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The article presents titles and abstracts of papers related to geography. A presidential address entitled "The Influence of Geographic Conditions Upon Current Mediterranean Stock Raising," will be presented by Ellen Church Semple. The abstract entitled "Significant Changes in the Utilization of Agricultural Land," as shown by the 1920 Census mentions that the statistics available from the 1920 census show significant changes in the utilization of land during the decade. There was an increase in farm land of 84 million acres in the western half of the U.S.

The article presents summaries of papers delivered at the 125th annual meeting of the American Statistical Association. The meeting took place on September 1965 in Philadelphia, Pennsylvania. In the paper "On the Construction of Stochastic Working Life Tables," by Haskel Benishay, stochastic working life tables are constructed and evaluated. The essence of the construction of stochastic rather than the traditionally deterministic working life tables is in the utilization of the realistic assumptions that the number of births, the number of entries into the labor force, the duration of life, and the duration of working life, are random variables. The end result is a working life table with a double entry in each cell rather than the single traditional one. The implications of this approach for the evaluation of fluctuations in various subcomponents of the labor force are evaluated. Another paper "Measuring Elasticities of Air Travel," by Samuel L. Brown, summarizes research on the response of demand for air travel to differences of fares, incomes, and elapsed travel time. There are three kinds of studies. Multiple regression studies of time series of air traffic, fares and income in the national domestic market yield short-period fare elasticities and income-elasticities. A quarterly first-difference model stands well the usual statistical tests.

The article presents abstracts and titles of abstracts submitted for papers presented at the 1969 Annual Meetings of the American Statistical Association and Biometric Society in New York. Some of the abstracts are Financial and Non-Financial Factors Affecting Post-High School Plans, 1939-1965," by Walter Adams, "Experimental Designs and Mathematical Models," by Sidney Addelman, "Consistency of Linear Least Squares Estimate in a Regression Model with Lagged Variable," by M. Ashanullah, "The Use of Prior Information in Testing of New Drugs," by David M. Allen, "A Comparison of Probability Density Estimates," by Gary Anderson, "Stochastic Models of City Population Density," by Robert T. Amsden, "ldentification and Input Signal Synthesis Problems in Discrete-Time Stochastic Control Systems," by Masanao Akoi, "A Computer Language for the Analysis of Variance," by David J. Aemor, "A Generalized Mathematical Model for Biological Recovery with Applications in Radiation Biology," by George M. Angelton."

Since the nineteenth century, American geographers have applied mathematical concepts to geographic research, and they have increased the level of mathematical sophistication associated with their research. To some extent geographers have traditionally been interested in developing methods of quantitative geographic analysis; however, it was not until the turn of the twentieth century that there was concentrated effort to develop special programs of quantitative methods training and to expand the scope of quantitative geographic research. This paper attempts to examine certain aspects of expansion of quantitative methods training and research for the period 1954–1965. Since the early 1950's the number of major geography departments offering specialized training in quantitative methodology has risen from three percent to over seventy-eight percent. Today many departments require training in statistics and mathematics and roughly one third of the major American doctoral training centers now allow their students to substitute mathematics training for one foreign language requirement. This trend is paralleled by an increasingly large number of quantitative dissertations and quantitative research papers found in a sample of the major geographic journals. Our studies indicate that these trends originated at the University of Washington, and certain Midwestern universities, but after a short period of time, the quantitative revolution spread throughout American geographic centers. [ABSTRACT FROM AUTHOR]

The model considered in this paper is simple linear regression (Ey[sub i] = beta[sub 1] + beta[sub 2] x[sub 1], i = 1, ..., n), and the problem is to make statistical inferences about an unknown value of x corresponding to one or more additional observed values of y. The maximum likelihood estimator x of x and the classical (l - alpha) 100% confidence set S for x have some undesirable properties. For example, x has infinite mean square error and P {S = (- infinity, + infinity)} > 0. The purpose of this paper is to demonstrate that insight and understanding, as well as a useful class of solutions, can be obtained by looking at the problem from a Bayesian point of view. A result which follows from a general Bayes solution is that the inverse estimator [4] is Bayes with respect to a particular informative prior. [ABSTRACT FROM AUTHOR]

