Despite frequent calls for the overhaul of null hypothesis significance testing (NHST), this controversial procedure remains ubiquitous in behavioral, social and biomedical teaching and research. Little change seems possible once the procedure becomes well ingrained in the minds and current practice of researchers; thus, the optimal opportunity for such change is at the time the procedure is taught, be this at undergraduate or at postgraduate levels. This paper presents a tutorial for the teaching of data testing procedures, often referred to (...) as hypothesis testing theories. The first procedure introduced is Fisher's approach to data testing—tests of significance; the second is Neyman-Pearson's approach—tests of acceptance; the final procedure is the incongruent combination of the previous two theories into the current approach—NSHT. For those researchers sticking with the latter, two compromise solutions on how to improve NHST conclude the tutorial. (shrink)