By Jon Hasenbank (Grand Valley State University) and John Appiah-Kubi (Grand Valley State University)
Information
Discover the k-test, a new tool for statistical inference whose results agree closely with the traditional t-test but which does not use the standard deviation (SD). The k-test relies on the MAD (mean absolute deviation), a measure of numerical variability introduced in the 6th grade Common Core Standards and used in middle school data investigations. The k-test improves upon intuition-based reasoning (e.g. do the distributions appear to overlap?) and other simple heuristics (e.g. is the difference greater than twice a measure of variability) by providing precise significance thresholds that can be used to find p-values and calculate confidence intervals. For instance, if two samples of size 15 have a mean difference of at least 0.97 sample MADs, the difference is significant (alpha = 0.05). Our session aims to establish these MAD-based inference methods as pedagogically accessible alternatives that improve upon the existing informal heuristics. These new methods open new avenues for educational research. In an early pilot, we worked with a middle school teacher to develop a mini-unit for 8th graders aligned with Common Core standard CCSS.7.SP.B. Students collected random samples, expressed the mean differences as a multiple of the MAD, and then used a MAD-based threshold to assess meaningful differences. Our observations suggested students understood the relevance of using the MAD-based thresholds and were able to correctly interpret their findings in the context of the investigation. In our debriefing, the partner teacher expressed enthusiasm for the approach and reported that she intended to share the unit with her peers so that “no one else has to ask, how am I even going to teach this”. The results apply at two levels. At our university, we present these tools in our secondary math education program for preservice teachers in a statistics education class that has Intro to Statistics as a prerequisite. The typical class size is 10-20 students. The results are also applicable to middle and high school teaching, where the k-test is a developmentally appropriate alternative to the t-test for either informal (middle school) or formal inference (high school), based on the recommendations from the Common Core Standards (2010) and the PK-12 Guidelines for Assessment and Instruction in Statistics Education II (ASA, 2020). More research is needed to explore the pedagogical implications, but these new tools open many possibilities for supporting inferential reasoning at a variety of levels.