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This paper discusses two different forms of identifying restrictions and compares them in a Monte Carlo framework. A similar analysis is performed to illuminate how the identification procedures affect problems of mis-specification. It is found that, using ordinary least squares as the estimating technique, the two types of identification perform much differently and thus they should not be confused. Similar results hold in the mis-specification case. [ABSTRACT FROM AUTHOR]

The article presents response of Leland B. Yeager, Professor emeritus of economics at Auburn University to the critical analysis of his paper related to measurement as scientific method in economies published in the journal "American Journal of Economics and Sociology." The progress in physical science is toward increasing precision in numerical results that can be obtained repeatedly by workers in different countries and at different times. No satisfactory numerical expression for the intensity of that preference has been devised. The distinction hinges not on the precision with which numbers may be measured but on the general validity of numerical formulation. The criteria or standards governing acceptance of assertions as warranted are broadly the same in economics as in all science, namely, ability of the observations and logic supporting the assertions to stand up under repeated check by qualified students. Much introspective knowledge underlying economic theory does meet the tests of warranted assertibility since human beings can communicate with one another and compare their introspections and since human beings reveal themselves as broadly alike in certain basic respects describable in terms of desires and motives and purposive actions.

The present paper provides a proof of the existence of a utility function and the converse of that theorem using decision theory. In particular the development uses probability mass functions. The authors believe that this approach provides a useful alternative to existing proofs and, in addition, ties the analysis to well-understood concepts in probability theory. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper an attempt is made to use the methodology of economics and operations research for determining the optimum allocation of resources among different methods of preventing or curing diseases. First, after comparing the different indices proposed to measure the output of health services, a very simple one is adopted: the number of deaths. The objective of health planning is assumed to be the minimization of the number of deaths. Next, the optimum distribution of resources between prevention and cure of one particular disease is studied in some detail, and a numerical example is presented. Finally, the generalization of this model to include several diseases, under both static and dynamic conditions, is considered. [ABSTRACT FROM AUTHOR]

In this paper a Monte Carlo sampling study consisting of four experiments is described. Two error distributions were employed, the normal and the Laplace; and two small sample sizes (20 and 40) were tested. The question of simultaneousequation bias called for two-stage estimators. The L1 norm was employed as a means of comparing the performance of the L2 or least squares estimators. A relatively new algorithm for computing the direct least absolute (DLA) and two-stage least absolute (TSLA) estimators was employed for the experiments. The results confirmed the hypotheses that for non-normal error distributions such as the Laplace the least absolute estimators were better. [ABSTRACT FROM AUTHOR]

The article reports on the observations in the uses of cluster analysis in Botany. This paper focuses on the ecological examples which highlights the expanding use of computers. Numerical methods of analysis are explained along with the methods used in examining three sets of ecological data including a grass heath on limestone, acid hydrosene and selected northern Scottish grasslands. Details of the research are described giving the differences in each site. Interpretation of the results are discussed further.

Today analytical techniques, numerical algorithms, and computation facilities have made it possible to solve many hydrologic problems. The emphasis on numerical solutions requires that the hydrologist have some basic knowledge of numerical methods, i.e., the calculus of finite differences. Flow of water in its various phases comprises a large part of hydrologic studies. These processes described by partial differential equations (generally nonlinear) require finite difference approximations for tractable computations. Considerations of convergence, order of approximation, and stability of these difference quotients again require some background in finite difference methods. Through brief discussions, several examples, and a list of references, this paper attempts to introduce some of the above considerations. [ABSTRACT FROM AUTHOR]

The article presents a study regarding species-sampling problems encountered in the numerical investigation of complex rain-forest communities. The author suggests that if floristic classification is to be conducted, the problem with regard to the large number of species should be solved. Using their subsets, 818 species from eighteen sites were reclassified while 10 synusil subjects were used wherein they were individually matched by a subset that has the same number of randomly selected species. Original classification was duplicated by the subset of 269 trees. In addition, results showed that species contribute very little to classification.

