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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 an appendix note on a statistical question raised in the preceding paper.

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."

This paper discusses the theories of and the relationships between the direct and indirect methods of standardizing death rates for males, females, and persons. The author notes that the standardization procedures have two objectives, to eliminate the disturbing influences of varying age and sex distributions, and to provide reliable indications of the overall comparative mortalities of different groups. The author also points out that the Registrar General's methods and publications have always fulfilled the objectives in a thorough and practical manner.

Comments on a paper by T.E. Kurtz, R.F. Link, J.W. Tukey and D.L. Wallace titled 'Short-Cut Multiple Comparisons for Balanced Single and Double Classifications: Part 1, Results,' which appeared in the May 1965 issue of 'Technometrics.' Philosophy of the statistical analysis of experimental data; 'Easy calculation' methods of statistical analysis; Discussion on error rates.

Comments on various statistical studies , featured in the August 1971 issue of the periodical 'Technometrics.' Estimation of linear parameters in nonlinear regression; Mean square error prediction as a criterion for selecting variables; Method of picking and transforming variables; Difference between integrated mean square error and mean square error.

Comments on the paper 'The effect of increasing sample size on the precision of an estimator' published in the Journal of The American Statistician. Applicability of the sampling to an infinite theoretical population; Considerations in sampling from finite population; Dependence of the estimator on the design.

The article presents information on the book, Foundations of Statistical Inference, edited by V. P. Godambe and D. A. Sprott. This book contains the Proceedings of a Symposium sponsored by the Rene Descartes Foundation and held at the University of Waterloo during ten days of April 1970. Rarely does one find the state of an art and the state of its artists revealed to such an extent under one cover. The book's twenty-eight papers and related discussions provide a comprehensive view of the world of statistical inference. J. Neyman presented the first paper in the Proceedings, on the Foundations of Behavioristic Statistics. It contains some nice historical notes, including a fascinating description of the development of sequential sampling and hypothesis tests having power equal to unity. Several papers, including those by Irwin D. J. Bross, I. J. Good, E. T. Jaynes, Oscar Kempthorne, H. E. Kyburg Junior and Herman Rubin deal with either philosophical issues or general criticisms of the foundations. The philosophy is typically quite loose and the criticisms do not lead to positive suggestions for replacing existing paradigms by new ones. The rest of the book deals mainly with mathematical-logical foundations, particularly with the status of Fraser's structured model for inference, aspects of the subjectivist Bayesian model, the status of likelihood methods and the special problems of sampling finite populations.

In a set of two papers, one of them published in this journal in July 1965, W. H. James defends the menstrual statistics of E. J. Farris and his co-workers and exploits these data to propose a new formula of calendar rhythm that allegedly provides maximum protection for a given amount of abstinence. The present paper argues that Farris's data are open to a suspicion of serious bias. James's estimates of various parameters of the menstrual cycle are questioned mainly on grounds of deficient data. However, it is concluded that his methods of estimation will prove useful in future analyses of menstrual variation. [ABSTRACT FROM AUTHOR]

Assuming that the monthly chance of conceiving, fecundability, is constant for any one woman during the period of observation, but varies from one woman to another in an unspecified way, this paper investigates the expected incidence of first conceptions and the distribution of conception delays. The expected monthly incidence of first conceptions is a decreasing function of time. The mean, variance and higher moments of the distribution of fecundability (p) may be estimated from incomplete data referring to only the first few months of exposure. The distribution of conception delays is distinguished from the distribution of the number of trials needed for conception, and the moments of each are derived. When appropriate data are available to calculate the moments of the conception delay or the number of trials, the squared and cubed deviations of i/p about the harmonic mean fecundability can be estimated. These statistics may be useful descriptions of the discrepancy between an observed distribution and theoretical values expected in a homogeneous population. The correlation between two successive conception delays is also discussed in the article.

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 intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]

A method is described for the determination of a large number of points on the variance-length curve with a high degree of accuracy and in a reasonably short period of time. A capacitance-type irregularity tester is employed, together with data-logging equipment for transferring details of strand linear density onto punched paper tape. Points on the variance-length curve can then be calculated by feeding this tape directly into a digital computer. [ABSTRACT FROM AUTHOR]

In the following paper certain fads and tendencies in the field of university education in Sweden will be reviewed and some original findings reported, which all seem to have a bearing on the social role of universities in modern society. In one respect the situation in Sweden is by no means unusual though it raises important questions. Measured by student enrollment or similar statistics, universities are currently growing at a rate which has no earlier parallels. Another feature is less common and therefore deserves particular attention. There is relatively little selection between the senior secondary school stage and the university stage, a large proportion of those who graduate from the former proceed to a university or a professional school of equivalent status. There is selection social and intellectual at an earlier stage; the transition from the junior secondary school, or the new comprehensive school, to the gymnasium. In the earlier part of the paper statistical and other information will be offered which is national and overall in coverage, that is to say, describes the system as a whole or major branches of it. The later part will be based on a more intensive study of a panel of students in Lund, Canada who have been interviewed or approached by a questionnaire and followed through their first university years.

