"David, if you obtain a p-value, what would it tell you about your proposed null hypothesis (H) of absolutely no correlation between distance D & relatedness R? A p-value will only indicate the probability of data at least as extreme as what you observed, assuming H; it’s a statement about data, rather than about H. Besides, I would have a difficult time accepting a priori that H could be true in the first place, & since I’m already (almost) sure H is false, I have little reason to test it."
the null hypothesis of no correlation between distance and relatedness represents what would be expected if the bees dispersed to a random site within their patch (which is certainly very plausible). if the pearson correlation coefficient was negative and the p-value was low (less than 0.05 for my purposes) i could infer that dispersal is probably not random, but that the bees disperse only short distances and set up nests close to their sisters (which is also plausible). conversely, if there was statistically significant positive correlation, that would suggest the bees actively disperse as far away as possible from their sisters, which again is ecologically interesting and plausible (e.g. to avoid competing against their relatives).
"If I was in your position I think I would rather determine the probability that the correlation coefficient (rho, say) is within some practically meaningful range, [a,b]. viz., the approach should rather be one of estimating the correlation, not seeing whether the correlation is exactly zero."
if there is a real correlation i have no reason to expect that the correlation will be a particular value (or within a particular range of values) and in fact it isn't particularly important in my case as (for what i am researching at this stage anyway) it doesnt really matter if the correlation is 0.3 versus 0.5 say - the ecological implications would be similar. in contrast, the ecological implications of any correlation (whatever its exact value) would be different from no correlation. hence at this stage im really only interested in testing whether my observed correlation is statistically different from zero. however certainly in the future testing whether any correlation is within a particular range of values could be an interesting follow up question and i thank you for the suggestion.
but at this stage im still just looking for a way of conducting a permutation-based significance test (2-tailed) for the pearson correlation between the 2 variables. if anyone has any suggestions it really would be a huge help.
david
To: Statisticians_group@...
From: khahstats@...
Date: Sat, 2 May 2009 21:35:13 -0700
Subject: Re: [Statisticians_group] pearson correlation test with permutation
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David, if you obtain a p-value, what would it tell you about your proposed null hypothesis (H) of absolutely no correlation between distance D & relatedness R? A p-value will only indicate the probability of data at least as extreme as what you observed, assuming H; it’s a statement about data, rather than about H. Besides, I would have a difficult time accepting a priori that H could be true in the first place, & since I’m already (almost) sure H is false, I have little reason to test it.
If I was in your position I think I would rather determine the probability that the correlation coefficient (rho, say) is within some practically meaningful range, [a,b]. viz., the approach should rather be one of estimating the correlation, not seeing whether the correlation is exactly zero.
When all the data (D & R) are i.i.d., this can be done using the posterior probability distribution for rho given in http://www.pubmedce Your case may be a little more complicated because, as you note, the data between any pair of nests A & B depend on the data between (say) A & C (i.e., whenever pairs of nests share a member). I don’t have any experience with this type of spatial analysis; however, I would guess that since you are trying to infer something about the relation between D & R, rather than D & R themselves, I would guess that taking all 21*20/2=210 pairs of D & R as independent would not bias the sample statistic (rho-hat); it would only complicate the calculation of the variance of rho-hat (conditional on rho) & hence of the spread of the posterior probability distribution of rho.
You are looking for an answer ASAP. Therefore, without researching this in depth, I would say that you could
You could do something similar, I imagine, comparing 2 ways of calculating the variance of rho-hat (conditional on rho), making an adjustment for the square root of the sample size.
I don’t know how good is this method of handling the dependencies; someone else may be able to provide a better answer. Nonetheless, I do feel strongly that the focus should be on estimation rather than significance testing. Best wishes. --- On Sat, 5/2/09, slop badgerd <slopbadgerd@
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