Statistical Terminology Research Articles

Estimation of Average Concentration in the Presence of Nondetectable Values

Abstract In the attempt to estimate the average concentration of a particular contaminant during some period of time, a certain proportion of the collected samples is often reported to be below the limit of detection. The statistical terminology for these results is known as censored data, i.e., nonzero values which cannot be measured but are known to be below some threshold. Samples taken over time are assumed to follow a lognormal distribution. Given this assumption, several techniques are presented for estimation of the average concentration from data containing nondetectable values. The techniques proposed include three methods of estimation with a left-censored lognormal distribution: a maximum likelihood statistical method and two methods involving the limit of detection. Each method is evaluated using computer simulation with respect to the bias associated with estimation of the mean and standard deviation. The maximum likelihood method was shown to produce unbiased estimates of both the mean and standard deviation under a variety of conditions. However, this method is somewhat complex and involves laborious calculations and use of tables. Two simpler alternatives involve the substitution of L/2 and a new proposal of L/2 for each nondetectable value, where L = the limit of detection. The new method was shown to provide more accurate estimation of the mean and standard deviation than the L/2 method when the data are not highly skewed. The L/2 method should be used when the data are highly skewed (geometric standard deviation [GSD] approximately 3.0 or greater)

Statistics for Clinical Monitors and Drug Regulatory Personnel

This is the third of a series of articles presented in this Journal introducing statistical terminology and methods useful in the design and analysis of clinical trials. This article introduces the concepts of statistical estimation and statistical inference. These articles are based, in part, on material presented in greater detail in the book, Pharmaceutical Statistics, by the author (1).

Basic Statistics for the Behavioral Sciences

Basic Statistics for the Behavioral Sciences

A computer program package for relative survival analysis

A computer program package has been constructed for use in patient survival analyses for chronic diseases based on aggregated data. The central concept of the analyses — the relative survival rate — is the ratio of the observed survival rate of the patients to the survival rate expected in a group in the general population similar to the group of patients at the beginning of the follow-up (interval), with respect to age, sex and calendar time. This quantity is used to measure patient survival adjusted for the effect of mortality attributable to the competing risks of death without employing information on causes of death of individual patients. The package contains three alternative methods of estimating the relative survival rates, two different ways of estimating the expectation of life for the patients, and five methods of testing the relative survival pattern using information on the whole follow-up period. Conventional survival and competing risk analysis can also be performed with the package. It is hoped that the package will facilitate standardization of statistical methodology and terminology in long-term survival studies for chronic diseases.

The lack of uniformity in statistical audit sampling terminology

There is currently no standard terminology in statistical audit sampling that is commonly accepted and used in all auditing textbooks. As a result, students and professionals are faced with the frustrating and arduous task of learning new symbols and terms when attending advanced auditing classes and continuing professional education courses and the public accounting profession has difficulty in testing adequately CPA candidates' proficiency in the statistical sampling area. This article examines the extent of the problem of lack of uniformity and suggests a possible solution.

Statistical basis for exploring schizophrenia.

The authors illustrate the use of multivariate statistics as a tool for exploring diagnostic factors in schizophrenia in two areas: the derivation and replication of the 12-point flexible diagnostic system and the definition of schizophrenic subtypes. They suggest an interactive approach between clinician and statistician to ensure the optimal combination of clinical judgment and systematic data analysis. Statistical concepts are presented with a minimum of statistical terminology.

Gender Differences in Performance on Variables Related to Achievement in Graduate-Level Educational Statistics

To assess gender differences in performance in three graduate level courses in educational statistics, responses from students to a question concerning gender, mathematics pre- and posttests, cloze pre- and posttests, and final exams in statistics were analyzed. Males performed slightly better on the mathematics pretest. When gender and mathematics and cloze pretests were used in multiple regression analyses to predict final examination performance, gender was not a significant predictor for any course. However, the interaction between gender and cloze pretest performance was significant for the Ph.D. level course on multiple regression. Mathematics pretest performance was the primary predictor for performance in the Master's level statistics course; both cloze test and mathematics test performance influenced scores on posttest measure in the Ph.D. level courses. Apparently the influence of entering mathematics ability, comprehension of statistical terminology, and gender varies by the primary emphasis of the course taken. While mathematical ability is most important in basic statistics, it is less important in higher level courses in which an adequate mathematics background is assumed by instructors. In consequence, the importance of comprehension of concepts increases from the Master's level to the advanced Ph.D. level in the educational statistics courses analyzed in this study.

