Showing papers on "Pairwise comparison published in 1991"

On distribution-free multiple comparisons in the one-way analysis of variance

Abstract: Two methods are described for conducting distribution-free multiple comparisons of k > 2 populations. The Steel-Dwass method, based on pairwise rankings, possesses several desirable properties that are investigated. New large sample approximations are given, that are less conservative than those of the Bonferroni type suggested by Dunn (1964), and small sample tables for k = 3 populations are provided. Simultaneous confidence intervals are derived for all the pairwise location differences. Finally, an example illustrates the methodology.

On making multiple comparisons in clinical and experimental pharmacology and physiology

Abstract: 1. It is a central thesis of this review that in clinical and experimental pharmacology and physiology the goal of statistical analysis should be to minimize the risk of making any false-positive inferences from the results of an experiment (experimentwise Type I error). 2. It is common in clinical and experimental pharmacology and physiology for the effects of several treatments to be tested within a single experiment. Specific intercomparisons of these several effects, made in a pairwise or more complex fashion, inflates the risk of making false-positive inferences unless special statistical procedures are used. 3. A number of multiple comparison procedures is described and their ability to control experimentwise Type I error is evaluated critically. 4. When only a few (less than 5) of all possible pairwise or more complex comparisons are made between treatment groups, the Dunn-Sidak procedure provides maximum protection against excessive experimentwise Type I error and is very convenient to use. 5. When a control group is compared with all other treatment groups in a pairwise fashion, especially when the number of groups is large, the Dunnett procedure is more powerful than the Dunn-Sidak. 6. If investigators insist on making all possible pairwise comparisons among treatment groups, the Tukey-Kramer procedure provides maximum protection against false-positive inferences but inflates the Type II error rate. If it is especially important to avoid Type II error then the more complicated, stepwise procedures of the Ryan-Peritz-Welsch variety should be considered.

Orthogonal approaches to time-series analysis and system identification

Abstract: Some recent, efficient approaches to nonlinear system identification, ARMA modeling, and time-series analysis are described and illustrated. Sufficient detail and references are furnished to enable ready implementation, and examples are provided to demonstrate superiority over established classical techniques. The ARMA identification algorithm presented does not require a priori knowledge of, or assumptions about, the order of the system to be identified or signal to be modeled. A suboptimal, recursive, pairwise search of the orthogonal candidate data records is conducted, until a given least-squares criterion is satisfied. In the case of nonlinear systems modeling, discrete-time Volterra series is stressed, or rather a more efficient parallel-cascade approach. The model is constructed by adding parallel paths (each consisting of the cascade of dynamic linear and static nonlinear systems). In the case of time-series analysis, a non-Fourier sinusoidal series approach is stressed. The relevant frequencies are estimated by an orthogonal search procedure. A search of the candidate sinusoids is conducted until a given mean-square criterion is satisfied. >

Locating emergency vehicle bases when service time depends on call location

Abstract: This paper deals with the problem of locating emergency vehicles in an urban area. We formulate an optimization model that extends previous work by allowing stochastic travel times, unequal vehicle utilizations, various call types, and service times that depend on call location. The basis of the model is a procedure for approximating the performance of spatially distributed queueing systems. In previous work the model has been validated using data from the Tucson Emergency Medical Services (EMS). We test the computational effectiveness of pairwise interchange heuristics on 192 test problems. Demand and service time components of the test data are generated using characteristics of the Tucson data set. For these test problems, simple pairwise interchange techniques yield reasonable solutions with little computational effort. Also, solutions obtained from the model differ from those generated using methods previously presented in the literature.

Multiple species effects and spatial autocorrelation in detecting species associations

Abstract: . The traditional approach to the analysis of species association within a community, based upon co-occurrence in sampling units such as quadrats, has been to test all pairs of species, using a 2 × 2 contingency table for each pair. It has long been recognised that all these tests are not independent of each other, but there is an additional problem in that the association between any particular pair may depend on the combination of the other species that are present or on the environmental factors that determine that combination. We use a 2k contingency table to examine this problem and find that pairwise associations are not independent of the other species. The second problem that we consider is the effect of spatial autocorrelation in the data which makes the statistical tests too liberal. In the absence of a derived solution for a deflation factor to correct the test statistic calculated from a 2k table, we describe a Monte Carlo approach that provides an approximate solution to this problem. In our data the amount of deflation that is necessary for a 2k table is small compared to the amount required for the 2 × 2 tables used to test pairwise association.

Three-locus systems impose additional constraints on pairwise disequilibria.

Abstract: Combinations of allele frequencies and pairwise linkage disequilibrium terms, each of which is permissible at the two-locus level, may not always be permissible at the three-locus level. These additional constraints on the possible maximum and minimum values for the pairwise disequilibrium terms are formally determined and numerically analyzed. In some cases, the three-locus constraints on a pairwise disequilibrium (D) may be equivalent to the usual two-locus constraints, while in others, the positive or negative range may be restricted. This can result in situations where the allowable values of D are limited to only positive or only negative values up to the extreme case where there is only a single admissible value. No additional restrictions are placed on pairwise disequilibrium values when four loci are considered, other than those imposed by the three-way combinations containing the two loci of interest. A new measure of normalized pairwise linkage disequilibrium, allowing for the three-locus constraints, is defined and illustrated by an application to data from the human histocompatibility antigen (HLA) system. An analogous normalized three-way disequilibrium measure is also formulated.

