What Quantity Appears on the Vertical Axis of a Normal Distribution? A Student Survey
19 Pages Posted: 27 Aug 2018 Last revised: 4 Feb 2020
Date Written: February 4, 2020
Final-year students in statistics, physics, and finance were asked to label the vertical axis on a normal distribution, explain their label, identify units, and answer a question about the impact of x-axis rescaling. Fewer than 4% of the students could both label the vertical axis correctly (as probability density) and explain their label. The most common incorrect vertical axis label was “probability.” Performance on individual survey questions differed significantly by academic discipline, but overall survey performance varied very little, ranging between only 8.8% and 12.5% of survey answers being correct across disciplines. To fill these demonstrated gaps in statistics education, we give counterexamples to demonstrate why “probability” cannot be the correct vertical axis label; we explain why “probability density” is the correct label; and we give an intuitive explanation of probability density and its units. We also 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, and we discuss the impact of x-axis rescaling. This paper is intended for all levels of statistical education.
Keywords: probability density; linear denisty; pdf; pmf; cdf; resclaing
JEL Classification: A20
Suggested Citation: Suggested Citation