ANOSIM: significant p-value and small R-value. How?


New Member
I am analyzing data of a large sample size ('000's of samples) via one-way ANOSIM.

Results appear contradictory: Highly significant p-value (0.001) and very small R-value (0.02).

How is this possible? What is the correct interpretation of these results?

nMDS shows no clustering.

Thanks very much for any assistance.


New Member
Are you able to explain how this affects the interpretation of the p-value? I've had difficulty finding information.

Thank you.


Omega Contributor
Not familiar with your approach but typically in test statistics the standard error is a component of the denominator. Large sample sizes make the error smaller and effects larger. For a general idea look at the t -test. What is the denominator, square root of standard deviation divided by the sample size. The bigger the sample size the smaller the denominator. Thus with the exact same numerator but bigger sample size the test statistic value will get bigger and bigger.


Super Moderator
The results are not contradictory. The p value tells you the probability of seeing a test statistic as or more extreme than that observed in your sample if the null hypothesis is true in the population. The R-value tells you about the size of the differences found.

With a very large sample, even a very small relationship (or group difference) could produce a significant p value and allow you to reject the null hypothesis.

A small p value does not indicate that the relationship or different found is large, or practically significant.