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INTRODUCTORY statistics courses are taken each year by hundreds of thou sands of students across the country. These students come from many fields: the life sciences, humanities, education, agriculture, business, but above all from the social sciences. They rarely take sta tistics voluntarily. They sign up for the course because of departmental or grad uation requirements. The great majority has minimal preparation in mathematics, rarely more than they bring along from high school. They carry over into statis tics their prejudices of mathematics and quite often, justifiably so. Teachers of sta tistics courses should then ask themselves how they can make the introductory sta tistics course statistically meaningful and not simply an exercise in mathematics or, what may even be worse, a meaningless compendium of statistical techniques. A recent report, Introductory Statistics Without Calculus, by the Committee on the Undergraduate Program in Mathe matics (CUPM) addresses itself to this question. (Free copies of the report may be obtained by writing to CUPM, P.O. Box 1024, Berkeley, Calif. 94701.) The report strongly recommends courses whose main objectives are understanding of basic statistical concepts, rather than technical facility or the extensive study of the prob abilistic background of statistics. The report concerns itself in consider able detail with what it calls the conven tional approach, the approach taken by the large majority of present-day intro ductory statistics texts. Three other approaches, referred to as the decision theoretic, nonparametric, and problem oriented approaches, are discussed much more briefly. In this paper, we shall com pare the conventional and nonparametric approaches. The author has been using the nonpa rametric approach for quite a number of years and feels that it offers important advantages. These advantages stem from the fact that problems such as estimating the center of a population, comparing the observations in two samples, or measuring the strength of relationship in pairs of ob servations, which in the conventional ap proach are solved by methods appropriate for normally distributed populations, in the nonparametric approach are solved with the help of nonparametric procedures, that is with the help of procedures that are not tied to parametric population models like the normal model. Nonpara metric techniques not only require less preparatory work than normal-theory techniques, but are also conceptually much simpler than the latter as the paper will try to show. In connection with the first point, let us refer to descriptive statistics and the

After providing some background for the need to consider estimates other than those resulting from normal theory, there is a brief review of some nonadaptive robust estimators. We introduce adaptive estimators using those of Tukey and McLaughlin, Jaeckel, Johns, Birnbaum and Mike, Takeuchi, Hajek, van Eeden, and Beran. Adaptive estimators based on preliminary testing and Stein-like procedures are then considered, and recommendations are made on how to select the amount of trimming. Various proposals for estimating regression coefficients are also considered. Adaptive distrubution-free tests look very promising for improving the power of nonparametric tests, and some of these techniques can be used effectively in data analysis. Asymmetric trimmed means, adapted to the particular sample, can easily be used with data and provide good descriptive statistics having an approximate error structure. Finally, it is conjectured that estimators based on “cliff-hangers” might be extremely effective if there ...

Analogs of Pearson's coefficient of racial likeness and of Mahalanobis' distance measure have been proposed as descriptive statistics for comparing two individuals. This paper shows that two different definitions of “uncorrelated” variables—one associated with an inverse transformation and the other with a principal-axis transformation—give rise to these two descriptive statistics. The effects of putting the data into certain forms, such as equalizing the variances of the variables or equalizing the means of the persons, prior to using either of the two transformations, are discussed.

The paper shows the results of studying the characteristics of the temporal dynamics of productivity of a perennial five-component grass stand in various parts of the agrolandshaft of the finite moraine ridge. The studies were carried out at the agroecological training ground of the All-Russian Research Institute of Reclaimed Lands - Branch of the Federal Research Centre V.V. Dokuchaev Soil Science Institute in 2003-2013. Observations of the dynamics of grass yields were carried out on the transect - a physico-geographical profile that intersects the main landscape positions of the moraine hill, at 120 points regularly located. Yield monitoring results were processed using descriptive statistics methods, as well as variance, cluster and correlation analysis. To interpret the results of observations, we used the parameters of agroclimatic conditions for the growing periods of the research years. Studies have shown that the most convenient for studying the dynamics of crop yields are data derived from its point values, since they are devoid of "emissions" and are closest to the normal distribution law. A fairly informative method for identifying areas with the same yield dynamics on the terrain is cluster analysis, the results of which can be represented as sets of points on a map or profile. A study of the relative positions of space points belonging to different clusters showed that they are located in the form of associations gravitating to certain agromicrolandscapes - mesorelief elements. The initial statistical analysis of cluster parameters, as well as the construction of histograms of their distributions, makes it possible to divide them into groups determined by landscape features. Correlation analysis makes it possible to determine the factors that shape the nature of the dynamics of crop yields within a particular cluster. It was revealed that these factors largely depend on the microlandscape features of the agrogeosystem. Based on information on the nature of the temporal dynamics of crop yields in various parts of the agrolandscape, one can predict its productivity and adapt packages of measures to optimize the use of a specific field in agricultural practice.

The Plochere Color System is a collection of 1248 painted papers, the colors being produced by systematic pigment mixtures. The Munsell book notation of each of the samples is given, and certain regularities and singularities in the system are discussed.

The aim of this paper is two-fold: (1) To give a unified treatment of the theory of order statistics when the parent distribution is not necessarily continuous. (2) To assess the effects of grouping on the distribution of order statistics and to indicate the convenience, under suitable conditions, of using order statistics for the estimation of parameters from grouped data with or without censoring.

This article proposes a new descriptive statistic related to the second order parabola in the same manner in which the familiar correlation coefficient is related to the regression coefficient. The parabolicr describes in standard terms simultaneously the general trend of the regression and the extent and nature of its curvilinearity, and is relatively easy to compute and easy to communicate. Formulas for its standard error and its limits are derived and it is applied to a number of regressions.