Teaching research: an introduction to statistical concepts and research terminology.

Concerns for establishing priorities in occupational therapy research and positive responses to these concerns are reviewed. Growth in occupational therapy research can be expected, but it is important that the research process not be limited to educators and graduate students alone. Involvement of occupational therapists in scientific inquiry is often deterred by misconceptions of the research process. Realistic acceptance of research is needed to replace these misconceptions. One major problem is understanding the language of research. It is suggested that the acquisition of research language can begin in regular occupational therapy classes. To introduce students to research concepts, frequently used statistical symbols and research terms are discussed. Limitations in applying "ideal" research methodology to clinical research are noted.

STATISTICAL TERMINOLOGY: DEFINITIONS AND INTERPRETATION FOR FLOOD PEAK ESTIMATION1

ABSTRACT: Considerable effort is expended each year in making flood peak estimates at both gaged and ungaged sites. Many methods, both simplistic and complex, have been proposed for making such estimates. The hydrologist that must make an estimate at a particular site is interested in the accuracy of the estimate. Most methods are developed using either statistical analyses or analytical optimization schemes. While publications describing these methods often include some statistical measure of goodness‐of‐flt, the terminology often does not provide the potential user with an answer to the question,‘How accurate is the estimate?’ That is, statistical terminology often are not used properly, which may lead to a false sense of security. The use of the correct terminology will help potential users evaluate the usefulness of a proposed method and provide a means of comparing different methods. This study provides definitions for terms often used in literature on flood peak estimation and provides an interpretation for these terms. Specific problems discussed include the use of arbitrary levels of significance in statistical tests of hypotheses, the identification of both random and systematic variation in estimates from hydrologic methods, and the difference between accuracy of model calibration and accuracy of prediction.

The Use of Sports Data for Integrating Topics in Introductory Statistics

Nearly every college or junior college has an introductory statistics course designed for students from many disciplines including mathematics. Ideally, this course introduces the -student to statistical techniques that he will need in his field of study. Unfortunately, it is difficult to cover all the topics needed with enough emphasis on the integration of these techniques to solve common problems. For this reason, many schools will follow the basic statistics course with second course in the specific discipline. This course concentrates on experiments and statistical modeling commonly needed in that discipline. i At the University of Northern Colorado, the Department of Mathematics offers beginning, one quarter, 3-hour statistics course with the intent of introducing students to (1) statistical terminology, (2) common statistical inference procedures, 'and (3) assumptions needed for the procedures. The most important aspect of the course is to prepare the student to converse with statistician. The old adage, a little knowledge is more dangerous than no knowledge at all, is particularly applicable. At this level, it is impossible for student to learn enough about statistics in 3-hour course (or six hours for that matter) to be able to handle experiments requiring statistical analysis. My objective for this course is to acquaint the student with the basic concepts, assumptions, and uses of statistics so that he will be able to consult with statistician when the need arises. The student needs an appreciation for the relationships of the many statistical procedures he learns. He should see how one experiment may require varied techniques in order to reach the experimental objectives.

A geometrical formulation of an unsolved problem in fractional factorial designs

This paper presents a rigorous contribution towards the mathematical understanding of some of the problems “which arise in fractional factorial designs. Specifically, it shows how choosing a saturated main effect fractional replicate of the 2n factorial is equivalent to choosing a simplex in the n-dimensional Euclidean space En, The formulaLion of this equivalence is achieved by employing certain important concepts in geometry. A complete illustration is given using the 23 factorial as an example. Statistical terminology has been limited so as to make the paper accessible to any mathematician with a slight understanding of statistics.