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]

The article reviews some work on the fertility of the Jewish population of Palestine under British mandate which has until now been available in Hebrew only. Statistics regarding marriage, fertility and mortality are quoted for different sub-sections of the Jewish population, classified by origin, geographical location and profession. Most of the analysis refers to the years of the Second World War for which detailed data were available. The paper observes marriage as a factor influencing fertility. The data given shows that marriage was almost universal among Palestinian Jews. The proportion of either sex who had never been married by the end of the reproductive period was extremely low. In Palestine, the probability of marriage was high among all sections of the Jewish population. The later censuses show that the mean age at marriage has risen, but in the settlements, women seemed to marry earlier than in the rest of the country. Occupational differences in age at marriage in the towns were similar to those encountered in other countries. It is shown that wives of men in the higher occupational groups in towns married later than those of men in the lower occupational groups.

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Mathematical demography traditionally has been concerned with the dynamics of the growth and structure of a population that is undisturbed by migration. Recently, however, increasing attention has been directed at the relationships between interregional migration flows and the growth and structure of multiregional population systems that are open to internal migration. This paper contributes to that emerging body of knowledge by generalizing the notion of a life table to the multiregional case and showing how such a generalization leads to a mathematical theory of multiregional population growth that is consistent with the currently accepted single-region theory. [ABSTRACT FROM AUTHOR]

This article focuses on the use of the employment-shift technique in analyzing causes of changes of economic activities in a region. The purpose of this paper is to show that this technique yields biased results when unemployment patterns are neglected. By means of the employment-shift technique the total change in regional employment can be separated into three additive components. The first of these is the "national-change effect." Over a period of years there is a strong tendency for a region to change in the same manner as the nation. The national-change effect measures this force. The deviation between the observed regional change and that which would have been expected on the basis of the national-change effect is attributed to two factors: the "regional-share effect" and the "industry-mix effect." The regional-share compares employment change of the industries within a region with that for the same industries in the rest of the nation. The industry-mix effect is a measure of expected regional employment change based on the difference between the growth rates of regional industries and the average growth rate for all industries in the country. This article also shows an example of these effects.

This paper compares four major schemes used for forecasting mean demand to be used as input into an inventory model so that 'optimum' stockage levels can be obtained. The inventory model is the classical order up to S, infinite horizon model with carry-over from period to period and complete back-ordering. Maximum likelihood, exponential smoothing, standard Bayes and adaptive Bayes schemes are used and results, via Monte Carlo simulation, are obtained on the average costs per period for (1) stationary demand, (2) long-term trend and (3) 'shock' changes in mean demand. [ABSTRACT FROM AUTHOR]

This paper deals with the development of a mathematical model for controlling inventory in a real-life situation. The wide gap between mathematical theory and the building of an actual model is stressed, particularly the necessary, and often difficult, task of adapting known theoretical results to a specific problem. The inventory model chosen is one which approximates optimality and has been modified to accept, as input, demand forecasts from a forecasting model. The inventory-control procedure utilized is of the continuous-review trigger-point order-quantity type, where the trigger point and order quantity 'float', that is, are adjusted periodically depending on the demand forecasts issued. Simulations are performed comparing the proposed inventory and forecasting models with current operating procedures to determine an estimate of the magnitude of the savings possible under the new system. Finally, discussion on how the new system can be implemented is presented. [ABSTRACT FROM AUTHOR]

This paper examines the nature of the cyclic interference which may occur when two machines doing unrelated jobs are serviced by one operator.
A mathematical model is developed to cover the general case and this leads to a step-by-step procedure for interference calculation which may be computerized. The model facilitates analysis of the range and variability of interference so that rules for the economic grouping of future jobs may be developed. [ABSTRACT FROM AUTHOR]

Command and noise signals expected to operate on specific control systems are often only scantily known at the design stage. This paper considers some of the problems which may arise in choosing a system transfer function when supplied with such inadequate information. A first order linear filter has been considered, and for synthesis purposes both command and noise signals have been represented by flat power spectra. The total power content and bandwidth of both signals have been varied, and the optimum transfer function for the various combinations determined by using the mean square error criterion.
With the above assumptions, it is shown that under the circumstances most likely to be met in practice, and in the absence of more specific information, a time constant of one-quarter of the inverse of the expected command signal bandwidth will yield reasonable mean square error performance. [ABSTRACT FROM AUTHOR]

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]

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.