Search

The article presents the author's comments on an article "Optimum Sample Size for a Problem in Choosing the Population With the Largest Mean," by statistician Paul N. Somerville, published in the June 1970 issue of "Journal of the American Statistical Association." In the article Somerville described a procedure for selecting the population with the largest mean from normal populations with unknown means and a common known variance. The author claims that his procedure gives a unique minimax solution and that the minimax is a reasonable solution to the problem. According to the author, Somerville has not made it clear that his procedure gives only the local minimax solution. This makes practical applications of his procedure severely limited for it is difficult to think of a situation in which an experimenter would like to determine a local minimax value.

The process of evaluating papers for journal publication is a measurement process, similar to the other measurement processes of qualitative material in the social sciences. A good qualitative measurement technique rarely has a reliability coefficient of more than about 0.50 i.e., a correlation of 0.50 of one measurement with another measurement by the same technique. The square root of the reliability of a measure is the upper limit of its validity. If it is assumed that journal editing as a measurement process is as good as good qualitative measurement can possibly be, given this experience in the social sciences it would estimate the validity of a judgment of article quality to be about 0.70. The two major journals in Sociology accept about 16 per cent of the papers submitted to them. If the quality of papers judged is approximately normal, then one can say that papers judged to be 1 standard deviation or more above the mean of papers submitted will be accepted. Assuming a correlation of 0.70 between the true quality of the paper and the judged quality, one can estimate the proportion of acceptances of papers of different quality.

The article discusses the pattern in vegetation, in which the peaks in the graph of mean square against block size are interpreted. To analyze the peaks in the graph, a logarithmic transformation to both the variance and the spacing is applied, and fitted a polynomial regression of log-variance on log-spacing. The apparent fit by linear regressions results from failure to allow for the occurence of overall trends in representation of species, the rising curve to be expected for random distribution, and the application of logarithmic transformation to the variance data.

Based on a completely random three-stage nested model, five fundamental sampling structures are defined. From the five fundamental structures, 61 designs were enumerated such that each design contained no more than three fundamental structures and a multiple of twelve third-stage samples such that the designs would permit the ANOVA estimation of all three variance components. The table of designs contains in addition to the design structure, a design code for classifying the designs as well as a set of four coefficients that simplify the computation of the expected mean squares for the design. General formulas for the variances and covariances of the ANOVA estimators are presented in an appendix. Three criteria derived from the covariance matrix of the variance component estimators are proposed and then used to compare the designs as well as determine the optimum design for 49 different variance component configurations and 10 different sample sizes. [ABSTRACT FROM AUTHOR]

This paper uses the statistical tool of analysis of variance to look at the recommended operating values for chemical machining. The results obtained agree in general with those published by The Chem-Mill Division of Turco Products Inc., except that there was an indication of some deterioration of surface finish when using sodium aluminate in the solution. The results obtained should not be used in general, but only applied where the material arid method are comparable to the one used in the study. [ABSTRACT FROM AUTHOR]

This paper provides the solution to the problem of the distribution of busy periods of the single-channel queue characterized by a time-dependent Poisson-distributed arrival rate and a general class of holding times. The notation is chosen in such a fashion that the main body of computations and mathematical analysis is identical with what was required in the solution of the general queuing equations considered in a previous paper which should be read first [4]. The solution of the problem for winch the traffic intensity is constant and the holding time distribution is Pearson type III is derived in closed form in terms of the Ink functions introduced previously. [ABSTRACT FROM AUTHOR]

The article discusses the effects of accounting variations on decision making and the paper "An Experimental Design for Study of Effects of Accounting Variations in Decision Making" by R.E. Jensen. The statistical methodology and design used by Jensen in his research of the effects of alternative accounting reporting techniques in the selection of portfolios and their security evaluation is examined as is the data collection. The limitation of whether or not there was adequate control over the research environment and the probability level of the statistical tests is not known in Jensen's paper because he does not mention these issues.

A conference paper pertaining to the application of sampling to agricultural statistics is presented. The author notes the use of Pre-Harvest Wheat Surveys conducted by the United States Department of Agriculture. Also discussed are issues surrounding the variables of sample size and standard deviation.