Comprehension of Statistical Terms by Special Education Students

Since special education students have been expected and often required to read in professional journals, a basic knowledge of statistics would seem to be helpful in effectively reading and evaluating research reports. Therefore, this investigation was designed to ascertain the level of comprehension of statistical terminology in a sample of 122 special education students from The University of Texas at Austin. Results suggested that students may not have the tools necessary to determine the worth of an article. There was indication that the problem might be alleviated through either inservice or preservice study in statistics.

The stepwise regression algorithm seen from the statistician’s point of view

abstract (introduction; abridged): the purpose of this paper is to explain in statistical terms how the algorithm works which is used in computer programmes for stepwise regression. stated more precisely, the purpose is to do this for one of severalpossible, closely related variants of the algorithm. the paper will contain nothing substatially new but may yet perhaps shed some new light on well-known facts. there are two reasons why the author has thought it worthwile writing this paper. one is that stepwise regression programme descriptions are usually written by computer people who tend to use flow-chart terminology rather than statistical terminology. an example in case is the standard reference, efroymson (1960). the other reason for writing the paper is the author's belief that the computer algorithm may serve as a vehicle for teaching students some important aspects of multiple regression. section 7 below is written with this latter point of view in mind.;

A Profile of the Undergraduate Russian Major 1958-1968

Introduction. The launching of the first Soviet space satellite on 4 October 1957, stimulated an upsurge of interest in studies in the US. The subsequent decade has seen a rapid growth of all aspects of and Slavic teaching and research in America, from high school beginning classes to Ph.D. dissertations.? One interesting manifestation of this growth, which has been less studied than others, is bachelor's degree recipients majoring in or Slavic (henceforth Russian BAs). And from the vantage point of today, a decade after the Sputnik-inspired rise in enrollments and majors began to be felt (in the 1958-1959 academic year), it is instructive to draw up a detailed profile of the undergraduate careers and previous background of BAs during that period at one university. Previous studies of enrollment, degrees, etc., have been mostly of the extensive type, with the advantage of nation-wide coverage, and the disadvantage of incomplete data (failure to identify all concerned institutions, their failure to respond) and non-comparable data (nomenclature and standards varying widely from institution to institution). The present study is an intensive analysis of all the BAs at one institution. Such a microcosm can be examined in greater detail than that currently possible in an extensive study, and may provide guidelines for the compilation of just such an extensive study in the future. The institution analyzed, for reasons of access to complete data and direct contacts with the students, is the University of Illinois.2 Its Department of Slavic Languages and Literatures also has the advantage of being typical-neither the smallest nor the largest, neither the best nor the worst-of those Slavic departments which reached national importance within the last decade. The data of this study represent only Urbana, but may offer some interest for comparison with other Slavic departments, and serve as a clue to general developments in the field. The data will be presented as directly and simply as possible, avoiding sophisticated statistical terminology. For those who might wish to extend the analysis to include other schools, or to make more complex calculations

Selection of an Appropriate Index for the Study of the Variability of Lizard and Snake Body Scale Counts

