I want to find the relationship between two variables- one is a population and other the site of its origin. I have only three sites of origin and have to plot the mean of the samples from that population. Probably the correlation analysis could not be performed using only three samples ( as it would not give significant results at any cost due to very small sample size). It is not possible for me to increase the no of sites. If I use individual sample from each population, I must be practicing pseudoreplication. How can I use my this data to find the relationship between my variables. Is there any alternative method to do this. Is performing correlation on such a small data set reasonable. I got r value of as high as 0.9 but with non significant p value. I know the reason is small sample size but cannot increase it. What should I do?

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    $\begingroup$ What is the research question? Depending on the question, you can consider mixed-modeling, which would allow you to use all samples rather than just the means and use a random effect term to account for clustering within a site. $\endgroup$ – half-pass May 25 '15 at 15:32
  • $\begingroup$ Ok, to be more specific I have to find phenotypic plasticity from the mean of the populations and then find the correlation between this phenotypic plasticity and the site of origin. Now as the estimation of phenotypic plasticity involves the mean of the samples how could I use this as random. $\endgroup$ – Akanksha Singh May 26 '15 at 11:47
  • $\begingroup$ But that is still describing a modeling approach. What is it that you want to learn about phenotypic plasticity? Do you want to know when phenotypic plasticity is different, on average, across sites? Site of origin is not continuous, so it does not make sense for it to be in a Pearson correlation in the first place. Is there some characteristic of site that you're interested in? $\endgroup$ – half-pass May 26 '15 at 14:56
  • $\begingroup$ Yes, I want to find the difference in the phenotypic plasticity from each of the three populations and compare them to find whether there is a trend in their difference that they follow with respect to the latitude of their site of origin. $\endgroup$ – Akanksha Singh May 27 '15 at 7:06

Instead of treating each site as the unit of analysis and reducing a rich dataset to only 3 points, you can use an approach like mixed-effects modeling to treat each individual measurement of phenotypic plasticity as the unit of analysis. Because latitude is the true effect of interest rather than site, consider a model specification in which there is a fixed effect of latitude and a random intercept by site (the latter of which accounts for the fact that observations are correlated within a site – this is the pseudoreplication problem that you were rightly concerned about). Make sure to put some thought into whether your scientific hypothesis warrants treating latitude as continuous or as ordinal.

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  • $\begingroup$ For me latitude acts as continuous variable. I have 4 sites or say replicates for each latitude. So according to you I should treat each replicate as an unit of analysis. This is pseudoreplication. Isn't it? Will it be right to do so? $\endgroup$ – Akanksha Singh May 28 '15 at 5:25
  • $\begingroup$ Like I said, you should fit a random intercept by site in order to account for correlation of replicates within a site. $\endgroup$ – half-pass May 28 '15 at 15:07
  • $\begingroup$ Great. If that answers your question, you could mark it as accepted. $\endgroup$ – half-pass May 30 '15 at 15:24
  • $\begingroup$ This is not able to solve my problem. I have to apply correlation on the result of a function (described as Max mean-Min mean/Max mean of a population), which is calculated by mixed model approach itself. The value of function has also been generated using bootstrapping. I get only three values for function corresponding to each population. How could I incorporate mixed model here again. Your suggestion would have been valid if we apply correlation directly to population mean and not on the function. Any further suggestion please ... $\endgroup$ – Akanksha Singh Jun 10 '15 at 10:05

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