The role of significance testing: some data with a message

In the context of experimental data, allowance for data-snooping in significance testing is found to conflict with power considerations. Appendices give (a) specific results for the nonparametric statistics employed, (b) general theorems concerning expected significance level and (c) general theorems concerning allowance for data-snooping. In (b), a correction is made of a lacuna of Dempster and Schatzoff.