Frequency distributions of body scale counts show a positive skewness. Plots of sample standard deviations against sample means confirm the log-normal nature (i.e., the variance proportional to the mean) of scale count distributions. Moreover, variation is conservative, so that related species tend to possess similar coefficients of variation for homologous counts. If certain conditions are fulfilled (approximation to linear relationship, origin intercept, and proportio-nality of scatter to standard deviation), the mean coefficient of variation not only serves as a short-cut method of obtaining a least squares regression estimate of variation, but simultaneously serves as an index of variability uneffected by changes in the mean scale count. The bodies of lizards and snakes are covered by an epidermal coat of scales. The scales are folds of tissue, capped by a keratinized layer, that assume highly variable configurations. The purpose of this paper, however, is not to review the diversity of external scale morphology, a subject adequately covered by a number of general texts (e.g., Smith, 1946; Ludicke, 1962), but to examine statistically the degree and kind of variation in the number of body scales in naturally occurring local populations of lizards and snakes. As a first step, some means of mathematically describing the variability of scale counts is necessary. Basically, all statistical symbols and terminology follow Snedecor (1966). I have added subscripts to avoid confusion in certain circumstances. Early work by Klauber (1941b) demonstrated that the ventral scute counts of snakes and the body scale counts of some lizards (Sceloporus, Cnemidophorus) appear to conform to a normal distribution. Table 1, summarizing Klauber's calculations, presents the probability that the observed scale counts of the corresponding species fit a normal distribution. The probability that the differences are due to chance is tabulated. This close fit has allowed the use of normal statistics in the systematic study of lizards and snakes. The level of treatment of this subject historically has been largely a taxonomic one. Often the degree of dispersion of scale counts about a calculated sample mean is used to compare the significance of an observed difference between two or more means, or the departure of an isolated value (by the familiar t test). Occasionally (Klauber, 1940, etc.; Fox, Gordon, and Fox, 1961; Duellman and Wellman, 1960; and others to a lesser extent), the relative dispersion of scale counts about the same or different mean values has been compared using the coefficient of variation. At this point it should be noted that all the larger samples examined by Klauber (1941b) showed a slight positive skewness, an indication of a log-normal distribution, viz., the variance is proportional to the mean (Simpson, Roe, and Lewontin, 1960: 145-146). In the normal distribution, the mean and the variance are independent. If the distribution of scale counts is indeed log-normal, rather than normal, then the coefficient of variation could be valuable for comparing the relative variability of scale coiunts between different taxa. To date the application of the coefficient of variation as a systematic tool has not been justified for meristic scale counts in lizards and snakes. The use of the coefficient of variation, which is the sample standard deviation (s) divided by the sample mean (x), assumes the parametric

A Theory of the Budgetary Process

There are striking regularities in the budgetary process. The evidence from over half of the non-defense agencies indicates that the behavior of the budgetary process of the United States government results in aggregate decisions similar to those produced by a set of simple decision rules that are linear and temporally stable. For the agencies considered, certain equations are specified and compared with data composed of agency requests (through the Bureau of the Budget) and Congressional appropriations from 1947 through 1963. The comparison indicates that these equations summarize accurately aggregate outcomes of the budgetary process for each agency.In the first section of the paper we present an analytic summary of the federal budgetary process, and we explain why basic features of the process lead us to believe that it can be represented by simple models which are stable over periods of time, linear, and stochastic. In the second section we propose and discuss the alternative specifications for the agency-Budget Bureau and Congressional decision equations. The empirical results are presented in section three. In section four we provide evidence on deviant cases, discuss predictions, and future work to explore some of the problems indicated by this kind of analysis. An appendix contains informal definitions and a discussion of the statistical terminology used in the paper.

Measurement of the thermal parameter /rho ck/ 1/2 for clear fused quartz.