Recent theoretical and empirical work in portfolio theory has exhibited a natural evolution from the two-moment EV model popularized by Markowitz through the higher moment models to selection on the basis of the entire probability function. This latter approach, referred to as the Stochastic Dominance (SD) approach to portfolio selection, has been shown to be theoretically superior to all of the "moment methods" and has been the focus of an increasing volume of empirical work. In comparison with the EV model, however, the SD approach has one potentially significant deficiency from the standpoint of empirical testing. With a given set of portfolios to evaluate, the computer processor time required for the determination of the EV efficient set is quite short. One can calculate and sort means and variances on several hundred portfolios in a matter of seconds. In contrast, the processor time required for the determination of the SD efficient set for the same number of portfolios can be prohibitive. The purpose of this paper is to examine the factors responsible for the relatively time-consuming nature of empirical tests of SD efficiency and to present the major results of our search for efficient algorithms for conducting SD tests. Section I briefly examines the time-consuming nature of the tests for SD efficiency. Section II presents and evaluates; our most efficient algorithms for obtaining true SD efficiency results. Section lit examines an approach that yields approximate SD efficiency results with further reductions in required processor time. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to derive the relationship of the geometric mean of a distribution of positive values to the conventional first four moments — arithmetic mean, variance, absolute skewness, and absolute kurtosis — and to empirically evaluate certain approximations involving these four moments for estimating the geometric means of monthly and annual holding period returns for individual stocks and for portfolios. The geometric mean is shown to be positively related to the arithmetic mean and absolute skewness and negatively related to variance and absolute kurtosis. In the case of a normal distribution a very good approximation to the geometric mean is revealed to be a function of just the arithmetic mean and variance. Additionally, empirical evidence indicates that even though a number of the monthly and annual distributions deviate significantly from normality, the approximation involving only the mean and variance produces quite accurate estimates of the geometric means of these distributions. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to examine the adequacy of variance as a measure of risk. Despite the abundance of literature on risk and portfolio diversification, virtually all of which uses variance as the measure of risk, there has been little progress on this problem beyond the original contributions. Tobin has pointed out that variance is the appropriate measure of risk if either the probability distribution of returns can be fully described by two parameters (e.g., normal) or the investor utility functions can be approximated by quadratics. Markowitz has suggested the possibility of using the semi-variance as a measure of risk, but for the most part his analysis of risk and portfolio diversification closely parallels that of Tobin. The subsequent literature has in general used variance as a measure of risk without further consideration. Moreover, those studies which have examined the measurement of risk explicitly either have provided only minor modifications to the Tobin-Markowitz analysis or have proposed alternative measures of risk which have been generally ignored. Thus, whether for reasons of convenience, theory or tradition, variance continues to be almost universally used as the measure of risk in portfolio models. The present paper takes a different approach to the problem of using variance as a measure of risk and reaches the conclusion that variance is ambiguous and yields conflicting results when calculated from information generally available to decision makers. If variance is in fact the best measure of risk (and thus appropriate for computing the locus of efficient portfolios and calculating the discount for uncertainty in capital asset prices) the question remains: which variance? In the case of a stock portfolio, the variance in the rate of return for an individual stock may be calculated from price information recorded over a shorter or longer period of time; moreover, observations from the same period of time when aggregated u... [ABSTRACT FROM AUTHOR]

The article presents the use of Laspeyres indexes, proposed by German economist Étienne Laspeyres, in calculating variances in direct costs and in production and sales. The Laspeyres indexes will be used throughout for calculating variances in direct costs and in production and sales. It should be noted that the conventional price variance includes the joint effect due to changes in quantities. Variance analysis in cost accounting has been given an economic meaning in this paper. By using Laspeyres indexes the meaning of variance analysis in direct costs and in production and sales has been elucidated. The quantity variance is often split into two components: mix and volume variances. The price and quantity variances are found to be multiplication of the total budget by the respective average change. Further, a way to allocate the joint variance between price and quantity variances is suggested. The new interpretation of variance analysis, as developed in this paper, has an additional advantages that it is more informative to managers and it is easier to compute.

This paper describes a simulation model of capital budgeting under uncertainty. It analyzes the effects of two types of uncertainty which influence the cash flows of the potential investment projects. Techniques of simulation and stochastic linear programming (using Weingartner's Basic Horizon model of capital budgeting) are employed to compute the expected return (with an associated measure of the risk involved) of different portfolios of projects. The manager can then select the portfolio which is closest to his personal risk-return preference. The model provides a practical guide to management in the entire process of project search, portfolio generation, and portfolio evaluation which characterizes the capital budgeting decision. [ABSTRACT FROM AUTHOR]

Several writers have studied the problem of obtaining confidence bands for a straight line regression under the requirement that the bands be at a specified confidence level, (1 - α) say, for values of the independent variable restricted to a pre-specified closed interval. The bands studied by other writers have been either bands of equal width throughout the interval or trapezoidal bands. This paper studies confidence bands of the classical hyperbolic type under the restriction noted above. Relevant distribution results differ according to whether the pre-specified interval on the independent variable is symmetric or asymmetric about the mean of the independent variable values in the experiment. In the former case the problem under study, is shown to be equivalent to a problem studied by Halperin et al (JASA, Sept. 1967) for which distribution theory and tables are already available. The symmetrical case is generalized to obtain confidence bands in multiple linear regression at level (1 - α) for an ellipsoidal region on the independent variables centered at the point of means of the independent variable values used in the experiment. For straight line regression some numerical comparisons are made with bands of the other types mentioned above. These comparisons suggest that the bands proposed in this paper are uniformly superior to bands of equal width in the sense of having smaller average width; the proposed bands appear to be superior to trapezoidal bands in the same sense for intervals of practical interest, i.e. within or reasonably close to the range on the independent variables used in the experiment. [ABSTRACT FROM AUTHOR]

Causal modelling procedures developed in economics and biology provide social scientists with powerful methodological tools that permit them to bridge the gap between theory and research. In this paper one type of causal modelling technique involving a structural set of equations that are recursive in form has been used to reanalyze the data from two empirical studies that have appeared in the literature. The paper demonstrates how models of this form broaden the scope of the usual regression analysis. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The author discusses the pattern analysis of variance of sample estimates of plant cover changes as the distance between samples increases. The author mentions the disagreement between his work and the data from the similar studies conducted by Greig-Smith at Bangor. The author argues that variance between samples could often be satisfactorily represented by a linear regression connecting log variance with log spacing; and that in any case such a linear regression would account for by far the major part of the differences in variance observed.