The article discusses moments of the distribution of sample size, N in a sequential probability ratio test (SPRT). The present paper provides variance, the third and the fourth moments of N. The details are worked out in five common applications of the SPRIT. The relation of the variance of N to the truncation of a SPRT is discussed is also discussed in the paper. Scholar A. Wald indicated in passing how one can obtain the moments of N, but the only published literature where the author encountered a general expression for the variance of N. However, their expression is incorrect. Using scholar J. Wolfowitz's results, which they do, or differentiating Wald's, fundamental identity twice one gets provided. In many practical applications of the SPRT, μ and moments in an equation derived are differentiable functions of a real-valued parameter. The limiting expressions for the moments can then be determined by standard methods of mathematical analysis. However, for the third and fourth moments the actual technique may involve an excessive amount of arithmetic.

In an earlier paper [5] the authors compared the power of the BLUS test with the probability of a correct decision of the Durbin-Watson bounds test. A method to compute the distribution of the Von Neumann ratio under the null hypothesis and under the alternative hypothesis was given. In the present paper the latter method is used to tabulate the BLUS-test statistic and to compute the exact significance points of the Durbin-Watson test for several examples. Powers of both tests are computed and compared. It appears that, for the cases considered, the power of the exact Durbin-Watson test exceeds that of the BLUS procedure, while the latter is greater than the probability of a correct decision in the Durbin-Watson bounds test. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an easily applied test useful in determining whether or not a supplier's data have been truncated. The proposed test has the following desirable properties: (I) it is the uniformly most powerful rank test, (ii) it is asymptotically uniformly most powerful, (iii) power computations can easily be made for arbitrary sample sizes, formulas for such computations being given in the paper. Although formulated in the context of verifying a supplier's data, the test can be applied to other situations in which false representation of data in the form of truncation is important. Such is the case, for example, in reliability demonstrations or legal suits involving physical measurements. [ABSTRACT FROM AUTHOR]

This paper presents spectral criteria to evaluate seasonal adjustment procedures, and applies them to the estimated spectral properties of the monthly unemployment series, as adjusted by past and present methods of the Bureau of Labor Statistics (BLS) and of the Census Bureau. It also re-examines some conclusions reported in the Gordon Committee Report (1962) and in Nerlove (1964) on past methods of adjustment. The paper concludes that (1) the loss in spectral power between the unadjusted and adjusted series spectra over most of the frequency range could arise with a satisfactory adjustment, (2) the excessive loss of spectral power at seasonal and trend-cycle frequencies present in past methods of adjustment has been reduced in present methods, (3) the effect of deviations from desired spectral properties on the uses of seasonally adjusted data must be examined in the time domain; for certain applications they have been found to be unimportant. [ABSTRACT FROM AUTHOR]

This paper describes a method of estimating the number of marriages during an inter-censal period among a group of never-married persons. Two alternative procedures are suggested: the first based on data on the never-married category and the second based on data on the ever-married category. The essential data needed are marital distributions by quinquennial age-groups from two successive censuses. The marital data from the 1951 and 1961 censuses of India are used to discuss the methodological problems involved in the estimation of marriage frequencies and in the construction of nuptiality tables based on them. Marriage and death are taken as the two attrition factors for decrement of single population. Gross and Net Attrition Tables for the single population of India are constructed for each sex. Section 5 describes various nuptiality measures derived from the Attrition Tables. It is suggested that the approach developed in this paper can be utilized for reliable marital and, subsequently, fertility projections. [ABSTRACT FROM AUTHOR]

The Bradley-Terry model for a paired-comparison experiment with t treatments postulates a set of t 'true' treatment ratings π1, π2, ..., π1 such that π1 is ≥ 0, σpi;i = 1 and the probability for preferring treatment i to treatment j is π2 (π2 + πj)-1. Thus, according to this model, every comparison of two treatments results in a definite preference for one of the two. This is an unrealistic restriction since when there is no difference between the responses due to two treatments, any method of expressing preference for one over the other is somewhat arbitrary. This paper considers a modification of the Bradley-Terry model by introducing an additional parameter, called threshold parameter, into the model. This permits 'ties' in the model. The problem of estimation and tests of hypotheses for the parameters of the modified model is also dealt with in the paper. [ABSTRACT FROM AUTHOR]

