Research for Distributions

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Primary Flight Training, UHPT, and Pipeline Selection
January 1, 1994
The Navy trains pilots to fly a variety of aircraft. At present, all student pilots attend primary training in the fixed-wing T-34 training aircraft and are then assigned to specialized advanced training 'pipelines.' In this paper, we document the Navy's use of observed flight performance in primary to assign student pilots for advanced training. We examine the ability of the Navy to predict student pilot performance before primary begins and early in primary. First, we predict primary flight performance before flight training begins, using the data employed to screen candidates into flight training. Next, we predict primary performance using flight stage grades earned early in primary. We address two major policy issues: (1) how would pipeline selection be affected if the Navy had two separate primaries, one for helicopter training and another for fixed-wing training? and (2) how would pipeline selection be affected if helicopter pilots were selected early in primary training?
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Polynomial Families of Distributions
March 1, 1992
It is often necessary to estimate the population distribution of a random variate from a sample of observed values. Standard parametric families may not provide satisfactory fit to the data. A polynomial family is constructed by assuming that the distribution function G is a constrained polynomial of the cumulative distribution F of a convenient parametric family. Polynomial families offer great flexibility in data fitting, while retaining the important feature of parametric families that information in the data is condensed into a moderate number of values. This research contribution presents some theory of polynomial families.
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Comparison of Three Procedures for Smoothing Score Distributions
June 1, 1991
Distributions of test scores need to be smoothed in equating and/or norming. Popular parametric smoothing procedures are based on beta-binomial and log-linear models. A new approach has been developed using polynomials of the beta-binomial cumulative distribution function. The same approach was also applied to extend the beta-binomial family to more than four parameters. These methods were compared using cross-validation in two examinee samples who took the Armed Services Vocational Aptitude Battery. Results show that the log-linear and extended beta-binomial families fit the data about equally well.
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Robust Estimation Using Student's t Distribution
December 1, 1990
Robust estimators are useful when observations contain gross errors or are sampled from a heavy-tailed distribution. Student's t distributions with small degrees of freedom have heavy tails. Therefore, maximum likelihood estimation using these distributions provides simultaneous robust estimates of location and scale. In addition, the likelihood values can be used to choose among the available t distributions, making it unnecessary to make a subjective choice of an estimator. Monte Carlo results show these estimators to be as efficient as the bi-weight estimators of location and scale.
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On Tail Probabilities of Test Statistics
October 1, 1988
Reported tail probabilities of test statistics are based on the assumption that the method is applied to all samples from the population. This assumption is incorrect when data analysts test the underlying assumption, e.g., symmetry, and refrain from using the method if the assumption is rejected. Hence the standard tables are invalid. This is illustrated by generating samples from a Cauchy distribution.
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Bayesian Estimation of n in a Binomial Distribution
October 1, 1987
A method has been developed to estimate the total number of trials, 'n', from a Bayesian perspective when the probability of success, 'p', is either known or unknown. The prior distribution for 'n' is assumed to be the discrete uniform distribution. In the case when 'p' is unknown, 'p' is assumed to have a beta prior distribution. The estimate for 'n' is then the mode of the posterior distribution. Additionally, guidelines for selecting shape parameters for the beta distributions are discussed.
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Confidence Interval for Parameter n in a Binomial Distribution
January 1, 1987
A simple procedure to approximate a confidence interval for the parameter n in a binomial distribution is presented in this research memorandum. A simulation procedure to verify the coverage of confidence intervals is presented in appendix A. An interactive computer program is included in appendix B. The program is written in the FORTRAN language, which is readily available in most computing environments. Tables with 90 percent and 95 percent confidence coefficients are included in appendix C.
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The Translation of Supervisory Ratings into Measurements of Relative Value
July 1, 1986
The goal of this study was to develop a procedure for determining the magnitude of the performance differences between different categories of enlisted personnel. The professional judgement of Marine Corps officers is used as the basis for building a scale that translates the current performance evaluation system into a measure of an individual's relative value to the service.
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Evaluation of Alternative Compositions of the Armed Forces Qualification Test (AFQT)
May 1, 1986
This paper evaluates seventeen ASVAB composites that were proposed as alternatives to replace the current AFQT. The alternatives are evaluated primarily on the basis of their predictive validity and their effects on the applicant pool.
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Effect of the Medium of Administration on ASVAB Item Response Curves
April 1, 1986
Within a few years the Department of Defense may begin administering the Armed Services Vocational Aptitude Battery (ASVAB) using Computerized Adaptive Testing (CAT). Each test item is characterized by an Item Response Curve (IRC), which describes how the probability of correctly answering the item increases with ability. One important question in the CAT project is whether the IRCs are the same in paper-pencil and CAT administrations. This paper examines this issue.
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