Using statistical significance test to validate cluster analysis results I am surveying the use of statistical significance testing (SST) to validate the results of cluster analysis. I have found several papers around this topic, such as


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*"Statistical Signiﬁcance of Clustering for High-Dimension, Low–Sample Size Data" by Liu, Yufeng et al. (2008)

*"On some significance tests in cluster analysis", by Bock (1985)
But I am interested in finding some literature arguing that SST is NOT appropriate to validate results of cluster analysis. 
The only source I have found claiming this is a web page of a software vendor
To clarify:
I am interested in testing whether a significant cluster structure has been found as a result of cluster analysis, so, I'd like to know of papers supporting or refuting the concern "about the possibility of post-hoc testing of the results of exploratory data analysis used to find clusters". 
I've just found a paper from 2003,  "Clustering and classification methods" by Milligan and Hirtle saying, for example, that using ANOVA would be an invalid analysis since data have not have random assignments to the groups.
 A: It is fairly obvious that you cannot (naively) test for difference in distributions for groups that were defined using the same data. 
This is known as "selective testing", "double dipping", "circular inference", etc.
An example would be performing a t-test on the heights of "tall" and "short" people in your data. The null will (almost) always be rejected. 
Having said that- one may indeed account for the clustering stage at the testing stage. I am unfamiliar, however, with a particular reference that does that, but I suspect this should have been done. 
A: Instead of hypothesis testing with a given test, I would recommend bootstrapping means or other summary estimates between clusters. For instance you could rely on percentile bootstrap with at least 1000 samples. The key point is to apply clustering independently to each bootstrap sample. 
This approach would be quite robust, provide evidence for differences, and support your claim of significant between-cluster difference. In addition, you could generate another variable (say between-cluster difference) and bootstrap estimates of such difference variable would be similar to a formal test of hypothesis.