Using harmonious houses for visual pairwise comparison of multiple criteria alternatives

Abstract: In this paper, we consider the problem of evaluating decision alternatives, which are described by means of several criteria. Our aim is to develop an approach which enables a decision-maker to present value information on the basis ofa visual representation. The underlying ideas used in the approach are based on the use of symmetry and harmony. These principles are operationalized by using “harmonious houses”. The theoretical approach is implemented as a decision support system, which makes pairwise comparisons possible between alternatives. To perform sensitivity analysis is also possible. In our pilot tests, the idea has proven very promising.

Software tools for analyzing pairwise alignments of long sequences

Abstract: Pairwise comparison of long stretches of genomic DNA sequence can identify regions conserved across species, which often indicate functional significance. However, the novel insights frequently must be windowed from a flood of information; for instance, running an alignment program on two 50-kilobase sequences might yield over a hundred pages of alignments. Direct inspection of such a volume of printed output is infeasible, or at best highly undesirable, and computer tools are needed to summarize the information, to assist in its analysis, and to report the findings. This paper describes two such software tools. One tool prepares publication-quality pictorial representations of alignments, while another facilitates interactive browsing of pairwise alignment data. Their effectiveness is illustrated by comparing the beta-like globin gene clusters between humans and rabbits. A second example compares the chloroplast genomes of tobacco and liverwort.

Experiments and an Improved Method for Solving the Discrete Alternative Multiple-criteria Problem

Abstract: A number of interactive methods that use convex cones for solving the discrete alternative multiplecriteria problem have appeared in the literature. Convex cones are used to identify inferior alternatives based on the previous responses of the decision-maker. The aim is to identify as many inferior alternatives as possible using the cones so that the decision-maker will be required to make as few pairwise comparisons as possible. In this study we make experiments to see the effects of a number of cone generators, the selection procedure of cone generators, and the order in which pairwise comparisons are made, on the total number of pairwise comparisons. We also develop an algorithm based on the results of the experiments. Our computational experience shows that the algorithm performs well compared with algorithms that require similar information input from the decision-maker.

The prioritization of technologies in a research laboratory

Abstract: The prioritization of technologies at the Army Materials Technology Laboratory are considered and the criteria and the technologies to be evaluated are identified. A mathematical model was developed to combine the subjective criteria with a single objective criterion. The criteria weights were determined by the analytic hierarchy process through a hierarchical representation and pairwise comparisons. The results were aggregated to yield a prioritized list of technologies to be used by the management of the laboratory for funding decisions of projects within technology areas. >

Static valuation of combat force potential by the analytic hierarchy process

Abstract: A hierarchical weapon systems valuation model framework is discussed and the applicability of the analytic hierarchy process (AHP) in establishing relative values of military weapon systems is investigated. The model is a modified version of the weapon effectiveness index/weighted unit value method (WEI/WUV), a conventional method of static valuation of ground weapon systems as well as a combat unit's force potential. The hierarchical structures gives some unique features to the application of AHP. A calibration study for the model with AHP-based pairwise comparisons has been conducted for some weapon systems in Korea. Its results confirm the applicability and practicality of the 1-9 scale AHP by group judgments in measuring the relative values of weapons. >

Four pairwise balanced designs

Abstract: We construct pairwise balanced designs on 49, 57, 93, and 129 points of index unity, with block sizes 5, 9, 13, and 29. This completes the determination of the unique minimal finite basis for the PBD-closed set which consists of the integers congruent to 1 modulo 4. The design on 129 points has been used several times by a number of different authors but no correct version has previously appeared in print.

A technique to incorporate new information in evaluating generation alternatives

Abstract: Generation alternatives are characterized by fuel prices, system load characteristics and generating system characteristics. The utility planner has to look at these alternatives from the viewpoints of utility dispatchability, operational availability, fuel diversity, environmental impact, financial viability of the offerer and the security of the contract. The task of evaluating these generation alternatives is complex and often unmanageable, not only because there are so many factors but also because quantitative information is not available for many of them. The method of interdependent data analysis (IDA) is applied to estimate the impact of attributes which are not fully analyzed. The IDA technique uses theory of statistics to model judgments and experience as applied to decision making. In this process the attributes characterizing various generation alternatives are ranked using pairwise comparison. The effect of incorporating the environmental impact on several generation alternatives is analyzed using IDA. It is shown that this technique can provide good estimates of the impact of a factor not previously considered. >

Random Utility Representations of Binary Choice Probabilities

Abstract: One way to model probabilistic choices is by postulating the existence of a random variable for each alternative, representing its “utility”. This model turns out to be equivalent to one in which the choice probabilities are generated by a probability distribution on the collection of all rankings of the alternatives. The problem of finding necessary and sufficient conditions for such a representation is investigated for the case where only pairwise choices are given. A couple of new necessary conditions are derived, one generalizing a previously known condition.

