People, scientists and the like, want to know if a result is statistically significant. No one cares about the significance level or critical levels, because most of the time, those levels are fixed. Thus, your point about statistical significance being a consequence of choosing a significance level is a non sequitur. Statistical significance is also consequence of calculating means and standard errors. And in non-parametric cases, in terms of rank. Does that mean we should rename this article in terms of mean differences?     