In statistics courses, students often find it difficult to understand the concept of a statistical test. An aggravating aspect of this problem is the seeming arbitrariness in the selection of the level of significance. In most hypothesis-testing exercises with a fixed level of significance, the students are just asked to choose the 5% level, and no explanation for this particular choice is given. This article tries to make this arbitrary choice more appealing by providing a nice geometric interpretation of approximate 5% hypothesis tests for means.<br>Usually, we want to know not only whether an observed deviation from the null hypothesis is statistically significant, but also whether it is of practical relevance. We can use the same geometrical approach that we use to illustrate hypothesis tests to distinguish qualitatively between small and large deviations.
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