The limited information maximum likelihood and two-stage least squares estimates have the same asymptotic normal distribution: the ordinary least squares estimate has another asymptotic normal distribution. This paper considers more accurate approximations to the distributions of the so-called ‘k-class’ estimates. An asymptotic expansion of the distribution of such an estimate is given in terms of an Edgeworth or Gram-Charlier series (of which the leading term is the normal distribution). The development also permits expression of the exact distribution in several forms. The distributions of the two-stage least squares and ordinary least squares estimates are transformed to doubly-noncentral F distributions Numerical comparisons are made between the approximate distributions and exact distributions calculated by the second author. [ABSTRACT FROM AUTHOR]

This paper is concerned with the so-called k-class estimators of structural parameters in a simultaneous system. The structural equation being estimated is assumed, as is common in other small-sample investigations, to consist of two endogenous variables; and the number of the exogenous variables (included or excluded) as well as the number of equations in the system are arbitrary so long as the identifiability condition of the estimated equation is satisfied. Moreover, we assume that the system contains no lagged endogenous variables and disturbance terms of each period are independently distributed as multivariate normal. The exact finite-sample moments of the k-class estimators are evaluated for 0 ⩽ k ⩽ 1. For k > 1 it is proved that the estimator does not possess even the first-order moment. The exact moment functions are expanded in terms of the inverse of the noncentrality (or concentration) parameter. This expansion sheds more light on the comparative study of alternative k-class estimators. Numerical calculations of the mean square error and the bias for some specific cases are also given for illustrative purposes. [ABSTRACT FROM AUTHOR]

Computer systems simulation may be defined as a study of a system by experimentation on a computer model of the system in a manner which enables the results of the experiments to be used to make valid inferences about the system itself. This article presents some of the basic concepts of the simulation approach and discusses the primary decisions that must be made by managers and analysts in the process of conducting a simulation study. A selective survey of the existing literature demonstrates the power of this approach. In addition, extrapolations are made from some recent work to speculate about future developments in conpurer simulation. [ABSTRACT FROM AUTHOR]

The article presents an introduction to the study on error analysis for quantitative chemistry. The author aims to introduce some of the problems of error in scientific measurement such as errors encountered in doing laboratory procedure due to the limitations on the precision of the equipment used. Examples are derived from quantitative analysis and concentrate on error in gravimetric and volumetric work. The method is not limited on the field of chemistry but is also applicable to the other field of sciences where quantitative data are taken in the laboratory and the precisions of the instruments are either known or can be approximated. Different publication related to the study is also included in the list of references.

The apparent free space of Vallisneria gigantea leaves has been determined by radiosulphate, using two different methods of extrapolation from the curves of absorption and loss. The values obtained are 7.7 ±0.8 per cent and 5.7 ±0.6 per cent respectively on a weight/weight basis. In V. spiralis the value is about 4.5 per cent. Earlier results of others, failing to recognize this passive uptake, are discussed and explained: an extremely strong metabolic accumulation of ions made it experimentally impossible to distinguish the ion quantity representing the outer space. - As for active sulphate uptake, light has a retarding influence. The protoplasts loose actively accumulated radiosulphate in a slow process when the leaves are again transferred to inactive solutions. [ABSTRACT FROM AUTHOR]

The article reports on the recent trends in clinical psychology. In an effort to achieve a more representative evaluation of research trends in the field of clinical psychology the writer has chosen to go directly to the journal literature, on the assumption that it is the most direct expression of actual research activity as contrasted with "vest pocket projects." An analysis of the 154 tabulated studies yields several points worthy of comment. In the first place, a crude estimate was made of the total number of separate articles, exclusive of short notes, carried by the four journals during the three-year interval. This estimate was based on an extrapolation from the exact data for 1946 and is probably an underestimate of the true total.

The article discusses the econometric literature suggesting an exact F-test on a specific class of hypothesis in the context of a structural equation. The authors' consideration on is based on the consistency of the test which is similar to the recent asymptotic test, and the unique characteristic which is the possibility of the test to obtain an exact analytical expression for the power. Mathematical equations using different formula including that of matrices, as well as several dependent variables are also presented in the paper.

We discuss, with examples, the use of numerical methods to describe and compare patterns of differentiation between populations of organisms at low taxonomic levels. The role of such methods as adjuncts to the orthodox methods of experimental taxonomy is illustrated by an account of differentiation in Solanum L. Section Solanum (Maurella). [ABSTRACT FROM AUTHOR]

Five numerical zonation methods have been applied to two sets of pollen data from deposits o Flandrian age at Scaleby Moss, Cumberland and Red Moss, Lancashire. The zonations suggested by these methods generally correspond to the conventional Flandrian pollen zones with the exception that the ‘elm-decline’ is not consistently distinguished as a zone boundary. Reasons for this omission are discussed in terms of the weightings implicit in the various numerical methods. [ABSTRACT FROM AUTHOR]

The article presents a discussion of the numerical analysis of complex rain forest communities in New South Wales. The article implies that the numerical analysis was used to measure the quantitative data gathered from Canberra metric and three forms of partitioned diversity of species. Complete data were acquired in large sites and diverse forest types, homogeneous sites, and sites with soil discontinuity. The results of the study is discussed in the article using a general context of floristic primary survey of tropical and subtropical rain forest.

