To my understanding Blomberg's K (a measure of the strength of phylogenetic signal) is computed along with an associated p-value by comparing the real data to a null distribution obtained by random permutations of the data. This would mean that the null expectation is a random pattern in the data, and so only K-values with significant p-values (typically p > 0.05) can be interpreted to indicate non-random patterns (i.e. phylogenetic signal).
For my data (macaque tooth size variation) I obtain many K-statistics with values below 1, but they have non-significant p-values. What is the interpretation of this? That these data do not show a pattern that is significantly different from randomness? The literature seems to suggest that the null hypothesis for Blomberg's K can be K = 0 or K = 1. K is designed in such a way that when K < 1, it indicates low phylogenetic signal, possibly indicating convergent evolution. But I would like to know if this interpretation only holds when K < 1 with significant p-values.
(I used the function 'multiphylosignal' of the 'picante' package to calculate K for my data.)
A non-significnt p-value means exactly that any pattern you may see in the data is just what you might expect from random variation and not selection, convergent evolution or any other biological - non random process.
Any time you get a non-significant result, of course, means simply that the data provide no evidence that the process is non-random. However, this may simply mean that the power of the test is too poor to detect a pattern because of noisy data or small sample size.
A non-significnt p-value means exactly that any pattern you may see in the data is just what you might expect from random variation and not selection, convergent evolution or any other biological - non random process.
Any time you get a non-significant result, of course, means simply that the data provide no evidence that the process is non-random. However, this may simply mean that the power of the test is too poor to detect a pattern because of noisy data or small sample size.
Nicole -
I do not know your subject matter, but I do know that Patrice has a very good point about sample size. The p-value is overused in many disciplines, and very often misinterpreted. An isolated p-value without a power or other sensitivity analysis, in my opinion, is to be avoided. At the least, you need to avoid using a level of 0.05 for "significance," universally. But it takes a power analysis or similar to determine what level to use. (Even the word "significance" is misleading. Better to know about the effect size.)
https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS
Cheers - Jim
Article Practical Interpretation of Hypothesis Tests - letter to the...
Dear Patrice and James,
Thank you both for your answers. You raise good points, which I had come to realise myself in the meantime. I agree that 'statistical significance' is a highly imperfect and rather arbitrary standard against which to measure and interpret results.
Cheers,
Nicole
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