Harry V. Roberts

Time-Series Modeling for Statistical Process Control

In statistical process control, a state of statistical control is identified with a process generating independent and identically distributed random variables. It is often difficult in practice to attain a state of statistical control in this strict sense; autocorrelations and other systematic time-series effects are often substantial. In the face of these effects, standard control-chart procedures can be seriously misleading. We propose and illustrate statistical modeling and fitting of time-series effects and the application of standard control-chart procedures to the residuals from these fits. The fitted values can be plotted separately to show estimates of the systematic effects.

Reverse Regression, Fairness, and Employment Discrimination

Possible salary discrimination can be studied by comparing mean salaries of, say, males and females, after statistical adjustment for differences in job qualifications. The adjustment is often made by regression, with salary as dependent variable, and job qualifications and sex as independent variables. One might also regress job qualifications on salary and sex, a procedure called reverse regression. Ideas about fairness as well as technical concepts are relevant to discrimination studies. There are two distinct aspects of fairness, one based on comparisons of salary and the other based on comparisons of qualifications. Both concepts are needed to evaluate fairness.

Data Analysis for Managers

Abstract Concrete suggestions are offered for reorientation of elementary business-statistics courses so as to give more prominent emphasis to tools useful in actual business practice and to instruction in the proper use of these tools so that business students can see more clearly what statistics has to offer.

Informative Stopping Rules and Inferences about Population Size

Abstract It is a consequence of the likelihood principle that identical likelihood functions imply identical inferences. If the rule by which sample size is determined—the stopping rule—is reflected in the likelihood function, as it should be, apparently identical likelihood functions (without allowance for stopping rule) may in fact be different. This can happen if the stopping rules are informative. If the stopping rule is informative, the analysis must take the rule into account, and additional information may be recovered by so doing. Examples of informative stopping rules are given for two simple problems in estimation of the size of finite populations, and an illustrative Bayesian analysis is shown in each problem. Other informative stopping rules are briefly discussed.

Rejoinder to Comments on "Reverse Regression, Fairness, and Employment Discrimination."

1. The effects of bringing in additional data upon tentative conclusions about fairness 1 and fairness 2 (Ferber and Green). 2. The appropriateness of direct and reverse regression for causal modeling of employer behavior (Goldberger). 3. The mathematical relationships between direct and reverse regression outcomes and consistency with fair employment practices (Greene and Miller). 4. The role of traditional economic theory about productivity and wage determination (Michelson and Blattenberger).

Differencing of random walks and near random walks

Abstract The traditional rationale for differencing time series data is to attain stationarity. For a nearly non-stationary first-order autoregressive process—AR (1) with positive slope parameter near unity—we were led to a complementary rationale. If one suspects near non-stationarity of the AR (1) process, if the sample size is ‘small’ or ‘moderate’, and if good one-step-ahead prediction performance is the goal, then it is wise to difference the data and treat the differences as observations on a stationary AR (1) process. Estimation by Ordinary Least Squares then appears to be at least as satisfactory as nonlinear least squares. Use of differencing for an already stationary process can be motivated by Bayesian concepts: differencing can be viewed as an easy way to incorporate non-diffuse prior judgement—that the process is nearly non-stationary—into ones analysis. Random walks and near random walks are often encountered in economics. Unless ones sample size is large, the same statistical analyses apply to either.

Analysis of employment discrimination through homogeneous job groups

Abstract In legal studies of employment discrimination, regression models are often used to evaluate possible salary discrimination. Potential confounding arises when the data represent a heterogeneous work force. The estimated salary differences from the regression model may be confounded with nondiscriminatory differences in salaries across jobs. One way to avoid this confounding is to estimate the regressions within relatively homogeneous job groups. The usual objection to conditioning on homogeneous jobs is that employers influence the selection of employees for jobs, which may itself be discriminatory. This objection can be met by separate study of the placement process. We consider a two-stage approach that focusses attention on definition of homogeneous job groups and corresponding candidate pools to study both salary and placement discrimination.

Making control charts more effective by time series analysis: three illustrative applications

Control charts contribute to the monitoring and improvement of process quality by helping to separate out special cause variation from common cause variation. By common cause variation we mean the usual variation in an in-control process. Special causes can be thought of as disturbances, possibly transitory, impacting a process that is in a state of statistical control. However, there is no clear place in this scheme of special causes and common causes for systematic non-iid variation, such as trend, seasonal, autoregression variation, and intervention effects from efforts to improve the proess. When systematic non-iid variation is present, time series modeling and fitting can fill in this picture. In the time series framework, observations influenced by special causes can be treated as outliers from the currently-entertained time-series model and can be detected by outlier detection methods. We discuss three data sets that illustrate how this can be done in order to make control charts more effective. We...

Statisticians Can Matter

Abstract Statisticians fall far short of their potential as guides to enlightened decision making in business. Two important explanations are: (1) Decision makers are often more easily convinced by concrete examples, however fragmentary and misleading, than by competent statistical analysis. (2) The effective use of statistics in the process of decision making requires hard thinking by decision makers, thinking that cannot be delegated entirely to the statistical specialist. Modern developments in interactive statistical computing may help to reduce the force of these limitations on exploitation of statistics; used properly, computing can encourage, almost force, the student or business user of statistics to think statistically.

For what use are tests of hypotheses and tests of significance

Tests of sharp null hypotheses, although frequently computed, are.rarely appropriate as the major end product of statistical analyses, except possibly in some, areas of the natural sciences. But procedures closely akin to tests, although often less formal, are needed in almost every investigation in which exploratory data analysis is used to help to decide upon the statistical model appropriate for the final analysis. The term “diagnostic check”has been suggested by Box and Jenkins for these procedures. Traditional statistical tests often suggest useful diagnostic checks -and this, in my view, is what tests are mainly good for-but visual examination and interpretation of data plots are often equally important. Biere is also much to be gained by the development of new diagnostic checks, and testing theory may be useful as one guide to this development.