The article offers information on the numerical classification method of information analysis, which is also an agglomerative polythetic method. Questions are raised concerning issues about the usefulness of the methods when applied to relatively species-poor data. Problems include the relative effectiveness of numerical and traditional methods for eliciting structure from phytosociological data, the efficiency of presence data compared with quantitative data, the differences between normal and inverse analyses and their resolution, and the interpretation of numerical models in terms of the ecological models.

This article compares the properties of floristic and physiognomic-structural data in the numerical analysis of complex rain-forest communities. The article discusses previous work on the use of physiognomic-structural characters for the classification of vegetation and environmental types. It analyzes the data by both agglomerative polythetic and divisive monothetic methods. It notes that an analysis of the relative efficiency of recovery of environmental information for descending hierarchical levels provided no support for the familiar suggestion that structural characters are less efficient at lower levels.

The article presents a synecological study of rainforest vegetation in eastern Australia. It examines the ecological significance of some soil physical properties by using them as attributes in numerical analysis, and then examining the relation of the resulting soil groupings to floristic and structural types of forest vegetation. It aims to evaluate the relative importance of soil physical and chemical factors under defined ecological conditions. The study findings suggest that the relationship between the chemical composition of the soil parent material and the physical properties and mineral status of the soils supporting complex rainforests suggests that such forests require, not only adequate water, but also good aeration and high amounts of plant nutrients.

The article defines a method for the numerical analysis of forest micropattern which is based on contiguity of species. The use of the analysis is illustrated by applying it to the study of a small area of subtropical rain forest in northern Queensland. It also demonstrates the power of the analysis in revealing significant environmental factors, and its superiority in this respect over conventional plot sampling. It discusses the difficulties of elucidating small-scale pattern in forest vegetation, with particular reference to earlier work on plot sampling and single-nearest-neighbour techniques.

This article presents a study which investigated the use of the information statistic in the numerical classification of heterogeneous systems. The study found that the use of information analysis and other methods which are symmetrical for presence and absence is shown to be inappropriate in the classification of heterogeneous systems. It is suggested that methods which take into account joint presences only should be used to erect hierarchies on such heterogeneous data and that the information statistic be used as a probabilistic test to decide.

This article presents a study which investigated the successional changes in an area of rain forest and the numerical methods that are potentially profitable for use by ecologists studying comparable problems. A brief background on the study areas, a review of previous related literature and a description of the study's methodology are provided. A brief exploration of the five numerical methods used to analyze the data collected is provided. The ecological implications of the results are considered in relation to earlier successional studies.

This article presents a study which investigated the relation between mean square and block size in the analysis of similar plant patterns. Models of basic patterns have been prepared and the analysis of these suggests that the starting point for sampling is of importance. If the series starts towards the centre of a clump there is a strong possibility that the indicated peak mean square will be one block size smaller than the actual. A new method of field sampling is suggested which involves taking a slightly larger series of samples, and performing a number of analyses.

The article examines the numerical analysis of 18 complex communities of rain forests. The study analyzed the presence or absence of 818 vascular species by four numerical methods. Those species were defined by a set of date relating to 18 rain forest sites. A Gower ordination proved the single most informative method yet computational considerations imply that classification should be undertaken primarily, and ordination appealed only if classification shows unprofitable. Because of this, comparable considerations apply to the new method of concentration analysis. Through the study, the original intuitive physiognomic-structural classification was recovered imperfectly. The results show that the fundamental floristic units are not synusial but vertically integrated.

The article discusses the use of an index of non-randomness based on point-to-plant distances in the study of plant population. Eight plant species were studied and each of these species 100 point-to-plant distances were measured. It was observed that by using this index, it will reveal all the non-randomness present and not merely the smallest scale of non-randomness, which an index based on plant-to-plant distances would. Also discussed is the effect of using biased samples of plant-to-nearest-neighbor distances.

