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The perspective of the naive intuitive statistician is outlined and applied to explain overconfidence when people produce intuitive confidence intervals and why this format leads to more overconfidence than other formally equivalent formats. The naive sampling model implies that people accurately describe the sample information they have but are naive in the sense that they uncritically take sample properties as estimates of population properties. A review demonstrates that the naive sampling model accounts for the robust and important findings in previous research as well as provides novel predictions that are confirmed, including a way to minimize the overconfidence with interval production. The authors discuss the naive sampling model as a representative of models inspired by the naive intuitive statistician. Keywords: subjective probability, calibration, confidence intervals, overconfidence, sampling model

In the present article, a commonly used meta-analytic procedure for handling dependent effect sizes from a single sample was examined, and 2 revised procedures that estimate and incorporate the degree of interdependence were proposed. The authors' simulation results reveal that the commonly used procedure that averages the effect sizes from a single sample (denoted as the samplewise procedure) underestimates the degree of heterogeneity. The proposed variations are less biased than the samplewise procedure in estimating the degree of heterogeneity in most of the situations that we examined. Future directions to further improve the procedures for handling dependent effect sizes from a single sample are discussed.

This research presents the inferential statistics for Cronbach's coefficient alpha on the basis of the standard statistical assumption of multivariate normality. The estimation of alpha's standard error (ASE) and confidence intervals are described, and the authors analytically and empirically investigate the effects of the components of these equations. The authors then demonstrate the superiority of this estimate compared with previous derivations of ASE in a separate Monte Carlo simulation. The authors also present a sampling error and test statistic for a test of independent sample alphas. They conclude with a recommendation that all alpha coefficients be reported in conjunction with standard error or confidence interval estimates and offer SAS and SPSS programming codes for easy implementation.

Motivated by an actual problem, we discuss a sampling situation involving estimation of the incidence rate of a rare phenomenon in connection with the functioning of an electronic toy. Because of a manufacturing fault, such toys may have a built-in loose metallic piece which moves freely while the children play with the toy. As soon as the freely moving metal lands into a designated potential danger zone inside the toy, it gives an electric shock! The problem is to provide point and interval estimators of the chance of this event happening which is a priori known to be rather negligible. KEY WORDS: Maximum likelihood estimator; Multinomial distribution., 1. INTRODUCTION Recently a study was brought to our attention regarding estimation of the very low incidence rate of a hazardous event in connection with electronic toy manufacturing. We are [...]

With the advent of general purpose packages that support multiple imputation for analyzing datasets with missing data (e.g., Solas, SAS PROC MI, and S-Plus 6.0), we expect much greater use of multiple imputation in the future. For simplicity, some imputation packages assume the joint distribution of the variables in the multiple imputation model is multivariate normal, and impute the missing data from the conditional normal distribution for the missing data given the observed data. If the possibly missing data are not multivariate normal (say, binary), imputing a normal random variable can yield implausible values. To circumvent this problem, a number of methods have been developed, including rounding the imputed normal to the closest observed value in the dataset. We show that this rounding can cause biased estimates of parameters, whereas if the imputed value is not rounded, no bias would occur. This article shows that rounding should not be used indiscriminately, and thus some caution should be exercised when rounding imputed values, particularly for dichotomous variables. KEY WORDS: Fully normal imputation; Missing completely at random; Missing data., 1. INTRODUCTION Missing data is a common occurrence in most datasets. An increasingly popular method for parameter estimation with missing data is the method of multiple imputation (Rubin 1978). The [...]

A sequential discovery sampling procedure is to randomly sample and audit one record at a time until either a first record containing a major fault is discovered or a pre-determined maximum number of successive fault-free records has been sampled. If a major fault is discovered, the sampling is terminated and the account is rejected. If no major fault is discovered, the account is accepted and the auditor provides a confidence interval and associated confidence level for the tree proportion of records in the account containing major faults. A dynamic programming model incorporating the auditor's degree of belief regarding the existence of records in the account containing major faults, sampling costs and the value of discovery of a major fault is presented. The implied confidence level associated with the optimal maximum sample size of the dynamic programming model provides valuable supplementary information for an auditor in the provision of the confidence level for the required confidence interval. Journal of the Operational Research Society (2002) 53, 119-122. DOI: 10.1057/palgrave/jors/2601270 Keywords: discovery sampling; dynamic programming; Bayesian model

