A dangerous trend toward nonrandom sampling mechanisms has been observ
ed in several fields of the applied sciences. These sampling designs a
re attempts to avoid tail observations, resulting in smaller estimated
standard errors and inflated claims of statistical significance. Ofte
n, the researchers go to some lengths to make the sampling mechanisms
appear random; yet, they clearly are not. The effect of these pseudora
ndom sampling designs on the power and size of the hypothesis tests is
investigated and shown to be substantial.