What Quantity Appears on the Vertical Axis of a Normal Distribution? A Student Survey. Issue 2 (6th August 2021)

• Record Type: Journal Article
• Authors: Chaput, J. Scott; Crack, Timothy Falcon; Onishchenko, Olena
• Is Part Of: Journal of Statistics and Data Science Education. Volume 29:Issue 2(2021)
• Page Start: 192
• Page End: 201
• Publication Date: 2021-08-06
• Subjects: cdf -- Linear density -- pdf -- pmf -- Probability density -- Rescaling
• DOI: Https://www.tandfonline.com/doi/10.1080/26939169.2021.1933658
• Languages: English
• ISSNs: 2693-9169

Abstract

Abstract: How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the normal distribution correctly, and of these, only five students (i.e., 3.4%) could explain their label. Performance on individual survey questions differed by degree program, as might be expected, but overall survey performance varied very little, ranging between only 8.8% and 12.5% of survey questions answered correctly across degree programs. Common misconceptions included labeling the vertical axis as "probability, " "count, " or "frequency." To address these demonstrated gaps in statistics education, we give counterexamples to show why these labels cannot be correct; we explain why "probability density" is the correct label; and we give an intuitive explanation of probability density and its units. We also discuss the impact of horizontal-axis rescaling, and we indicate how the units of probability density change if the probability density function is for a bivariate or trivariate distribution instead of a univariate distribution. This article is intended for all levels of statistics education.