John M. Abowd is Professor of Labor Economics, Cornell University, Ithaca, NY 14853; Distinguished Senior Research Fellow, U.S. Bureau of the Census, and affiliated with the Centre de Recherche en Economie et Statistique (CREST) and the National Bureau of Economic Research (E-mail: John_Abowd@cornell.edu). Bruno Crepon is Head of the Division Marches et Strategies d'Entreprises, Institut National de Ia Statistique et des Etudes Economiques (INSEE)-CREST, 15, bd Gabriel Peri, 92245 Malakoff Cedex, France (E-mail: crepon@ensae.fr). Francis Kramarz is Head of the Department de Ia Recherche, CREST-INSEE, 15, bd Gabriel Peri, 92245 Malakoff Cedex, France and affiliated with Center for Economic Policy and Research (E-mail: kramarz@ensae.fr). Abowd acknowledges the support of the National Science Foundation (SBER 96-18111 to the NBER). The authors thank Geert Ridder, Jean Marc Robin, participants of the CREST microeconometrics seminar, two editors and two referees for helpful comments. They also thank Philippe Lag arde for his assistance with the INSEE firm data. The opinions expressed in this article arc the authors' and not those of any government agency. No U.S. Title 13 confidential data were used in this article, which was substantially completed before Abowd's appointment at the Census Bureau began. The data used in this article are confidential but the authors' access is not exclusive. For further information contact CREST, 15, bd Gabriel Peri, 92245 Malakoff Cedex, France. All programs used in this article are available from the authors., ********** We study the effects of the attrition of firms from longitudinal samples on the estimates of dynamic labor demand models. The reasons for attrition from business-based longitudinal samples are [...]

Data sharpening involves perturbing the data to improve the performance of a statistical method. The versions of it that have been proposed in the past have been for bias reduction [...]

A stratified multistage clustered sample model is applied to labor market data drawn from the British Household Panel Survey. Analysis shows that sample model type may be relevant when examining labor market behavior for men and women.

George Casella is Professor and Chair, Department of Statistics, University of Florida, PO Box 118545, Gainesville, FL 32611-8545 (E-mail: casella@stat.ufl.edu). Michael Lavine is Professor, ISDS, Duke University, Box 90251, Durham, NC (E-mail: michael@stat,duke,edu). Christian P. Robert is Professor, Universite, Paris 9, Dauphine (E-mail: xian@ceremade.dauphine.fr). The first author was supported by National Science Foundation Grant DMS-9625440. We thank the editor and two refen2es for valuable comments that improved the presentation., ********** In 1996, Propp and Wilson introduced coupling from the past (CFTP), an algorithm for generating a sample from the exact stationary distribution of a Markov chain. In 1998, Fill [...]

Richard H. Browne is Research Program Administrator, Texas Scottish Rite Hospital for Children, 2222 Welborn Street, Dallas, TX 75219 (E-mail: richb@tsrh.org). The author thanks the two referees and an associate editor for their careful reading of the article and their helpful comments, which led to a much clearer exposition., ********** Lacking a sample standard deviation to use as an estimate of [sigma] in sample size computations, consultants often divide a sample range (R) by a constant to estimate [sigma] [...]

An evaluation is presented on physiologically structured population models (PSPMs) and their use in developing size-dependent, individual-based community theory for ecological processes. PSPMs are found to provide a higher level of precision, realism and testing ability than other models, such as non-structured or lumped stage-based models.

Research is presented on patent statistics within the framework of social science research using two methodologies, simple regression and a complex approach that models disturbances in a series. The authors posit that regression is appropriate for large annual patent issuances, but that examinations of innovation at the industry or company level requires the complex approach.

A three-level nested model for interpreting census data is examined, which contains an individual level, an enumeration district level, and a ward level. Using 1991 census data from the United Kingdom as an example, studies show that should one of the levels be ignored, the variation it contains is redistributed to the two other levels.

Four types of bias in ecogeographical sampling are examined, and a discussion is presented on the negative effects they produced in a genebank collection of wild potatoes from Bolivia. Species bias consists of oversampling of a single representative; species-area bias is disproportionate sampling in a specific geographic location; hotspot bias is disproportionate sampling in an area of high diversity; and infrastructure bias is disproportionate sampling in areas near towns and roads.

An assessment is presented on the robust normalization method applied to school performance ratings obtained by geographic information systems. The method's advantage is that variable weights can be evaluated and the weighted absolute deviation can be obtained and mapped, providing an index quality measure.

The author presents a method of drawing incidence rate maps which avoids the modifiable areal unit problem, in which small, accurate spatial units present unreliable rates and large spatial units remove relevant geographical information. A Tokyo mortality map is used as a case study.

This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept has typically been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the 'wage gap' between unionized and nonunionized workers, decompose the wage differential between different socioeconomic groups (e.g. male-female and black-white), and evaluate the net benefits of a social programme.

Automated and conventional telemetry systems are increasingly being used by wildlife ecologists to determine habitat use and spatial distributions of ungulates. However, the use of radiotelemetry can have problems associated with nonrandom spatial variation in observation rate, which may result in models being biased towards habitats or locations with higher observation rates. A new study demonstrates the use of semivariograms to remove potential bias in automated telemetry systems.

