Considered normative from the second half of the 20th century (Danziger, 1990), null hypothesis statistical testing (NHST) has received consistent, largely unheeded criticism. Critiques have received more attention in recent years with the recognition of the replication crisis in the social sciences and the American Statistical Society's statement and special issue on p values (Wasserstein & Lazar, 2016; Wasserstein et al., 2019). This paper seeks to provide a framework for understanding the issue by looking at the history of NHST and investigating some alternatives to the methodology. A brief review of the history, spread, and critiques of NHST is provided to help place the issues in context. Supplemental and alternative methods are described to demonstrate the range of available options to NHST. A selection of viable alternative methodologies and supplements to NHST are demonstrated using simulated data sets. Those methods that provide decision rules are compared with NHST using Monte Carlo method simulations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]