Null hypothesis significance testing (NHST) is one of the most widely used methods for testing hypotheses in psychological research. However, it has remained shrouded in controversy throughout the almost seventy years of its existence. The present article reviews both the main criticisms of the method as well as the alternatives which have been put forward to complement or replace it. It focuses basically on those alternatives whose use is recommended by the Task Force on Statistical Inference (TFSI) of the APA (Wilkinson and TFSI, 1999) in the interests of improving the working methods of researchers with respect to statistical analysis and data interpretation. In addition, the arguments used to reject each of the criticisms levelled against NHST are reviewed and the main problems with each of the alternatives are pointed out. It is concluded that rigorous research activity requires use of NHST in the appropriate context, the complementary use of other methods which provide information about aspects not addressed by NHST, and adherence to a series of recommendations which promote its rational use in psychological research.

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