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Non-Parametric, Computer-Intensive Statistics Course Modules for Engineers

Abstract

This NSF CCLI project develops materials for a new course in non-parametric computer- intensive (NPCI) statistics. This course is distinctly different from existing undergraduate statistic courses in that the NPCI methods do not depend on assumed distribution functions (non- parametric) and rely heavily on computer resampling (computer-intensive). By teaching the basic concepts of sampling, replication, and variation in a hands-on environment instead of calculus-based probability theory, students gain an immediate intuitive understanding of statistics, rather than memorize a series of poorly understood statistical “recipes”. The practical results are: 1) statistical concepts are more transparent, 2) students better retain understanding of statistical concepts, 3) students are capable of more sophisticated statistics than what they can do in a traditional engineering statistics course, and 4) the course can be taken earlier in an engineering curriculum than a traditional parametric, calculus-based course. The following modules have been used in a Junior-level Civil Engineering course: basic concepts, descriptive statistics, descriptive graphs, point estimates, confidence intervals using bootstrapping, hypothesis testing using permutation theory, regression using both bootstrapping and permutation, and a comparison to traditional parametric statistics. The modules are described and their effectiveness is discussed.

Introduction

In this project, the PIs have developed modules to teach an engineering statistics course based on non-parametric computer-intensive (NPCI) methods. In circles outside of statistics, these methods are not well known so a description of the methods is presented here. Three general characteristics of statistical methods are: parametric/non-parametric, calculus- based/non-calculus-based, and computer-intensive/non-computer-intensive. The last two are self-explanatory but the term parametric, as used in statistic circles, is not commonly used. Parametric methods assume a distribution of the data (e.g. normal, chi-squared, or binomial). Determining probabilities using parametric methods involves defining distribution functions and integrating them, thus requiring calculus. These three characteristics are illustrated in Table 1. NPCI methods gained ground in the late 1970s1,2.

Table 1. Various Statistical Methods Used in Statistics Courses Statistical Methods Course Parametric, Calculus-Based, Non-Computer Traditional Engineering Statistics Course Intensive Probability distributions are assumed and these functions are integrated using calculus. Parametric, Calculus-Based, Computer Monte Carlo Simulations Intensive Probability distributions are still assumed, but modeled with computer software using perturbations. Parametric, Non-Calculus-Based, Non- Traditional Non-STEM Statistics Course

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Mukai, D., & McDonald, T. (2009, June), Nonparametric, Computer Intensive Statistics Course Modules For Engineers Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5087