The effect of varying proportions of positive and negative instances on student misinterpretation of statistical hypothesis testing.

Abstract

A 2 x 2 factorial ANOVA unweighted means analysis was used to sense overall mean differences. Then, the Aspin-Welch version of Tukey's test was used to detect mean differences in all possible pair-wise comparisons among treatments.

The proportion of negative instances were two thirds, one third, or zero. A negative instance referred to misinterpretation of the two independent sample t in each of four situations: (1) When H(, 0) was rejected in a very high power test; (2) When H(, 0) was rejected in a very low power test; (3) When H(, 0) was accepted in a very high power test; (4) When H(, 0) was accepted in a very low power test.

The two-way ANOVA unweighted means analysis did not approach significance at the .05 level for the interaction between treatments and performance. The main effect for treatments, via ANOVA, was significant (P < .05). Among pair-wise comparisons, only two thirds negative vs. control comparison was significant (P < .05).

Twenty-seven volunteer students in the upper half of the class, and twenty-eight volunteer students in the lower half were randomly assigned to one of three experimental conditions, or to a control condition.

What is the effect of varying proportions of positive and negative instances on student misinterpretation of statistical hypothesis testing, using the two independent sample t, in an elementary non-calculus statistics class?