In a recent paper in this Journal, Rothenberg, Fisher and Tilanus [1] discuss a class of estimators of tile location parameter of the Cauchy distribution, taking the form of the arithmetic average of a central subset, of the sample order statistics. They show that the average of roughly the middle quarter of the ordered sample has minimum asymptotic variance within this class, and that asymptotically it eliminates about. 36 per cent of the efficiency loss of the median (the most commonly used estimate,r) in comparison to the maximum likelihood estimator (m.l.e.). Of course both the m.l.e, and the best linear unbiased estimator based on the order statistics (BLUE) achieve full asymptotic efficiency in the Cramer-Rao sense and there can be no dispute about the relative merits of the three estimators asymptotically, or about the inferiority of the median (with asymptotic efficiency 8/pi[sup 2] * This character cannot be converted in ASCII text) 0.8 compared with about 0.88 for the estimator of Rothenberg et al.). In any practical situation however, we will be concerned with estimation from samples of finite size and asymptotic properties will not necessarily give any guidance here. We are essentially concerned with two points in assessing the relative merits of estimators in small samples, their case of application and "small-sample efficiency" which is conveniently measured as the ratio of the Cramer-Rao lower bound to the variance of the estimator. In this paper various estimators of the location of the Cauchy distribution arc compared in these two respects for samples of up to 20 observations. The small-sample properties of the m.l.e. have been extensively discussed elsewhere (Barnett [2]) and relevant results are summarized where necessary. The main purpose of the paper is to discuss general linear estimators based on the order statistics, and to assess their utility in the present context. Since this paper was prepared a further interesting 'quick estimator', b [ABSTRACT FROM AUTHOR]

Given N points independently drawn from the uniform distribution on (0, 1), let p[sub n], be the size of the smallest interval that contains n out of the N points; let n[sub p], be the largest number of points to be found in any subinterval of (0, 1) of length p. This paper uses a result of Karlin, McGregor, Barton and Mallows to determine the distribution of n[sub p] for p = 1/k, k an integer. The paper gives simple determinations for the expectations and variances of p[sub n], for all fixed n > (N + 1)/2, and of n[sub 1/2]. The distribution and expectation of n[sub p] are estimated and tabulated for the cases p = 0.1(0.1)0.9, N =2(1)10. [ABSTRACT FROM AUTHOR]

This paper discusses a procedure for finding robust; estimators of the location parameter of symmetric unimodal distributions. The estimators are based on robust rank tests and the methods used are applicable to other one parameter problems. To every density function there corresponds an asymptotically most powerful rank test (a.m.p.r.t.). For a set F of density functions the maximin rank test, R, maximizes the minimum limiting Pitman's efficiency of R relative to the a.m.p.r.t. for each member of F. This maximin test, R, can be used to construct estimators according to the proposal of Hodges and Lehman; it generates another estimator T in the following manner. If the test based on R is the a.m.p.r.t. for samples from a density function g(x - theta), then the estimator T will be the best linear unbiased estimate (b.l.u.e.) of the location parameter for samples from g(x). Unfortunately, the estimator T is not necessarily consistent for all members of F. A class of rank tests which generate linear combinations of a few order statistics is introduced and a simple estimator using the 33 1/3rd, 50th and 66 2/3rd percentiles is proposed. The relationship of the present paper to the work of Huber is discussed and it is shown that the b.l.u.e. corresponding to his least favorable distribution is the trimmed mean. [ABSTRACT FROM AUTHOR]