Until recently the bases for designing inventory control systems have been poorly understood. This paper discusses the application of discrete variable servo theory to the analysis of inventory control systems, using the simplest periodic inventory replenishment case as an example. The objective is to design an inventory control scheme which will minimize the variance of the inventory balance subject to imposed conditions. A reorder rule is derived and shown to give minimum inventory variance. The 'obvious' reorder rule derived is one of several observed in practice in situations approximating the simple case. The dependence of the inventory level variance on the sales forecast error and system constants is stated explicitly. The principles and methods illustrated are applicable to more complex types of discrete control systems. [ABSTRACT FROM AUTHOR]

This paper investigates the potential reduction in decision-making effort in capital budgeting problems obtainable through the use of measures of risk in addition to variance. Specific measures of risk treated are Baumol's lower confidence limit and the maximum probability of loss. The primary purpose of the paper is to present a methodology which imposes certain "constraining relations" on acceptable investment programs rather than one which appeals to a specific utility function as the basis for ordering choices. In this connection a discussion of several different utility functions is presented, along with an analysis of their usefulness when the probability distributions of net present values for various investment portfolios cannot be taken as known. In addition, some of the logical problems involved in constructing a utility function are examined. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the effects of errors in the sales forecast on inventory changes and production rates. This is done by computing the ratio of the standard deviation of inventory change or production rate to the standard deviation of sales rate. By use of this ratio the effects of the average forecast error, the variance of the forecast error, and the serial correlation of sales can be studied. Both analytical method and simulation procedures are used. [ABSTRACT FROM AUTHOR]

Recently Simkowitz and Jones have noted the potential importance of the tools of multivariate analysis and simultaneous equation estimators of econometrics as tools for finance methodology. They note that empirical research in finance dealing with such variables as the value of financial securities has used, almost exclusively, cross sectional analysis "... where all firm effects other than those described by the independent variables are assumed away." More extensive estimation efforts require either the use of other multivariate techniques, such as cannonical correlation (for correlating sets of variables) or more explicit modeling of the structure of the relationships between, say, different firms' securities' prices before the simultaneous equations estimators can be successfully employed. The purpose of this paper is to propose an approach that is intermediate between these extremes but which will allow us to gauge the importance of unexplained joint effects as between different securities' prices. Additionally, it provides a means of extending the methods proposed by Fried for estimating single asset return equations as an input to the Markowitz model. [ABSTRACT FROM AUTHOR]

This paper reports an empirical test of the usefulness of a prediction method for multivariate budgets suggested by Theil. The method, based on information theory concepts, is described in the first three sections, and results of the test are presented in the remaining sections. These results show that the suggested prediction method outperforms both the actual forecasts made by the firms who provided the data and two naive forecasts. [ABSTRACT FROM AUTHOR]

The article presents a response to the paper "Observations on Jensen's Experimental Design for Study of Effects of Accounting Variations in Decision Making" by Thomas R. Dyckman and discusses the scale of observation in an analysis of variance (ANOV) model. Dyckman questions Jensen's research in proposing violations in the underlying assumptions of the ANOV model and whether or not these violations would appreciably affect the conclusions of his experiment. An interval scale was used during some of Jensen's data selection for discussion which Dyckman feels is incorrect in its additivity assumption.

More than ever, business firms are wanting to know what results are being achieved for their outlay of funds for advertising and promotion. This paper gives some experimental designs that have been successfully used in quantitatively measuring the effects of specific promotional efforts. [ABSTRACT FROM AUTHOR]

The article presents an examination into the shortcomings of the mean-variance approach to portfolio selection modeling, wherein the simultaneous estimation error problem is not accounted for. A particular scenario is presented where the estimation error becomes so large it invalidates the utility of the mean-variance approach. Implications and further questions on the model's inadequacies are also provided.

In this paper, we present evidence that local trends do exist in the Standard and Poor's Index. We begin by assuming that the logarithm of the price at time t[sub 1], say log P(t[sub 1]), has an expected value which is a linear function of time. That is, E log P(t[sub 1]) = at[sub 1] + b where a and b are arbitrary but fixed constants. Then we use the techniques of the analysis of variance to test whether any constants in the expression above satisfy the data. The tests show that these data are not explained by such an expected value. We conclude that the mean is different (certainly more complicated than at[sub 1] + b) over different intervals of time. The changes in expected value over these intervals are referred to as local trends. Finally, by repetition of the tests for different interval sizes, we find that the tests are significant for interval sizes up to approximately one year but not longer. Thus the evidence suggests that the local trends, when they occur, do not last longer than this period of time. [ABSTRACT FROM AUTHOR]