Modernizing How Interval Estimation is Taught in Undergraduate Statistics Courses

Music City Center 

Confidence interval estimation in undergraduate statistics textbooks is generally carried out using equations (for, e.g., normal means and binomial proportions) that, when derived, are derived using the so-called pivotal method. This approach has been motivated by the long-term use of statistical tables for evaluating interval bounds, and is thus inherently limited (and, in the age of computers, woefully inadequate). In this talk, we discuss a more modern approach to interval estimation that we follow when teaching mathematical statistics to undergraduates at Carnegie Mellon, which is based on the interval-estimation method dubbed "Pivoting the CDF" by Casella & Berger (2002; section 9.2.3). We show how, when the cumulative distribution function of the sampling distribution of the adopted statistic is known but not easily inverted, numerical estimates are easily achieved, and how, when the cdf is unknown, we can make estimates via simulation and numerical optimization. We argue that these non-analytic approaches to interval estimation make the process wholly accessible to students with minimal programming experience, including those in non-calculus-based introductory classes.

confidence intervals

mathematical statistics

statistical inference

instructional design

undergraduate statistics curriculum

statistical practice 

Section on Statistics and Data Science Education