EAT-TRANSFER measurement in shock tubes and shock tunnels with thin-film resistance thermometers is a well-established technique.1 The analysis of the thermometer signal, in terms of incident heat flux, is critically dependent on the accurate knowledge of the thermal properties of the substrate, to which the resistance film is bonded. Substrate properties normally appear in the lumped parameter (pck)112 in the equation for computing heat flux (the symbols represent substrate density, specific heat, and thermal conductivity, respectively). Pertinent data for #7740 Pyrex, a material almost universally used for substrates for heat flux sensors, have been published earlier together with a discussion of the experimental techniques employed.2 Although less popular in usage, clear fused quartz is used as a substrate in applications where its higher (relative to #7740 Pyrex) softening temperature and superior optical transparency are important. This Note presents experimental data obtained for (pck)112 for clear fused quartz (General Electric Company, Type 101) employing the same techniques as used for the Pyrex determination.2 A total of 14 test points were available for the determination of the absolute value of (pck)112 for clear fused quartz at room temperature (78°F). This total comprised results of tests on nine different samples plus five replicated measurements. The temperature dependence of the thermal parameter also was evaluated at two elevated temperatures (approximately 120° and 170°F) using ten different specimens. The mean value of the thermal parameter at 78°F was 0.0754 Btu ft-20F-! sec~1/2 with a standard deviation from the mean of 0.0015. Scatter in the data, as represented by the magnitude of the standard deviation, essentially is the same as that associated with the measurements on #7740 Pyrex.2 Because the mean values determined for clear fused quartz and #7740 Pyrex (0.0737) nearly are the same numerically, an analysis was performed to test the statistical significance of the difference in these two means. Using the Student's t Test3 and the experimental data giving rise to these two means, it was found that the probability of obtaining the difference (0.0017) by chance alone was less than 0.01. In statistical terminology, the difference observed is classified as highly significant. The use of these separate values for (pck)112 for clear fused quartz and #7740 Pyrex therefore is justifiable. The mean value for quartz of 0.0754 Btu ft~2°F-1 sec~~1/2 compares with 0.0752 found by Hartunian and Varwig4 and 0.0742 calculated from data in the General Electric Company, Fused Quartz Catalog Q7A. An analysis of variance was made using the room-temperature data for (pck)1'2 for clear fused quartz to determine what fraction of the total variance (square of the standard deviation) in the mean was the result of experimental variance and what fraction was the result of actual variance in sample properties. This analysis showed that the variance caused by experimental sources overshadowed the variance attributable to differences among specimens. Thus, the major portion of the total variance reported in the mean values of (pck)l/2 for clear fused quartz and #7740 Pyrex2 is of experimental orgin and does not represent truly the magnitude of variance in properties among samples which is much smaller, since the total variance is a simple sum of all the contributing variances. A detailed discussion of the experimental procedures and sources of error is given in Ref. 5. A straight line was fitted to test data for (pck)1'2 for clear fused quartz taken as a function of temperature. In the range from 78° to 170°F, the value of the thermal parameter increases with temperature at a rate of 0.86% per 10°F. This note has presented data that demonstrate a small but significant difference in the thermal parameter (pck)112 for clear fused quartz and #7740 Pyrex. Also, an analysis of variance has shown that the variance in this parameter is substantially the result of experimental treatment rather than differences among the specimens tested.

Statistical Terminology — Russian vs. English — in the Light of the Development of Statistics in the U.S.S.R.

Statistical Terminology — Russian vs. English — in the Light of the Development of Statistics in the U.S.S.R.

The measurement of uncertainty.

To express results of experimentation in statistical notation has become a common practice and standard requirement. Indeed, statistics has been adopted as routine aspect of the conduct of experiments to an extent which makes statistical terminology seemingly self‐evident. This clearly indicates how deeply the vocabulary of probabilistic thinking has molded our scientific and “common sense” habits of thought. Yet, usage of statistical terms is not commonly paralleled by an adequate appreciation of magnitude and scope of the intellectual revolution from which statistical methodology arose.

A Statistical Analysis of Water Works Data for 1955

pressive masses of numbers published recently by a nongovernmental organization. The survey comprised a wealth of information on physical systems, water use, rates, and finances of 497 United States water utilities serving populations of 10,000 or more. The combined population served by these utilities was just over 70,000,000 more than 60 per cent of the total population served by all water utilities. The data present at least two broad areas of interest which are open to a statistical approach. The first involves the presence (or absence) of general trends, as shown by averages, ranges, and frequencies, which may answer such questions as: Is a specific cost element affected by size of city? Do high rates affect water use ? Are rates keeping up with rising costs? What can be learned from a comparison of the current survey with the surveys of 1950 (2) and 1945 (3) ? The second area of interest is the possibility of determining norms or typical data for various aspects of water works operation so that the management of a particular utility can judge how it compares with other utilities operating under similar conditions. Statistical Terminology