Equivalence class formation: a method for teaching statistical interactions

Abstract

Many students struggle with statistical concepts such as interaction. In an experimental group, participants took a paper-and-pencil test and then were given training to establish equivalent classes containing four different statistical interactions. All participants formed the equivalence classes and showed maintenance when probes contained novel negative exemplars. Thereafter, participants took a second paper-and-pencil test. Participants in the control group received two versions of the paper-and-pencil test without equivalence-based instruction. All participants in the experimental group showed increased paper-and-pencil test scores after forming the interaction-indicative equivalence classes. Class-indicative responding also generalized to novel exemplars and the novel question format used in the paper-and-pencil test. Test scores did not change with repetition for control group participants. Implications for behavioral diagnostics and teaching technology are discussed.

Keywords: college students; computer-based training; equivalence classes; generalization to novel exemplars.

Figure 1

An example of the four members of each class of stimuli used during the equivalence training.

Figure 2

Two examples of questions on the paper pretest and posttest. The first question tests a B-A relation from Class 2, and the second question tests a D-C relation from Class 4.

Figure 3

The mean number of blocks needed for all experimental group participants to achieve mastery criterion during the computer-based equivalence training. Each training and testing phase of equivalence class formation appears as a separate bar, and the left to right position of each bar corresponds to the order in which each relation was trained or tested. The height of each bar indicates the mean number of blocks needed to form a baseline relation or to pass an emergent relations test.

Figure 4

The mean pretest–posttest scores for both experimental (filled squares) and control (open circles) groups. The I beams that bracket each data point indicated ± 1 SE.

Figure 5

A scattergram showing posttest scores plotted as function of pretest scores for each participant in the experimental (filled circles) and control (open circles) groups. Two participants in the experimental group produced identical pretest and posttest scores, indicated by the arrow. Separate regression lines are also shown for the data obtained from participants in the experimental and control groups.