Recently Professors T. J. Rothenberg, F. M. Fisher, and C. B. Tilanus published a paper proposing the class of trimmed means as estimators of the location parameter of the Cauchy distribution [5]. They showed that the asymptotic sampling variance of the estimators in this class is essentially minimized by using the middle 24% of the sample order statistics. The corresponding estimate has an asymptotic relative efficiency to the best estimator for complete samples (A.R.E.) of .87796 as compared to an A.R.E. of .81057 for the sample median. In this paper a few "quick estimators" are considered as estimators for the location parameter of the Cauchy Distribution. A "quick estimate" is a linear combination (a weighted average) of one or more order statistics. Our goal is to find a simple estimator, i.e. an estimator based on only a few order statistics, which has an A.R.E. of at least 90%. We found an estimator based on five order statistics which is considerably better than the optimum trimmed mean (using the middle 24% of the sample order statistics) and much better than the sample median. The A.R.E. of the optimum censored estimate with censored fractiles .38 and .62 is also found, and a comparison between the trimmed, censored, and proposed estimators is made. [ABSTRACT FROM AUTHOR]

Given a population of N units, it is required to draw a sample of n distinct units in such a way that the probability for the ith unit to be in the sample is proportional to its 'size' x. From the alternative methods of achieving this we consider here only the so-called systematic method which, to the best of our knowledge, was first developed by W. G. Madow (1949): The units in the population are listed in a 'particular' order, their x, accumulated and a systematic selection of n elements from a 'random start' is then made on the accumulation. In a more recent paper (H. O. Hartley and J. N. K. Rao (1962) ) an asymptotic estimation theory (for large N) associated with this procedure was developed for the case when the order of the listed units is random. In this paper we draw attention to certain properties of Madow's estimator: We utilize the fact that with systematic sampling the total number of different samples is N (rather than ([This eq. cannot be change in char.]) as with completely random sampling). This simplification in the definition of the variance of the estimator in repeated sampling enables us to identify the exact variance of Madow's estimator with a 'between sample mean square' in a special analysis of variance (see section 4) and compare it with the variance of the pps estimator in sampling with replacement as well as in other sampling procedures. We also develop two approximate methods of variance estimation (see section 5). We pay particular attention to the case when the units are listed in the order of their size. With this particular arrangement our method can be described as 'systematic with random start' and the gain in precision that we accomplish has of course, analogues in systematic sampling with equal probabilities employing ratio estimators in which there is a relation between the ratio ri =yi/Xi and xi Compared with other methods the present procedure combines the advantage of ease of systematic sample selection with the availability of exact variance formulas for any n and N. Moreover, it usually leads to a more efficient estimate. Its shortcoming resides in the fact that the estimation of the variance is based on certain assumptions. [ABSTRACT FROM AUTHOR]

In educational and psychological applications as well as in other applications, it may be necessary to make certain comparisons of two regression lines when the variances are unequal. Such problems arise, for example, in studies comparing two alternative curriculums or two different teaching methods. By generalizing an idea which Scheffe used to obtain a test for the Behrens-Fisher problem, this paper develops some tests for comparing two regression lines when the two sets of error terms are normally distributed but with two different variances. Scheffe's test itself is a randomized test, but in this paper we present both randomized and non-randomized tests. Both simple and multiple regression are considered, but the simple regression tests are computationally easier than the multiple regression tests. The basic test statistic which is used is the ordinary t-statistic. Essentially two types of problems are dealt with: (A) determining whether the two regression lines are identical when they are known to be parallel; and (B) determining whether the two regression lines are parallel. Confidence bounds as well as tests of hypotheses are available. For Problem A, a minimax estimator of the distance between the two lines is obtained. In addition to the Scheffe-type tests, we also consider some tests based on an approach of Welch and Hajek. A numerical example is presented. [ABSTRACT FROM AUTHOR]

The article presents information about Samuel S. Wilks, a great contributor to statistics. Wilks' behavior toward applications was peculiarly split, he encouraged his students to work on applications, not always an easy thing to do in a strongly theoretical mathematics department; he often told students about applications that he regarded as "neat" or "cute" or "clever"; the statistical colloquium he guided often had speakers on practical applications of mathematical statistics; he himself wrote some practical papers in statistics, but in the classroom he rarely discussed applications. Repeatedly, however, practical problems explicitly influenced both his own publications and those of his students and Wilks often used applications as motivation for the discussion of distribution theory, usually going well beyond the needs of the original problem. The papers to be discussed exhibit incompletely and fragmentarily a major influence on the work of the man and his students. Wilks watched the development of the statistical theory of order statistics closely. Indeed he wrote a masterful summary of the literature. The general area involves the study of the statistical properties of ordered measurements.

