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A reconceptualization of significance testing

Significance testing has been controversial since Neyman and Pearson published their procedure for testing statistical hypotheses. Fisher, who popularized tests of significance, first noticed the emerging confusion between that procedure and his own, yet he could not stop their hybridization into what is nowadays known as Null Hypothesis Significance Testing (NHST). Here I hypothesize why similar attempts to clarify matters have also failed; namely because both procedures are designed to be confused: their names may not match purpose, both use null hypotheses and levels of significance yet for different goals, and p-values, errors, alternative hypotheses, and significance only apply to one procedure yet are commonly used with both. I also propose a reconceptualization of the procedures to prevent further confusion.