Sample Coefficient Of Variation Research Articles

The Properties of Moment Estimators for the Weibull Distribution Based on the Sample Coeffkient of Variation

Moment estimators k* and b* for the shape parameter, k, and scale parameter, b, of the twoparameter form of the Weibull distribution, are given. The estimators are based on the sample coefficient of variation and are shown to be asymptotically efficient with respect to the Cramer-Rao lower bound, and to be asymptotically normally distributed. The asymptotic distribution is determined and a table for calculating the estimators and their approximate variance-covariance matrix is given. Examples of the use of the method and the construction of large sample confidence intervals and confidence regions are given.

Significance Tests for Coefficients of Variation and Variability Profiles

Sokal, R. R., and C. A. Braumann (Department of Ecology and Evolution, State University of New York at Stony Brook, Stony Brook, New York 11794) 1980. Significance tests for coefficients of variation and variability profiles. Syst. Zool. 29:50-66.-The distribution of sample estimates of the coefficient of variation is studied analytically and by Monte Carlo simulation. Derivations are given for the expected value of a coefficient of variation and for its standard error. Various proposed standard errors for coefficients of variation are evaluated. Standard errors are derived for differences between coefficients of variation for samples of independent and correlated characters. Methods are proposed for testing the homogeneity of sets of independent and correlated coefficients of variation. Tests of homogeneity of variability profiles as well as for parallelism of such profiles are furnished. [Coefficients of variation, variability profiles.] The employment of coefficients of variation in systematic research is of long standing. Various evolutionary hypotheses require for their examination the establishment of differences in the amounts by which characters vary in populations. Such differences can be examined for the same character across several populations of the same species or of different species, or the comparison may be within the same population but among different characters. Such comparisons of the amounts of variation are generally adjusted for differences in magnitude of the character means, hence the employment of the coefficient of variation, V. A recent renewal of interest in the coefficient of variation is due to two developments. Various studies, collectively called population phenetics, have probed the effects of evolutionary processes on variability patterns in animal and plant populations and have tried to establish the converse-the drawing of inferences about evolutionary processes from observed variability patterns. Studies such as those of Soule (1967), Soule and Stewart (1970), Rothstein (1973), Lande (1977), or Sokal (1976) come to mind readily. A second reason for an increased interest in coefficients of variation is the stimulating book by Yablokov (1974) introducing the study of variability profiles in mammalian populations. Variability profiles are graphs in which the amount of variation expressed as a variance or coefficient of variation is plotted against a horizontal axis representing the suite of characters under study. Examination of variability profiles within and among populations leads to inferences about the amount of developmental (and ultimately evolutionary) control of variability for different characters in the same population and among populations. There is a need for appropriate methods to examine the types of comparisons being considered. In this paper we shall briefly review the expectations and variances of coefficients of variation under the assumption of normality and examine the effects of appreciable departures from this assumption. We shall then turn to the comparison of two or more coefficients of variation for the same character from different populations. This account will be followed by a discussion of tests applicable to a single variability profile, which in turn will lead to the comparison of several profiles. These can be considered for the same hierarchic level, as in local population samples of the same species, or the comparison may be between different hierarchic levels representing natural sampling units, such as variability within local populations versus variability across populations. Analytical work on the expectations

A sensitive and specific enzymeimmunoassay for serum testosterone

A very sensitive enzymeimmunoassay for testosterone was developed using testosterone-penicillinase conjugate and an antibody to testosterone-3-(O-carboxymethyl)oximebovine serum albumin. The specificity of the assay was demonstrated, by the fact that eatradiol-17β, estrone, estriol, progesterone, 17α-hydroxy-progesterone, dehydroepiandrosterone, androstenedione, cortisol and cortisone were ineffective in crossreacting with testosterone while dihydrotestosterone was 8 times less crossreactive as compared to testosterone. The minimum detectable amount of testosterone was 10–15 pg per assay tube. Infra-assay and inter-assay coefficients of variation for samples containing 0.3–6ng/ml of testosterone were 6–8% and 8–10%, respectively. A high degree of correlation ( r = 0.97) was observed between serum testosterone values obtained by enzymeimmunoassay and radioimmunoassay. The levels of testosterone in the sera of normal men and women and those in hypogonadal males following stimulation with human chorionic gonadotropin determined by this enzymeimmunoassay appear similar to those reported by other investigators.