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

In a previous paper [12], an attempt was made to show how spectral techniques could be used to compare the effects of two seasonal adjustment procedures on the series to which they were applied. The two procedures compared were: (a) the technique currently used by the Bureau of Labor Statistics for seasonally adjusting employment, unemployment, and labor force monthly statistics, and (b) the so-called "residual" method, proposed by Brittain [2], Samuelson [16], and others. Spectra of the original and the seasonally adjusted series and the cross spectrum of the two were used to aid in the assessment of whether either procedure removed more than could be considered seasonal, introduced spurious regularities, and/or distorted temporal relationships. It was concluded that both techniques removed more than seasonal effects from, and produced some temporal distortion in, the series to which they were applied. Neither method appeared to be superior to the other. It is the purpose of this paper to carry the previous analysis one step further and to compare the BLS procedure with a modified version of the regression method of seasonal adjustment suggested by Cowden [3] and Mendershausen [11], and recently revived by Harman [9, 10] in an exceptionally sophisticated form. In addition to Hannan's work along the lines suggested, Nettheim [13] and Rosenblatt [15] have made studies. Rosenblatt [15] has carried out analyses similar to those reported here. [ABSTRACT FROM AUTHOR]

In this article, the author will talk about researcher R.A. Fisher's contributions to statistics. It is well-known that his work in genetics was of comparable status. It is largely represented by his book "The Genetical Theory of Natural Selection," though in his subsequent work his further association with ecological and experimental studies in evolutionary genetics, and his share in the development of studies in the human blood groups, might especially be recalled. Fisher's contributions to statistics began with a paper in 1912 advocating the method of maximum likelihood for fitting frequency curves, although the first paper of substance was his 1915 paper in the journal "Biometrika," on the sampling distribution of the correlation coefficient. Fisher tried to pose problems of analysis as the reduction and simplification of statistical data. He put forward his well-known concept of amount of information in estimation theory, such that information might be lost, but never gained, by analysis. His concept has been of great practical value, especially in large sample theory.

The use of simulation, as a technique for attacking difficult problems, has increased greatly with the availability of the digital computer. This is illustrated by the large number of references in Shubik's (1960) bibliography[sup 2] and in the large number of studies published since then. Simulation is essentially an extension of a technique known as empirical sampling, or distribution sampling, which has been used in the field of statistics for many years. The limitations of the technique, which are well known to statisticians, are apparently not as well known, or at least not as well recognized, by those using simulation today. The first part of this paper contains an historical survey of distribution sampling as used by statisticians. The material was originally prepared in 1953 and is reproduced here in slightly revised form to bring this history to the attention of present day simulators in order that the lessons that can be learned from this part can more readily be incorporated in the development of methodology today. The second part of this paper discusses the relevance of empirical sampling to the present day state of the art of simulation. The technique of generating random members, developed for empirical sampling can be applied directly to simulation. However in other aspects simulation is more difficult than empirical sampling and here the theory of distribution sampling does not have much to offer. The difficulties are due to lack of independence among time series, non-stationarity of the time series, and the large number of parameters. [ABSTRACT FROM AUTHOR]

This paper investigates the welfare implication of changes in the transportation system in two special areas. The first is when the origin-destination demand for transportation may be assumed to be fixed and the second case is where, considering only work trips, origins may vary but destinations may not. A technique is described that could be used to forecast the new origin-destination demand resulting from a change in the transportation system. The technique also provides an appropriate measure of the welfare implications. A particular objective of the paper is to point out the pitfalls of using transportation (generalized) cost saving as a welfare measure whenever origin-destination demand may not be assumed fixed. In this situation it is shown that the welfare measure must take into consideration the benefit derived from the increased choice in available housing sites. [ABSTRACT FROM AUTHOR]

