadth of the head of a bone). This is a relatively simple question in anatomical and statistical terms I think, so any statistical method for this purpose is useful to me. $\endgroup$ – Ana Apr 13 '18 at 8:23
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If your question is about the form of the relationships between several variables, I would try various linear/non-linear regression models for each pair and evaluate them based on some (penalized) goodness-of-fit measure(s) such as AIC, BIC, and/or parsimony/common sense. You might also try making comparisons based on Bayes factor or relative likelihood. If you are using statistical software, you can automate this process, then show this goodness-of-fit/comparison data somehow, probably with table or bar chart, perhaps alongside a subset of the scatterplots. Again, this won't be definitive (or even actual), but depending on the data could point strongly towards use of one model over another, which is the best we can do regardless.

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If you only have a sample size of 15 then, for any relationship to be statistically significant it would have to be either a) blatant or b) A result of overfitting or c) Type I error (that last one is not because you have so little data but because you seem to need to do a lot of tests).

If you really have no idea about the relationship, and want to investigate all sorts of fits, then you will need more data.

So, my suggestion is to look at scatterplots, then make hypotheses and then gather a bunch more new data in order to test those hypotheses.

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