Content Audit for p-value Principles in Introductory Statistics

ABSTRACT

Longstanding concerns with the role and interpretation of p-values in statistical practice prompted the American Statistical Association (ASA) to make a statement on p-values. The ASA statement spurred a flurry of responses and discussions by statisticians, with many wondering about the steps necessary to expand the adoption of these principles. Introductory statistics classrooms are key locations to introduce and emphasize the nuance related to p-values; in part because they engrain appropriate analysis choices at the earliest stages of statistics education, and also because they reach the broadest group of students. We propose a framework for statistics departments to conduct a content audit for p-value principles in their introductory curriculum. We then discuss the process and results from applying this course audit framework within our own statistics department. We also recommend meeting with client departments as a complement to the course audit. Discussions about analyses and practices common to particular fields can help to evaluate if our service courses are meeting the needs of client departments and to identify what is needed in our introductory courses to combat the misunderstanding and future misuse of p-values.     

Graduate Statistics Service Courses

This article describes our experience in, and recommendations for, teaching introductory statistics service courses to graduate students. Drawing on the student's research orientation, the instructor can present statistics as a valuable component of the scientific method, using examples from the student's particular discipline(s). Statistically qualified course instructors may be affiliated with statistics or other departments, and the course may be offered within any department. Course goals can range from training students to function independently as statistical analysts in future research to training students to consult a qualified statistician about design and analysis issues.     

Convergence of Known Distributions to Limiting Normal or Non-normal Distributions: An Elementary Ratio Technique

This article presents an elementary informal technique for deriving the convergence of known distributions to limiting normal or non-normal distributions. The presentation should be of interest to teachers and students of first year graduate level courses in probability and statistics.     

Current challenges in statistics: large-lecture courses

Each semester approximately 80% of the students taught by the Florida State University Department of Statistics are enrolled in STA 3014: Fundamental Business Statistics. During the academic year this course is taught in large lecture sections of 250 students each. It is either the only statistics course or one of two statistics courses taken in their undergraduate career for probably 90% of these students. A similar situation exists in many statistics departments around the nation.

These large introductory courses offer us the opportunity to introduce the power of statistics to a large fraction of our future business leaders. In the past it appears that this opportunity has often been missed. In fact, some suggest that these courses help contribute to the general public's negative attitude toward statistics courses, the discipline of statistics, and statisticians.

Hence, I propose that one of the current challenges in statistics is the challenge of improving the quality of these courses so that statistics may contribute to the improvement of quality and productivity in the United States, a vital national issue. In this paper I report on my experiences in grappling with this challenge in STA 3014.     

Teaching Introductory Statistics Courses So That Nonstatisticians Experience Statistical Reasoning

The most critical point in developing dynamic introductory statistics courses for nonstatisticians is deciding whether to teach statistical reasoning (concepts and thinking), statistical methods (computations), or both. Statistical reasoning should precede statistical methods. Workshop-based courses effectively provide situated learning and an intimate teaching environment. Use real (or realistic) data, graphics, and teach exploratory data analysis before classical methods. Evaluate the students' levels of statistical anxiety prior to and during the course.     

A Graphical Display of Large Correlation Matrices

This department includes the two sections New Development in Statistical Computing and Statistical Computing Software Reviews; suitable contents for each of these sections are described under the respective section heading. Articles submitted for the department, outside the two sections, should not be highly technical and should be relevant to the teaching or practice of statistical computing.

Large correlation matrices are hard to look at. In this article we present correlations as elliptical glyphs for a simple intuitive display of large matrices.     

Accent on Teaching Materials

This department includes the two sections New Developments in Statistical Computing and Statistical Computing Software Reviews; suitable contents for each of these sections are described under the respective section heading. Articles submitted for the department, outside the two sections, should not be highly technical and should be relevant to the teaching or practice of statistical computing.

An unbiased estimator of e is used to motivate a simple simulation exercise that requires only observations from the distribution uniform on (0, 1). Antithetic variables are introduced and applied to the simulation problem to give a second unbiased estimator of e with reduced variance.     

Confidence intervals following Box-Cox transformation

What is the interpretation of a confidence interval following estimation of a Box-Cox transformation parameter λ? Several authors have argued that confidence intervals for linear model parameters ψ can be constructed as if λ. were known in advance, rather than estimated, provided the estimand is interpreted conditionally given $\hat \lambda$. If the estimand is defined as $\psi \left( {\hat \lambda } \right)$, a function of the estimated transformation, can the nominal confidence level be regarded as a conditional coverage probability given $\hat \lambda$, where the interval is random and the estimand is fixed? Or should it be regarded as an unconditional probability, where both the interval and the estimand are random? This article investigates these questions via large-n approximations, small- σ approximations, and simulations. It is shown that, when model assumptions are satisfied and n is large, the nominal confidence level closely approximates the conditional coverage probability. When n is small, this conditional approximation is still good for regression models with small error variance. The conditional approximation can be poor for regression models with moderate error variance and single-factor ANOVA models with small to moderate error variance. In these situations the nominal confidence level still provides a good approximation for the unconditional coverage probability. This suggests that, while the estimand may be interpreted conditionally, the confidence level should sometimes be interpreted unconditionally.     