This paper describes the examination of an oversaturated signalized intersection with no turning permitted. During the green phase, data on the time between arrivals of successive vehicles at an intersection with no downstream bottleneck have been collected and analyzed. Measurements were made of only the vehicles in queue, i.e., vehicles that were stopped during the red phase and those that were stopped during the green phase because the starting wave had not traveled back far enough. Measurements were made only on weekdays from approximately 7:00 A.M. to 8:45 A.M. in order to restrict the sample, as far as possible, to commuters. It is shown that shifted Erlang density functions fit the data satisfactorily and that all vehicles from the third on may be considered as members of the same population with different means. The mean arrival times decrease from front to rear with all from the seventh on being the same. In addition, our statistical analysis leads us to accept the hypothesis that all interarrival times are independent. Experimental techniques and statistical methods are described. Two uses of these results are (1) to provide in- formation for Monte Carlo simulations of traffic phenomena in which oversaturated situations are being considered, and (2) to develop, as will be done in a subsequent paper, a renewal model that takes account of variability in the empyting process, and that may be used in formulating control policies for the oversaturated situation. [ABSTRACT FROM AUTHOR]

This paper provides a simple test for the statistical significance of accident reductions. Such a test is applicable when some change has occurred at a highway location and we wish to know whether or not the difference between the number of accidents 'before' and 'after' represents a statistically significant reduction. In arriving at a decision based on random data we run the risk of occasionally (a) claiming a reduction in accidents when there is none (i.e., type I error), or (b) failing to claim a reduction when it exists (i.e., type II error). A decision procedure is proposed that considers these errors and their costs, and provides curves that indicate trade-offs in the probabilities of making each of the two types of error. Most of the statistical theory used in this paper is generally well known. However, the selection of significance levels based on economic considerations represents an improvement over the all too common practice of arbitrarily selecting significance levels for type I errors and ignoring type II errors altogether. [ABSTRACT FROM AUTHOR]

Most futurologists seem to assume that the best way of coping with the future is to perfect methodologies of prediction, but the ability to forecast accurately may not be the crucial element in dealing effectively with the future. Rather, trying to create the future might be far more fruitful, a possibility this paper explores in some detail. [ABSTRACT FROM AUTHOR]

A recent paper published in this journal (Poole & Kuhn, 1973) has reported that ‘a relatively large family appeared to be no impediment to the educational achievements of middle-class children’. This finding, however, is based upon an analysis which fell into a relatively unknown statistical trap. Poole & Kuhn are only the latest in a long line of victims of this trap and some of their predecessors are reviewed below. [ABSTRACT FROM PUBLISHER]

Given N points distributed at random on [0,1), let np, be the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np ≥ n), for n> N/2, and for n < N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L × L determinants and is not computationally feasible for large L. The present paper derives such a computational formula. [ABSTRACT FROM AUTHOR]

This paper treats essentially the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties. A theory of robust estimation "near" strict parametric models is briefly sketched and applied to some classical situations. Relations between yon Mises functionals, the jackknife and U-statistics are indicated, A number of classical and new estimators are discussed, including trimmed and Winsorized means, Huber-estimators, and more generally maximum likelihood and M-estimators, Finally, a table with some numerical robustness properties is given. [ABSTRACT FROM AUTHOR]

The importance of the concepts of role and consensus has been so well documented that it can now be treated as an assumption by sociologists. Still, however, the measurement of role consensus is not without difficulty since the concept itself imposes a number of methodological problems. This paper represents a suggestion of an alternative measurement combining a number of innovations from our present body of sociological knowledge. In brief, this involves the merger of the following: (1) the problem of comparing intraposition with interposition consensus; (2) the utilization of dyadic consensus; (3) the application of a correlational measure based on ordinal assumptions; and (4) the possibility of furthering the concerns of both macroscopic and microscopic analysis. Our approach will be direct and somewhat abbreviated in terms of (1) a brief rationale; (2) a working hypothesis; (3) a description of the instrument; (4) measurement; and (5) discussion. [ABSTRACT FROM AUTHOR]

