This paper proposes an argument framework for the teaching of null hypothesis statistical testing and its application in support of research. Elements of the Toulmin (1958) model of argument are used to illustrate the use of p values and Type I and Type II error rates in support of claims about statistical parameters and subject matter research constructs. By viewing the application of null hypothesis statistical testing within this framework, the language and intent of statistical support for research can be more precisely understood and taught. (Contains 2 figures and 1 table.)