Simulation studies were conducted to study the theoretical, professional and empirical implications of auditing decisions based on the isolation or projection of sampling errors in an audit population. Results show that some conditions call for the use of a biased estimator, considering its ability to exclude errors under conditions of compromised sample size or frequencies of error in accounting populations. Results also show a propensity of auditors to rely on containment information when choosing to project based on compromised audit population.

A standard specification of the Bayesian linear model is presented. The required and sufficient conditions for the variance of the case-deletion importance sampling weights to be finite are derived. The conditions rely on simple relationships concerning the scale parameter of the prior distribution of the error variance and familiar frequentist quantities. The conditions are easy to check, therefore providing a quick and effective method for deciding whether or not crude importance sampling will generate reliable estimates of functionals with respect to the case-deletion posterior., 1. INTRODUCTION Importance sampling techniques can be used to reweight a sample from some distribution to estimate functionals with respect to a different distribution. This approach has found routine application [...]

Composite sampling is a method used by scientists to obtain sufficient samples that are needed to perform accurate analysis and to reduce analytical costs of samples. There are two types of measurements made on composite samples: grab and composite. A study comparing the models for grab and composite sampling revealed that the compositing strategy reduces the cost of analytical tests but it does not estimate the variance between sampling units. The results failed to show whether composite sampling is the optimum sampling protocol.

This paper resolves the vigorous debates between advocates of the sample selection model and the two-part model. Recent Monte Carlo studies by Hay, Leu, and Rohrer (1987) and Manning, Duan, and Rogers (1987) find that the two-part model performs better than the sample selection model even when the latter is the true model. We show that Manning, Duan, and Rogers' negative results regarding the sample selection model are caused by a critical design problem. We demonstrate that their data generating process produces serious collinearity problems that bias against the sample selection model. Once the design problem is rectified, the poor performance of the sample selection model evaporates. Our Monte Carlo results offer a more balanced view on the relative merits of the two models as each model performs well under different conditions. In particular, the sample selection model is susceptible to collinearity problems and a t-test can be used to distinguish between the two models as long as there are no collinearity problems. As an example, we employ Mroz's (1987) labor supply data to illustrate how his tests for selectivity bias might have been affected by collinearity problems. Key words: Sample selection model; Two-part model; Censored regression model; Col-linearity; Health economics; Monte Carlo simulation JEL classification: C15; C24; I10

This paper considers two-step estimation of a sample selection model in which there is heteroskedasticity of unknown form in the latent errors. We propose an estimator which uses recent developments in nonparametric regression estimation involving series approximations. The estimator is shown to be consistent and asymptotically normally distributed under reasonable conditions. A small Monte Carlo experiment demonstrates the usefulness of the estimator and highlights the bias inherent in the usual Heckman (1979) estimator when there is heteroskedasticity. Key words: Sample selection; Heteroskedasticity; Nonparametric; Semiparametric

A normative technique is developed for the selection of a sampling plan for an inspection lot. The method incorporates various factors from information economics, quality control, decision theory and financial portfolio selection. An information system based on expected payoff and standard payoff distribution is also considered. The model is shown to be effective in the determination of sampling plans for specific situations.

In this paper, we calculate semiparametric efficiency bounds for the regression coefficients in an 'outcome' equation subject to censoring under weak conditions on the form of the selectivity bias. It is assumed that the regression function for the binary selection variable which governs the censoring mechanism is nonparametric, as is the form of the selection correction term in the outcome equation. Our results extend those of Chamberlain (1986), who considered models with an underlying linear structure for the selectivity effect. The results are useful for evaluation of some recently-proposed 'two-step' estimators for these models and for construction of improved estimators.

Alternative interpolation formulas for oversampled band-limited functions are presented. The formulas are represented as multiplication by suitable windows in the spectral domain derived from the Fourier transform. Examples for several families of windows are likewise presented.

Computer-intensive algorithms, such as the Gibbs sampler. have become increasingly popular statistical tools, both in applied and theoretical work. The properties of such algorithms, however, may sometimes not be obvious. Here we give a simple explanation of how and why the Gibbs sampler works. We analytically establish its properties in a simple case and provide insight for more complicated cases. There are also a number of examples.

The historical development of sampling theory began with Charles-Jean Baron de la Vallee Poussin. His studies involved duration-limited functions which cannot be band-limited. Maria Theis was the first to establish convergence for continuous functions by replacing the kernel function sin x/x in de la Vallee Poussin's formula with (sin x/x) squared from Fejer's summation method for the Fourier series. K. Ogura, however, was the first mathematician to state and present a proof for de la Vallee Poussin's interpolation formula.

