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In their recent comment, published in Nature, Jeffrey T.Leek and Roger D.Pengdiscuss how P-values are widely abused in null hypothesis significance testing. We agree completely with them and in this short comment we discuss theimportance of sample homogeneity tests. No matter with how much scrutiny dataare gathered if homogeneity tests are not performed the significance testssuffer from sample homogeneity loophole and the results may not be trusted. Forexample sample homogeneity loophole was not closed in the experiment testinglocal realism in which a significant violation of Eberhard inequality wasfound. We are not surprised that Bell type inequalities are violated since ifthe contextual character of quantum observables is properly taken into accountthese inequalities cannot be proven. However in order to trust the significanceof the violation sample homogeneity loophole must be closed. Therefore werepeat after Jeffrey T.Leek and Roger D.Peng that sample homogeneity loopholeis probably just the tip of the iceberg.

Significance tests and sample homogeneity loophole