The article presents a study that examined the logarithmic series and its possible application to biological problems. It discusses the mathematical properties of the series and the various methods used that fit a logarithmic series to a particular known biological data. The author also notes the importance of knowing that random sampling may occur by units of by groups. Moreover, a summary of biological application of the logarithmic series and formulae connected with the series are also provided.

Recent work in demand forecasting has been done on a variation of exponential smoothing, which has been called a response surface. This response surface is analyzed, and an attempt is made to specify the nature of the sampling distributions involved. Then the response surface is compared to the basic single exponential smoothing forecast using actual demand data to see if it is a significantly better forecast. [ABSTRACT FROM AUTHOR]

The article discusses an appraisal and an alternative in the direction of the new science curricula. The deficiencies in psychological knowledge available for classroom action can be attributed to two main reasons: (1) external invalidity of findings of most connectionists' learning theories, (2) internal invalidity of findings of most curriculum research. Because most psychological principles used presently in teaching are either intrapolation or extrapolation of findings of experimental psychology and/or S-R learning theories, and because of the immensely different experimental settings of these theories.

Existing tests of musical ability, with the exception of the Seashore battery (1919), have made extensive use of musical material. Since the musical experience of individuals may differ in extent and type, some experiential bias may result. In the present study, a new series of tests of musical aptitude is described which makes no use of formal musical material, but which involves non-musical or quasi-musical forms. Analysis of results obtained with the tests suggests that such an approach is feasible, and that the battery operates in a meaningful and consistent manner. [ABSTRACT FROM AUTHOR]

Lists of all the taxa of vascular plants recorded from deposits of Late-Devensian, mid-Flandrian, and late-Flandrian age in twelve geographical regions of Britain were compiled. From these lists coefficients of floristic dissimilarity between the regions were calculated, and two-dimensional dispositions of points representing the regions were found for each time interval by non-metric multidimensional scaling. Distributional data for the present day were analysed in a similar way. The method demonstrates a marked north-south floristic gradient in the British Isles today, and analyses of the fossil data suggest that although a gradient was present in Late-Devensian and mid-Flandrian times it only became well developed in late-Flandrian times. Phytogeographical analyses of the flora in each region at each time interval also demonstrate the existence of some west-east floristic gradients, particularly in Late-Devensian times. It is concluded that, despite the many limitations of the primary floristic data, the numerical methods have considerable potential for handling and synthesizing large amounts of historical biogeographical data. [ABSTRACT FROM AUTHOR]

A numerical method is described for digital simulation of rate-zonal centrifugation of particles with known sedimentation and diffusion coefficients in sucrose gradients at given temperatures. A model rotor based on the geometry of a B-XIV titanium zonal rotor is used. The rotor chamber is divided into 207 annular segments by 206 equidistant cylindrical planes. Initially 207 paired values describing the concentration radius profiles of sample and gradient material together with some physical constants are provided as input data. The net fluxes of material across each plane during a short period of time are calculated. The concentrations in each segment axe adjusted accordingly, yielding new concentration radius profiles. New values of density and viscosity in each segment are calculated before the next transfer of materials is allowed to take place. The iterations are continued until a predetermined cumulative run time is reached. The advantages and the drawbacks of this approach are discussed, Comparison with an actual experiment revealed that the simulation method can be used to predict final particle distribution with rather good accuracy, Moreover, the hydrodynamic stability of sample particles can be evaluated at each time point and at each distance during a centrifugation. Hence, this numerical approach can be used to optimize experimental conditions in all types of zonal centrifugation. [ABSTRACT FROM AUTHOR]

The article investigates the relation of psychiatric evaluation adjectival category scales to numerical scales. It states that measurement of subjective judgmental continua by means of partition or category scale procedures has been widely used although such measurement schemes are known to be extremely open to error. When adjectives are used to label categories in such a partition type of scale, questions can be raised with respect to the measurement level attempted and achieved. Another possible contention pertains to the use of partition scale measurement with prothetic judgmental continua.

The article discusses the approaches to rating the mute patients. In the course of this study, three different approaches to for estimating the total morbidity score for the mute patient were tried: (a) the Ranking Method; (b) the Score Based on Total Distribution Method; and (c) the Forced Choice Method. By using the rank position given the patient in the global impressions ranking, it is possible through interpolation to calculate a score for the mute patient in the Lorr morbidity ranking. In the Forced Choice Method, raters are asked to rate all items, guessing at those they consider unratable because of limited communication from the patient. The Distribution Method provides scores for all the factors, but for only little of the factors is this score based on the patient's actual behavior.