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.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p= .05 to .005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of .05, .01, .005, or anything else, is not acceptable.

The 21st century began with a heated debate in scientific research, known as the 'replication crisis', 'reproducibility crisis' or 'crisis of confidence ' (Fanelli, 2018). Problems in replicating findings and reproducing scientific research began to be evident in many areas of research. The problems became highly visible thanks to essays and studies published in scientific journals and articles in the popular press (

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