Spatial and conjoint models based on pairwise comparisons of dissimilarities and combined effects : complete and incomplete designs

Abstract: In pairwise multidimensional scaling, a spatial representation for a set of objects is determined from comparisons of the dissimilarity of any two objects drawn from the set to the dissimilarity of other pairs of objects drawn from that set. In pairwise conjoint scaling, comparisons among the joint effects produced by pairs of objects, where the objects in a pair are drawn from separate sets, are used to determine numerical representations for the objects in each set. Monte Carlo simulations of both pairwise dissimilarities and pairwise conjoint effects show that Johnson's algorithm can provide good metric recovery in the presence of high levels of error even when only a small percentage of the complete set of pairwise comparisons are tested.

Pairwise comparison procedures for one-way analysis of variance designs

Abstract: Research in the behavioral and health sciences frequently involves the application of one-factor analysis of variance models. The goal may be to compare several independent groups of subjects on a quantitative dependent variable or to compare measurements made on a single group of subjects on different occasions or under different conditions. In analyzing data of this kind, it is usually of interest to determine which pairs of population means are likely to differ. In this paper, the selection of pairwise multiple comparison procedures for one-way analysis of variance designs is considered, following a discussion of Type I error and power issues as they apply to the testing of multiple hypotheses. Procedures are included which are appropriate when normality or variance homogeneity assumptions are violated. The focus is on procedures that are easy to understand and apply. Single-step procedures are emphasized because of their simplicity and because they allow for the construction of confidence intervals.

Ordering pairwise comparison structures

Abstract: Following an introduction to the merits of pairwise comparison methods, we present various ordering algorithms for complete binary preferential structures. These procedures generalize the well-known numbering algorithm to the intransitive case. A new form of independence of irrelevant alternatives is presented. Moreover, various other criteria and characterizations for these algorithms are presented. Aside from solving ranking problems and making explicit value criteria and structures of human preference, our algorithms are applicable to subjects such as task-sequencing and artificial intelligence projects.

Hierarchical decision process

Abstract: The author proposes a new development and some modifications to improve the analytic hierarchy process (AHP) in eliciting and evaluating subjective judgments. These include the constant-sum measurement scale (1-99 scale) for comparing two elements, the logarithmic least squares method (LLSM) for computing normalized values, the sum of inverse column sums (SICS) for measuring the degree of (in)consistency, and sensitivity analysis of pairwise comparisons matrices. In addition, the author discusses the process of constructing hierarchies: generating criteria, classifying criteria, and screening decision alternatives. >

Protective Behaviour in Matching Models

Abstract: This paper analyzes the use of a version of lexical maximim strategies, called protective behavior, in two-sided matching models. It restricts attention to mechanisms which produce stable matchings, that is, matchings which are individually rational and pairwise optimal. The main results of the paper show that truth-telling is the unique form of protective behavior in two such mechanisms. The first is the one which selects the student-optimal stable matching in the college-admissions model, while the second is the mechanism which selects the buyer-optimal matching in the Shapley-Shubik assignment model. Journal of Economic Literature Classification Numbers: C78, D81. (This abstract was borrowed from another version of this item.)

Pairwise-definable subdirect decompositions of general database schemata

Abstract: One of the most important results in the theory of decomposition of universal relational schemata is the equivalence of acyclicity of the hypergraph of the schema to numerous desirable properties regarding simplicity of constraints, correctness of query evaluation algorithms, and complexity of integrity maintenance. In this paper, we show that the thrust of these results is not specific to the relational model, but rather applies in a much more general context in which schemata are just sets and views are defined by surjective functions. This is accomplished by replacing the notion of hypergraph of a schema (which is specific to the relational model) with the much more general notion of pairwise definability, which is meaningful in the context of any decomposition into a set of views.

A characterization of acyclic preferences on countable sets

Abstract: In this paper a new numerical representation of preferences (by means of set-valued real functions) is proposed. Our representation extends the usual utility function (in case preferences are preorder-type) as well as the pairwise representation (in case preferences are interval-order type). Then, we provide a characterization of acyclic preference relations on countable sets as those admitting a set-valued numerical representation.

Correspondence analysis as an aid to multicriteria decision making

Abstract: Correspondence analysis is a relatively little used multivariate statistical technique in the English speaking world. This study aims to show how the technique can be used as an aid to multiple criteria decision making. Based on expressed pairwise indifferences, pairs of alternatives are classified into one of the three categories: ‘indifferent’, ‘indifferent-indifferent’ and otherwise. A coefficient of similarity is assigned to each category, and using this information, correspondence analysis is used to display these alternatives onto a map. The first principal axis of the map tends to be the axis of preference and groups of the most preferred and least preferred policies may be identified. Application of the method is further examined in the case of incomplete information and is found to be capable of providing an ‘accurate’ result. The maps are also compared with those obtained by Rivett using multidimensional scaling.