When observations in social research are selected so that they are not independent of the outcome variables in a study, sample selection leads to biased inferences about social processes. Nonrandom selection is both a source of bias in empirical research and a fundamental aspect of many social processes. This chapter reviews models that attempt to take account of sample selection and their applications in research on labor markets, schooling, legal processes, social mobility, and social networks. Variants of these models apply to outcome variables that are censored or truncated - whether explicitly or incidentally - and include the tobit model, the standard selection model, models for treatment effects in quasi-experimental designs, and endogenous switching models. Heckman's two-stage estimator is the most widely used approach to selection bias, but its results may be sensitive to violations of its assumptions about the way that selection occurs. Recent econometric research has developed a wide variety of promising approaches to selection bias that rely on considerably weaker assumptions. These include a number of semi-and nonparametric approaches to estimating selection models, the use of panel data, and the analyses of bounds of estimates. The large number of available methods and the difficulty of modelling selection indicate that researchers should be explicit about the assumptions behind their methods and should present results that derive from a variety of methods.

This article explores the ramifications of performing a linear regression on data obtained from a complex sample survey. The incorporation of sampling weights into estimated regression coefficients helps protect against the potential existence of missing regressors. In addition, the linearization variance estimator, computed by certain software regression packages designed specifically for use with survey data (e.g., SURREGR, SUPER CARP, and PC CARP), is robust against the likelihood of correlated errors and the possibility of heteroscedasticity. KEY WORDS: Linearization estimator; Primary sampling unit; Sampling design; Sampling weights.

The maximum likelihood estimation of the power of a future study based on the results of a previous study provides a good example in which maximum likelihood estimators perform poorly. In particular, they are inconsistent and, for higher dimensional treatment outcomes, are badly biased. This is easily demonstrated using the noncentral chi-squared distribution functions available in the computer package SAS.

A niche-based distribution model is used for stratifying samples and is applied to a rare, endangered plant in Switzerland. A significant statistical improvement was achieved over simple random sample methods, and may reduce field research time by up to 70%.

A statistical model based on a Bayesian mode of inference for the estimation of the sample size for an accurate analysis of bacterial subtypes in a specimen. The model gives probability distribution of strains in a specimen that is used to estimate the probability of identifying all strains present in the sampled colonies.

A dilemma arises for researchers who sample hidden populations, such as injection drug users (IDUs), and use financial incentives to recruit respondents. To prevent respondent duplication (a subject participates in a study multiple times by using different identities) and respondent impersonation (a subject assumes the identity of other respondents), researchers must confirm their subjects' identities. Documentation, however, introduces sampling bias against those who lack such identification, or who wish to remain anonymous. Definitive forms of identification like photography and fingerprints introduce a bias against the more distrustful members of the population, and scanner-based biometrics can be expensive. Most research projects therefore rely on staff to recognize former respondents, but staff turnover and a large number of respondents compromise accuracy. We describe and assess quantitatively the accuracy of a method for subject identification based on a statistical principle, the interchangeability of indicators, in which multiple weak indicators combine to form a stronger aggregate measure. The analysis shows that observable indicators of identity (scars, birthmarks, tattoos, eye color, ethnicity, and gender) and five biometric measures (height, forearm lengths, and wrist widths) provide the basis for a reliable and easily administered method for subject identification.

Consider the situation where observations are missing at random from a simple random sample drawn from a finite population. In certain cases it is of interest to create a full [...]

With the widespread availability of event-history data, demographers have increasingly eschewed registration-system data in favor of survey data. We propose instead using survey and registration-system data in combination, via a constrained maximum-likelihood framework for demographic hazard modeling. As an application, we combine panel survey data and birth registration data to estimate annual birth probabilities by parity. The general fertility rate obtained from registration-system data constrains the weighted sum of parity-specific birth probabilities. The variances about the parity-specific birth probabilities are halved when registration-system data are used to constrain the estimates. Other demographic applications are discussed.

Mean absolute percentage error (MAPE), the measure most often used for evaluating subnational demographic estimates, is not always valid. We describe guidelines for determining when MAPE is valid. Applying them to case study data, we find that MAPE understates accuracy because it is unduly influenced by outliers. To overcome this problem, we calculate a transformed MAPE (MAPE-T) using a modified Box-Cox method. Because MAPE-T is not in the same scale as the untransformed absolute percentage errors, we provide a procedure for calculating MAPE-R, a measure in the same scale as the original observations. We argue that MAPE-R is a more appropriate summary measure of average absolute percentage error when the guidelines indicate that MAPE is not valid.

The use of poststratified control and sampling variables, which increase the effectiveness of regenerative queueing simulations, are examined. The variance reduction methods are used with the projection techniques of replication analysis and regenerative analysis through the optimization of asymptotic joint normality of some standardized concomitant variables that are distinguished with each input process tested during the queueing simulation. The cuts in point-estimator variance and confidence-interval width that can be generated with each technique are evaluated in various closed and mixed machine-repair systems.