William C. Guenther

Use of the Binomial, Hypergeometric and Poisson Tables to Obtain Sampling Plans

A general procedure is given by which acceptance sampling plans can be quickly and easily obtained from published tables of the binomial, hypergeometric, and Poisson distributions...

Sample Size Formulas for Normal Theory T Tests

Abstract Formulas that yield minimum sample size for standard T tests are presented. Although the results are approximations, they usually yield the exact solution. Involving only standard normal quantiles, they could be used in an elementary course.

Power and Sample Size for Approximate Chi-Square Tests

Abstract Approximate chi-square tests for hypotheses concerning multinomial probabilities are considered in many textbooks. In this article power calculations and sample size based on power are discussed and illustrated for the three most frequently used tests of this type. Available noncentrality parameters and existing tables permit a relatively easy solution of these kinds of problems.

On the Determination of Single Sampling Attribute Plans Based upon a Linear Cost Model and a Prior Distribution

The linear cost model previously formalized by Hald [4], [5], [9] is reviewed. Techniques are described which permit easy determination of sampling plans based on that model. The degenerate, the beta, and the two point distributions are considered as prior distributions of p, the process fraction defective. For calculations only standard tables and a desk calculator are required.

A Procedure for Finding Double Sampling Plans for Attributes

A trial-and-error procedure, using widely available tables, is presented for finding double sampling plans based on the binomial, hypergeometric, and Poisson distributions...

One-Sided β-Content Tolerance Factors forthe Two Parameter Exponential Distribution

One-sided β-content tolerance intervals for the two-parameter exponential distribution are considered. The tolernace limits depends upon factors few of which were previously available. Equations whose solutions are the tolerance factors are derived and a table of factors is presented. It is shown that the factors can be obtained with a desk calculator and standard tables. Relationship to confidence limits for the reliability is discussed.

Desk Calculation of Probabilities for the Distribution of the Sample Correlation Coefficient

Abstract It is demonstrated that probabilities for the distribution of the sample correlation coefficient, such as those given by David [2] can be quickly and accurately calculated on modern desk calculators.

Some Easily Found Minimum Variance Unbiased Estimators

Abstract Several methods are available for finding minimum variance unbiased estimators for functions of distribution parameters. This paper concentrates on two which are rarely used but simple when applicable. The first, previously discussed by Davis (1951) and Tate (1959), yields estimators by differentiation when the range of nonzero probability for a continuous random variable depends on an unknown parameter. The second, which has wider applicability, permits estimators for some rather complicated functions to be found by using some well-known results from distribution theory. A number of examples are presented, many of which are suitable for classroom exercises.

A Simple Approximation to the Negative Binomial (and Regular Binomial)

An approximation for negative binomial sums involving a minimum of arithmetic is presented. Because of the relationship between negative binomial sums and regular binomial sums the approximation can be used for the latter also and for any distribution related to the binomial (such as the beta and F). The accuracy obtained is surprisingly good.

Evaluation of probabilities for the noncentral distributions and the difference of two T-variables with a desk calculator

It is demonstrated that integrals of the noncentral chi-square, noncentral F and noncentral T distributions can be evaluated on desk calculators. The same procedure can be used to compute probabilities for the distribution of the difference of two T-variables with equal degrees of freedom. The proposed method of computation can be used with any computer which yields probabilities for the chi-square and F distributions.