Merton points out that "the most precise significance of the word function is of course found in mathematics …. " But, says Martindale, "The work of most of the recent functionalists has been at the opposite pole from this meaning." Consequently, assertions made by functionalists have not always been received with the degree of confidence that their authors might consider appropriate. It is the purpose of this paper to suggest a way in which qualitatively formulated propositions of a functional kind may be translated into a language which points to empirical referents and thus, if all goes well, leads in the end to the formulation of mathematical equations. [ABSTRACT FROM AUTHOR]

In this article, the author points out the shortcomings in the paper "The Elusive Point of Minimum Travel" by Arnold Court. Court has shown that if the distribution is not rotated to the position which maximizes linear dependence, the angle will differ. In fact, the angle will be too large. Court describes efficient procedures for determining the slope of the bisecting line directly, as well as a direct method for determining the angle formed by the regression lines. These will become useful techniques only after the problem of initial rotation has been satisfactorily solved.

In this paper harmonic analysis is employed to investigate regional variations of the annual march of precipitation over Canada. In order to examine the regional variations of the annual march of precipitation, the researcher is confronted with the problem of presenting variations of space as well as time. A method of objectively describing and mapping these space-time characteristics of precipitation is that of harmonic analysis. Before proceeding to examine the area distribution of the two major variance components, the annual and semiannual, it is useful to establish the distribution of the total variance and also the relationship of the two major components to the total variance and to one another.

A large class of useful multivariate recursive time series models and estimation methods has appeared in the engineering literature. Despite the interest and utility which this recursive work has when viewed as an extension of regression analysis, little of it has reached statisticians working in regression. To overcome this we (a) present the relevant random-beta regression theory as a natural extension of conventional fixed-beta regression theory and (b) derive the optimal recursive estimators in terms of the extended regression theory for a typical form of the recursive model. This also opens the way for further developments in recursive estimation, which are more tractable in the regression approach and will be presented in future papers. [ABSTRACT FROM AUTHOR]

A method is described for assigning an observation to one of two normal populations with differing, unknown means and differing, unknown variances. The classification procedure rests on the likelihood ratio, which, for a given observation, is a function of four unknown parameters. Sample information is used to obtain a confidence region for these parameters. From this confidence region, a conservative confidence interval for the likelihood ratio is derived. Interpreting the likelihood ratio as a measure of the odds in favor of each population as the source of the observation, the interval can be used, in an obvious manner, for classification purposes. Simulation techniques are employed to examine the conservative nature of the interval Finally, as an illustration of the method, the results are applied to the determination of authorship of the disputed Federalist papers. [ABSTRACT FROM AUTHOR]

In regression analysis with heteroscedastic and/or correlated errors, the usual assumption is that the covariance matrix Sigma of the errors is completely specified, except perhaps for a scalar multiplier. This condition is relaxed in this paper by assuming only that Sigma has a certain pattern; for example, that Sigma is diagonal or partitionable into a diagonal matrix of sub-matrices. The method used for estimating Sigma is the standard procedure of equating certain quadratic forms of the observations (in this case, squares and products of residuals from regression) to their expectations, and solving for the unknown variances and covariances. A numerical example illustrates the method. [ABSTRACT FROM AUTHOR]

In many multiple correlation and regression studies the values of the variables are difficult to measure accurately. This paper attempts to discuss the effects of such errors of measurements on the squared multiple correlation coefficient. With independent errors and a multivariate normal model, the effect is very roughly that R[sup 2] becomes reduced to about R[sup '2] = R[sup 2] g[sub y] g[sub w], where g[sub y] is the coefficient of reliability of y and g[sub w] is a weighted mean of the coefficients of reliability of the x's. If most intercorrelations among the true X's ace detrimental to R[sup 2], the value of R[sup '2] may exceed R[sup 2]g[sub y] g[sub w] by 10 percent to 20 percent. The situation in which errors are correlated with the true values and the effects of errors on the interpretation of regression coefficients are briefly discussed. [ABSTRACT FROM AUTHOR]

Several approximations to the binomial distribution were compared in 1956 by Raft [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(l/n). In 1963, Bol'shev [2] gave two new Poisson-type approximations. In this paper, some of Raft's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values of p while the Camp-Paulson and Borges' approximations should generally be preferred for large p. [ABSTRACT FROM AUTHOR]

