Students Understanding of the Logic of Hypothesis Testing

Jimenez, A. V., & Holmes, P.
Fourth International Conference on Teaching Statistics, July
Marrakech, Morocco

Significance testing is one of the most controversial subjects in research (Morrison and Henkel, 1970) and also one of the most misunderstood topics in the learning of statistics (Falk, 1986: Falk and Greenbaum (in print)). In this paper we present the results from a theoretical and experimental study concerning University students' understanding about the logic of statistical testing. The theoretical study discusses epistemological issues concerning Fisher's and Neyman-Pearson's approach to hypothesis testing and their relationship to the problem of induction in experimental sciences. The experiment sample included 436 students from 7 different university majors. Some of these students had a theoretically oriented course in statistics, such as those reading Mathematics, whereas others had a practically oriented course in statistics, such as those reading Psychology. The item presented in this paper is part of a larger questionnaire, which includes 20 items, and refers to the kind of proof provided by the results of a test of hypotheses. Following the analysis of these students' arguments, we identify three main conceptions: a) the test of hypotheses as a decision rule which provides a criterion for accepting one of the hypotheses; b) the test of hypotheses as mathematical proof of the truth of one of the hypotheses and c) the test of hypothesis as an inductive procedure which allows us to compute the "a posteriori" probability of the null hypothesis.

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education