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.

摘要

统计学、物理和金融专业的最后一年学生如何准确地标记正态分布的纵轴、解释他们的标签、确定单位并回答有关横轴重新缩放影响的问题？我们的调查发现，在接受调查的 148 名学生中，只有 27 名（即 18.2%）能够正确标记正态分布的纵轴，其中只有 5 名学生（即 3.4%）能够解释他们的标签。正如预期的那样，个别调查问题的表现因学位课程而异，但总体调查表现差异很小，只有 8.8% 到 12.5% 的调查问题在不同学位课程中得到正确回答。常见的误解包括将纵轴标记为“概率”、“计数”或“频率”。为了解决统计教育中这些明显的差距，我们给出反例来说明为什么这些标签不正确；我们解释了为什么“概率密度”是正确的标签；我们对概率密度及其单位给出了直观的解释。我们还讨论了水平轴重新缩放的影响，并指出了如果概率密度函数适用于双变量或三变量分布而不是单变量分布，则概率密度的单位如何变化。本文适用于各级统计教育。如果概率密度函数用于二元或三元分布而不是单变量分布，我们会指出概率密度的单位如何变化。本文适用于各级统计教育。如果概率密度函数用于二元或三元分布而不是单变量分布，我们会指出概率密度的单位如何变化。本文适用于各级统计教育。