A totally automated system for enzyme immunoassay of theophylline in serum.

We describe a procedure for enzyme immunoassay of theophylline (1,3-dimethylxanthine) in which all phases of the assay are totally automated in a Kinetic Analyzer (KA-150). This system permits assay of 75 10-mul samples per hour, with results available at 30-s intervals after initial sample preparation and preincubation. We compared results for 138 clinical samples by an ultraviolet method (x) and the present method (y). The slope of the comparison curve was 0.902, the y-intercept 0.402, and the correlation coefficient 0.984. The coefficient of variation for samples run in duplicate on the same day was 4.9%; it was 8.1% for samples run on different days. Specificity, sensitivity, simplicity, speed, and small reagent requirement all make this an attractive alternative to chromatographic procedures.

Variability of the Reverse-Flow Concentration Technique of Measuring Plankton Respiration

Results from the reverse-flow concentration method used to determine community plankton respiration vary significantly because of metabolic inactivation or losses of a portion of the concentrated sample during the filtering process. These losses seem to be nearly constant at concentrations greater than 150X. The within sample coefficient of variation is 20–40% and is primarily a result of clumping and inadequate mixing before subsampling. A rapid processing of the samples is critical for best results.

On multivariate coefficients of variation

This paper reviews the distribution of the sample coefficient of variation (c. v.),\(v = s/\bar x\) as presented here in closed form in terms of the derivatieves of the moment generating function (m.g.f.) of the normal distribution.

Automated radioimmunoassay of choriomammotropin (human placental lactogen).

We describe a totally automated procedure for radioimmunoassay of choriomammotropin, in which all phases of the assay are automated in a single system ("Centria"). This system permits the simultaneous incubation and separation of many samples in a nonequilibrium assay, and measurements are obtained in less than 30 min. Results for clinical samples by reference radioimmunossay methodology and with the Centria system compared uniformly well: y=0.91x - 0.87;r=0.94. The coefficient of variation for samples run in duplicate on the same day was 5.2%, 7.4% for samples run on different days. The specificity, sensitivity, simplicity, and speed of this system makes it a useful new tool for kinetic, nonequilibrium immunoassay.

A Test for Randomness

A procedure is proposed for studying the hypothesis that a sequence of dichotomous random variables are independent and identically (randomly) distributed. The procedure is relatively sensitive to departures from randomness involving multiple clustering. An application to testing for Schwann cell disease is discussed. The distrubution of the sample coefficient of variation from an exponential distribution, a useful statistic in testing randomness for a continuous model, is also studied.

A radioimmunoassay for plasma aldosterone without chromatography.

A radioimmunoassay for plasma aldosterone has been developed which requires no preliminary chromatography. Purification consists of partitioning between cyclohexane and water, and periodate oxidation followed by a sodium hydroxide wash. The antibody affinity for aldosterone-γ-lactone was approximately 5 orders greater than for other interfering steroids. The specificity of the method was confirmed by the finding that additional purification by Sephadex column chromatography did not lower the observed values. Accuracy was confirmed by recovery studies from pooled plasma containing 70.6 pg/ml (recovery = 0.964 added + 74.9 ± 16.3 pg/ml in the range of 0 to 300 pg/ml added). The coefficient of variation for samples assayed on 5–7 different occasions was 10.6 to 14.1%. This assay is a rapid, efficient and accurate means for measuring plasma aldosterone.

Comparisons of Approximations to the Percentage Points of the Sample Coeffcient of Variation

It may be of some interest in certain statistical problems to have available percentage points of the sample coefficient of variation (S.C.V.). If the parent population is assumed to be normal, the obtaining of such percentage points from tables of the non-central t distribution might be thought to be simple. However, one does encounter difficulty in using these tables to calculate the percentage points of the S.C.V. One can, as an alternative, use the exact table of Iglewicz (1967). A number of approximations for the percentage points of the S.C.V. exists in the literature. These approximations may be useful as alternatives to either of the tables mentioned above. The applicability of several of these approximations is further enhanced by their simplicity. In this paper we compare these approximate results with the exact ones in order to determine the quality of the approximations.