Weiss [5] and Freeman and Weiss [2] have shown how to construct sampling plans which at least approximately minimize the maximum expected sample size in the case of Bernoulli and Normal populations. In this paper we construct sequential procedures of this type for the testing of an exponential parameter. An invariance property of the stepping region is presented which simplifies the construction of the Bayes regions. Several sampling plans are given and some of their properties are obtained, [ABSTRACT FROM AUTHOR]

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment +error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs. [ABSTRACT FROM AUTHOR]

Data editing by a computer program can be regarded as a form of statistical quality control. In that perspective, costs and benefits of alternative programs can be compared to one another and, of course, to no control plan at all. This paper outlines one approach to cost-benefit comparison and utilizes a realistic example to suggest that computerized data editing is generally superior to clerical editing. It also warns against edit programs which provide for record rejections and off-line review. Most importantly, it urges that a systematic comparison of costs can assist significantly in edit planning. [ABSTRACT FROM AUTHOR]

This paper presents statistical evidence, which seems to be conclusive, that there exists a particular pattern of mortality in Ceylon, India and Pakistan where, contrary to general experience, female mortality is higher than that of the males. The sex ratios of the enumerated population in these three countries are among the highest in the world, and the age pattern of the sex ratios is such that they increase from childhood to adulthood to the old ages. Abnormally high sex ratios and selective migration cannot account for this particular pattern, but there is evidence of a higher degree of under-enumeration of females than males. The main responsible factor, however, seems to be higher female mortality, in the ages of maternity as well as in childhood. This shows the need for a regional or local approach to some demographic problems. In this case, for instance, model life tables based on average international experience are not representative. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to illustrate a "give and take" type of interaction between the frequentist theory of probability and statistics, on the one hand, and research in science, on the other. Invariably, research in science involves some observations x and the unknown "true" state of nature sigma. Quite often, replication of the experiments reveals considerable variation in x, indicating that no mathematical treatment of the problem is possible without the assumption that x is a sample value of a random variable X, treated in terms of frequentist theory of probability. As to the true state of nature, sigma, situations vary. Indeed, there are cases where it appears natural to consider that sigma is selected at random out of a certain known set SIGMA, with either known or unknown probability law. Section 2 lists three typical examples in which the frequentist theory of probability can "give" something to science. In each example, however, the assumption of the randomness of sigma appears extraneous. Section 3 describes another example of research in science, again with a non-random sigma, which happened to "give" something to the frequentist theory of statistics. The motivation to reduce the frequency of erroneous conclusions in the general circumstances of the biological study had led to considering the possibility that a certain derivative may fail to exist. This created a problem of testing (Section 4) which does not appear to have been considered. A solution of the problem, in the form of optimal symmetric (C alpha) tests, is given in Section 5. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is how to combine estimators of the common mean from two samples corresponding to normal populations with different unknown variances. Attention is confined to the case where it is known that the variance of one specific population exceeds that of the other. Three classes of unbiased estimators are presented, one of which is based on a preliminary test of significance regarding the ratio of the population variances. The gain achieved by utilizing the knowledge that the ratio of variances exceeds one is investigated by comparing the efficiencies of these estimators with an estimator presented by Graybill and Deal [1] in which no restriction on the ratio of variances is present. [ABSTRACT FROM AUTHOR]

This paper presents the exact sampling distributions of the ordinary and the two-stage least squares estimators of a structural parameter in a structural equation with two endogenous variables in a complete system of stochastic equations. The results show that the distributions of the two estimators are essentially similar to each other. It can also be seen that both distributions depend crucially upon the deviation of a regression coefficient of disturbance terms of two endogenous variables from a structural parameter, and that the first estimator possesses moments up to the order N-2, while the second possesses them up to the order K-1, where N is the sample size and K is the number of exogenous variables excluded from the equation to be estimated. The small sample properties of the estimators are investigated by numerical evaluations of the density functions. [ABSTRACT FROM AUTHOR]