Easy-to-construct confidence bands for comparing two simple linear regression lines

This paper shows how to construct confidence bands for the difference between two simple linear regression lines. These confidence bands provide directly the information on the magnitude of the difference between the regression lines over an interval of interest and, as a by-product, can be used as a formal test of the difference between the two regression lines. Various different shapes of confidence bands are illustrated, and particular attention is paid towards confidence bands whose construction only involves critical points from standard distributions so that they are consequently easy to construct.     

Chartering strategies for shipping companies

This paper describes a model which may be used in the evaluation of the relative effectiveness of policies used in the areas of ship chartering and the switching of combined carriers between the dry cargo market and the tanker market. The policies for chartering and market switching are expressed in the form of ‘desired proportions’ of the fleet operating in a particular charter-mode or a particular market. Graphical illustration of this form of expression of policies can be easily understood, so that alternative policies can be designed with relative ease. The effectiveness of a particular form of policy under various freight market conditions can be determined from the model, the use of which is illustrated by its application to the deployment of the fleet of an hypothetical shipping company. It is assumed that the feedback connection between the company's actions and the marketplace is negligible.     

A method of power assessment for tests comparing several treatments with a control

A method of power assessment for the problem of comparing several treatments with a control is considered. Power assessment is based on the power function of a two-sided hypothesis test that none of the treatment is different from the control. Normally distributed data and binary response data are considered. Minimum power levels are found under certain easily interpretable range conditions on the treatment and control means or success probabilities. Expressions are provided allowing simple computer evaluation of minimum guaranteed power levels, and some illustrative tables of power levels are given.     

Testing the Equality of the Noncentrality Parameters of Two Noncentral t-Distributions with Identical Degrees of Freedom

The problem of testing the equality of the noncentrality parameters of two noncentral t-distributions with identical degrees of freedom is considered, which arises from the comparison of two signal-to-noise ratios for simple linear regression models. A test procedure is derived that is guaranteed to maintain Type I error while having only minimal amounts of conservativeness, and comparisons are made with several other approaches to this problem based on variance stabilizing transformations. The new procedure derived in this article is shown to have good properties and will be useful for practitioners.     

A combination multiple comparisons and subset selection procedure to identify treatments that are strictly inferior to the best

This paper considers the problem of identifying which treatments are strictly worse than the best treatment or treatments in a one-way layout, which has many important applications in screening trials for new product development. A procedure is proposed that selects a subset of the treatments containing only treatments that are known to be strictly worse than the best treatment or treatments. In addition, simultaneous confidence intervals are obtained which provide upper bounds on how inferior the treatments are compared with these best treatments. In this way, the new procedure shares the characteristics of both subset selection procedures and multiple comparison procedures. Some tables of critical points are provided for implementing the new procedure, and some examples of its use are given.     

Inferences on the difference between future observations for comparing two treatments

The comparison of two treatments with normally distributed data is considered. Inferences are considered based upon the difference between single potential future observations from each of the two treatments, which provides a useful and easily interpretable assessment of the difference between the two treatments. These methodologies combine information from a standard confidence interval analysis of the difference between the two treatment means, with information available from standard prediction intervals of future observations. Win-probabilities, which are the probabilities that a future observation from one treatment will be superior to a future observation from the other treatment, are a special case of these methodologies. The theoretical derivation of these methodologies is based upon inferences about the non-centrality parameter of a non-central t-distribution. Equal and unequal variance situations are addressed, and extensions to groups of future observations from the two treatments are also considered. Some examples and discussions of the methodologies are presented.     

Counting by weighing: construction of two-sided confidence intervals

Counting by weighing is widely used in industry and often more efficient than counting manually which is time consuming and prone to human errors especially when the number of items is large. Lower confidence bounds on the numbers of items in infinitely many future bags based on the weights of the bags have been proposed recently in Liu et al. [Counting by weighing: Know your numbers with confidence, J. Roy. Statist. Soc. Ser. C 65(4) (2016), pp. 641–648]. These confidence bounds are constructed using the data from one calibration experiment and for different parameters (or numbers), but have the frequency interpretation similar to a usual confidence set for one parameter only. In this paper, the more challenging problem of constructing two-sided confidence intervals is studied. A simulation-based method for computing the critical constant is proposed. This method is proven to give the required critical constant when the number of simulations goes to infinity, and shown to be easily implemented on an ordinary computer to compute the critical constant accurately and quickly. The methodology is illustrated with a real data example.     

The evaluation of general non-centred orthant probabilities

Summary. The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schläfli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most ( m −1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.     

Efficient Confidence Interval Methodologies for the Non Centrality Parameter of a Non Central t Distribution

This article considers the problem of constructing a confidence interval for the non centrality parameter of a non central t distribution. This has applications to the signal to noise ratio in regression problems and to the coefficient of variation for normally distributed data. A new procedure is developed that provides shorter confidence intervals than the standard procedure, and a program is available for its implementation. This new procedure will be useful for practitioners, and its development also provides some interesting theoretical results.     

Normal probability plots with confidence for the residuals in linear regression

Normal probability plots for a simple random sample and normal probability plots for residuals from linear regression are not treated differently in statistical text books. In the statistical literature, 1 ? α simultaneous probability intervals for augmenting a normal probability plot for a simple random sample are available. The first purpose of this article is to demonstrate that the tests associated with the 1 ? α simultaneous probability intervals for a simple random sample may have a size substantially different from α when applied to the residuals from linear regression. This leads to the second purpose of this article: construction of four normal probability plot-based tests for residuals, which have size α exactly. We then compare the powers of these four graphical tests and a non-graphical test for residuals in order to assess the power performances of the graphical tests and to identify the ones that have better power. Finally, an example is provided to illustrate the methods.