In the study of spatial behavior we are interested in finding the rules for spatial choice which, when applied to any unique distribution of spatial opportunities, are capable of generating spatial behavior patterns similar to those observed. Behavioral postulates in geographical theories should incorporate these rules rather than descriptive statistics of actual behavior in a spatial system, since the latter are incorporating knowledge of the same spatial system that the theory hopes to generate and, in so doing, to explain. The concept of revealed space preferences is proposed as the organizing concept for finding these rules. This concept is similar to that of revealed preference in the theory of consumer demand. If spatial choice is viewed as a comparison and evaluation of alternative spatial opprtunities against a personal preference function, then, from any consistent statement of preferences from the paired comparison of spatial opportunities, it ought to be possible to derive a unique ran...

Methods of computing standard errors were developed and applied for several statistics of importance in economic and social surveys. These statistics are based on ratio means r = y/x; x is often the variable sample size of complex samples. Some statistics involve weighted sums σWjrj, others concern the relatives R1 = r1/r0 = (y1/x1)/(y0/x0), the ratio of current (1) to base (0) mean. From these relatives the indexes are constructed, and changes, I2 – I1, in the index. We develop computing formulas and helpful approximations for standard errors of these statistics, and apply them to a series of data from our Center's Surveys of Consumer Attitudes & Expectations. A large group of empirical results yield evidence on the behavior of these statistics, with wide implications for the design of surveys to measure economic and social indicators.

This study assessed factors influencing the level of satisfaction with the Growth Enhancement Scheme among farm families in Kaduna State, Nigeria. Two hundred and ninety-six beneficiaries were selected randomly from four randomly selected wards. Descriptive statistics and multinomial logit regression model were used to analyze the data obtained. Results computed from a Likert Scale indicated that majority of the farmers were either satisfied (47.6%) or highly satisfied (14.3%) with the scheme; while 28.6% were dissatisfied and 4.1% were highly dissatisfied. The level of satisfaction with the scheme increased among families with higher farming experience (coefficient = 0.05) and education (coefficient = 0.008); while it decreased with age (coefficient = -0.394) and extension visit (coefficient= -0.328). The study recommended that the scheme be extended for another cycle of five years to consolidate on its achievements and alleviate the bottlenecks before handing over to the private sector.Keywords :GESS, inputs, satisfaction, subsidy.

This study examined the efficiency of resource use among smallholder okra farmers in Ika South and North Local Government Areas of Delta State, Nigeria. A two-stage sampling procedure was adopted in the selection of 113 okra farmers for the study using questionnaire. Data were analysed using descriptive statistics, multiple regression and marginal analyses. The result shows that most of the okra farmers were female. The mean age of the okra farmers was 47 year, while majority (90.3%) of the respondents were married. The mean household size was 5 persons, while the average farming experience was 20 years. The average farms size was 20.3 hectares. Three functional forms were tested and the linear function was chosen based on the number and significance of the parameters. The coefficient of multiple determination (R2) was 0.501which indicates that 50.1% of the variation in the output of Okra was accounted for by the independent variables in the model. The result of the marginal analysis showed that labour, farm size, fertilizer and planting material were underutilized as their ratios were greater than one, while herbicide on the other hand was over utilized. The study recommended that in other to increase the output of okra in the study area farmers have to increase the use of farm size, labour, fertilizer and planting materials since they are technically operating in stage 1 of the production process. Also, the use of herbicide should be decreased in other for these resources to be efficiently utilized.Key word: Resource-use. Okra production, multiple regression, marginal analysis

It is proposed to describe the speededness of a test by a new statistic, the Speededness Quotient (SQ). The SQ is derived by dividing the total number of unattempted items by the total number of errors. It is suggested that test publishers should report the SQ of a test especially when reporting the reliability as an odd-even correlation coefficient.

Formulas are given for a descriptive statistic related to the fourfold-point correlation but having always-attainablelimits ±1.

The theory and use of non-parametric statistics is a large subject in itself. As the name suggests, non-parametric statistics use tests whose models do not specify conditions about the parameters of the population from which the sample was drawn. Such tests are usually applied to nominal or ordinal observations (see section 1.2)—the weaker levels of measurements

This chapter discusses behavioristic points of view on mathematical statistics. The problem of stochastic models is of prime interest but is taken over partly by the relevant substantive disciplines, such as astronomy, physics, biology, economics, and partly by theory of probability. The primary subject of the modern theory of probability may be described as the study of properties of particular chance mechanisms. The questions as to what values should be ascribed to the parameters intervening in a stochastic model of given phenomena and regarding whether this stochastic model can be seriously considered as the mechanism underlying these phenomena are of prime importance. The conceptual background underlying the solution of such problems has some connections with probability theory but is clearly outside of it, and the current more or less generally accepted point of view on theory of statistics is that it is no more and no less than theory of statistical decision making. The once prevailing independent interest in descriptive statistics has faded away.

Summary Some historical relations between mathematical and descriptive statistics. Both mathematical and descriptive statistics may be said to have commenced in the middle of the 17th century; the former with a correspondence between Pascal and F e r m at (1654), and the latter with the observations on bills of mortality by John G r aunt(1662). These early stages are discussed in some detail, while the development of the statistical argument in later periods is more briefly mentioned. In section 8 the present structure of statistical thought is summarized. In a concluding section, falling slightly outside the scope of the paper, some opinions prevailing in the 17th century concerning Holland and its people are quoted.

Statistical Inference By Prof. Jerome C. R. Li.. Vol. 1: Pp. xix + 658. Vol 2: Pp. xiv + 575. (Ann Arbor: Edwards Brothers, Inc., 1964.) 10 dollars each volume.

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Thirteen measures of static strength, 13 body-size measurements, and the somatotypes of 77 male subjects were obtained and the interrelationships among these measures were investigated. Summary descriptive statistics are given for the 29 variables studied. Simple and selected partial correla