Teaching Elementary Bayesian Statistics with Real Applications in Science

University courses in elementary statistics are usually taught from a frequentist perspective. In this paper I suggest how such courses can be taught using a Bayesian approach, and I indicate why beginning students are well served by a Bayesian course. A principal focus of any good elementary course is the application of statistics to real and important scientific problems. The Bayesian approach fits neatly with a scientific focus. Bayesians take a larger view, and one not limited to data analysis. In particular, the Bayesian approach is subjective, and requires assessing prior probabilities. This requirement forces users to relate current experimental evidence to other available information–-including previous experiments of a related nature, where “related” is judged subjectively. I discuss difficulties faced by instructors and students in elementary Bayesian courses, and provide a sample syllabus for an elementary Bayesian course.     

A model for k-out-of-m load-sharing systems

ABSTRACT

In a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.     

Reassessing service courses in statistics

Service courses in statistics are frequently criticized by students as being unnecessary or Irrelevant to their educational goals. This article examine the teaching of undergraduates service courses. Indentifying several areas critical to the sucess of the courses.General Philosphing conceriningthe resoultions of the problems associated with the teaching of an undergraduates service courses are proposed as well as the specific suggestionsfor a course for a social science majors     

Statistical Quality Control in the First Statistics Course

Articles regularly apppear in the “Teacher's Corner” of The American Statistician and elsewhere discussing which topics to include in the first statistics course, the order of presentation, and relative emphasis. The basic premise of this article is that some aspects of statistical quality control (SQC) should be incorporated into that first course. In brief, three points are made: (a) SQC concepts are not now widely taught; (b) they should be; and (c) it is relatively painless to do so.     

Conditional tests in a competing risks model

Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors. The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests. In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data). The resulting conditional tests are initially developed for the case of k = 2 and are then extended to k > 2 by performing a sequence of two sample tests and by combining several risks into one. A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power. A real life example is also discussed to show how to implement such conditional tests.     

Projects in Introductory Statistics Courses

Introductory statistics courses should incorporate unstructured projects where students themselves generate the problems they choose to study, gather their own data, analyze the information using suitable computer software, and communicate their findings in a report. This article describes my experience with projects in the context of a large lecture course where projects are carried out in groups. Special problems that arise with group projects are discussed. Several successful student projects are described.     

The utility of experimental design short courses?

This paper describes the one‐day introduction to experimental design training course at GlaxoSmithKline. In particular, the use of paper helicopter experiments has been an effective and efficient method for teaching experimental design techniques to scientific and other staff. A good supporting strategy by which the statistics department provides back‐up following the course is essential. Copyright © 2002 John Wiley & Sons, Ltd.     

Ethical Numbers: Ethics Training in U.S. Graduate Statistics Programs, 2013–2014

As important members of research teams, statisticians bear an ethical responsibility to analyze, interpret, and report data honestly and objectively. One way of reinforcing ethical responsibilities is through required courses covering a variety of ethics-related topics at the graduate level. We assessed ethics requirements for graduate-level statistics training programs in the United States for the 2013–2014 academic year using the websites of 88 universities, examining 103 biostatistics programs, and 136 statistics degree programs. We categorized programs’ ethics training requirements as required or not required. Thirty-one (35.1%) universities required an ethics course for at least some degree students. Sixty-two (25.5%) degree programs required an ethics course for at least some students. The majority (77.4%) of required courses were worth 0 or 1 credit. Of the 177 programs without an ethics requirement, 19 (10.7%) listed an ethics elective. Although a single ethics course is insufficient for instilling an ethical approach to science, degree programs that model expectations through coursework point to the value of ethics in science. More training programs should prepare statisticians to consider the ethical dimensions of their work through required coursework. Supplementary materials for this article are available online.     

Confidence interval estimation and hypothesis testing for a common correlation coefficient

Several procedures have been proposed for testing the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it is then of interest to estimate and perhaps test hypotheses for the common correlation. In this paper, two versions of five different test statistics are compared via simulation in terms of adequacy of the normal approximation, coverage probabilities of confidence intervals, control of Type I error, and power. The results indicate that two test statistics based on the average of the Fisher z-transforms of the sample correlations should be used in most cases. A statistic based on the sample eigenvalues also gives reasonable results for confidence intervals and lower-tailed tests.     

On approximations to the inverse student’s-t distribution function

The inverse of the Student's t-distribution is often needed in computer simulation and applied statistics, e.g, in generating random variates from t-distributions and in computing tables needed for statistical procedures which do not assume known variances. The t-distribution algorithm of Dudewicz and Dalal (1972) can be used to approximate the inverset t distribution function. The author notes an algorithm for evaluation of this inverse d.f. which can be implemented in a fast, accurate and short computer program. The error analysis is also reported. An application is considered for the problem of testing the hypothesis that a sequence of random variates follows Student's-t distribution.     

Dependence of F Ratios Sharing a Common Denominator Mean Square

Much has changed since the widespread introduction of statistics courses into the university curriculum, but the way introductory statistics courses are taught has not kept up with these changes. This article discusses the changes, and the way the introductory syllabus should change to reflect them. In particular, seven ideas are discussed that every student who takes elementary statistics should learn and understand in order to be an educated citizen. Misunderstanding these topics leads to cynicism among the public at best, and misuse of study results by policy-makers, physicians, and others at worst.