Early Hominidae and cranial capacity.

WOLPOFF1 has recently argued that the cranial capacity of the type specimen of Homo habilis2 from Olduvai Gorge, Tanzania (Olduvai hominid 7), is not sufficiently different from those of South African Australopithecus africanus to warrant placement in a separate species. He arrives at this conclusion by pooling the sets of observations from Olduvai and South Africa, calculating the mean and standard deviation of this “sample”, and showing that the sample coefficient of variation is not unduly high. He also shows that Olduvai hominid 7 falls only 2.03 standard deviations from the sample mean.

On the Percentage Points of the Sample Coefficient of Variation

On the Percentage Points of the Sample Coefficient of Variation

Survey of Properties and Applications of the Noncentralt-Distribution

Applications are outlined of the noncentral t-distribution to tolerance limits, to variables sampling plans, to confidence limits on a quantile, to confidence limits on a proportion, to the distribution of the sample coefficient of variation, and to the power of Student's t-test. The basic assumption is that there is available a random sample from a normal distribution with mean and variance unknown. Some of the mathematical properties of the noncentral t-distribution are also outlined. An extensive bibliography has been prepared and cross-referenced to several review journals and books. The bibliography covers references to tolerance limits and sampling plans based on the normal distribution whether or not the noncentral t-distribution is directly involved. Some selected references to Student's t-distribution are also included.

A Statistical Application of Euler's Theorem

An inequality for the sample coefficient of variation was derived in an article by Summers [1]. An application of the result to variables sampling was discussed for one-sided variables sampling plans, using the derived rejection number for the mean and standard deviation. In the present paper a bound is derived for the ratio of the sample range R and sample mean Xi, R/X, using methods similar to those of Reference 1. This bound is also applicable to variables sampling, since a rejection number for one-sided variables sampling plans is derived for the mean and range.

An Inequality for the Sample Coefficient of Variation and an Application to Variables Sampling

An Inequality for the Sample Coefficient of Variation and an Application to Variables Sampling

An Inequality for the Sample Coefficient of Variation and an Application to Variables Sampling

An Inequality for the Sample Coefficient of Variation and an Application to Variables Sampling

Separation and colorimetric determination of trace quantities of magnesium in high-purity beryllium oxide

A colorimetric method is described for the determination of trace quantities of magnesium in beryllium metal and its oxide. Beryllium, which is known to interfere with the colorimetric determination of magnesium by the available chromogenic reagents, is separated from the magnesium by forming the beryllium perfluorobutyrate salt at pH 3 to 4, and then extracting it with several portions of diethyl ether. By increasing the number of equilibrations with ether, as much as 1 g of beryllium can be separated from 10 μg of magnesium. The magnesium is then measured spectrophotometrically as the highly coloured complex with Magon, sodium 1-azo-2-hydroxy-3-(2,4-dimethylcarboxanilido) naphthalene-1-(2-hydroxybenzene-5-sulphonate), which exhibits a peak of maximum absorbance at 510 mμ. Over the range of 0.04 to 0.40 μg of magnesium per ml, the absorbance conforms to Beer's law. The method has been applied successfully to the determination of quantities of magnesium as low as 10 μg. The coefficient of variation for samples which contain 200 μg of magnesium is 2 %.

Separation and Determination of Microgram Amounts of Sulfur

A method has been devised for the determination of parts per million of sulfur in uranium trioxide, sodium zirconium fluoride, and hydrofluoric acid. Sulfur trioxide evolved by fusion with vanadium pentoxide is reduced over copper at 950 deg C to the dioxide, which is absorbed in sodium telrachloromercuraie and determined spectrophotometrically with pararosaniline and formaldehyde. The coefficient of variation for samples containing 5 to 10 gamma of sulfur is 5. (auth)