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The article discusses descriptive statistics of data measured in ordinal and quantitative scales, and criteria for determining the statistical significance of differences between samples when it is impossible to analyze using parametric methods. Special attention is paid to the problem of multiple comparisons of this type of data. For each method, examples of processing data obtained in pharmacological studies are given.

Statistical methods are crucial for research studies in LIS to reach, analyze, and critique results. The current study aims to investigate the use of statistical methods in the Arab literature in LIS, provide a comprehensive review of commonly used statistical methods, and reveal the variables affecting the use of statistical methods. Research papers published in the eight Arab journals from January 2014 to December 2018 were investigated according to three categories of variables related to characteristics of article, author, and research methodologies. Statistical methods were classified into four categories: descriptive methods, parametric inferential methods, nonparametric inferential methods, and predictive methods. The total usage of statistical methods reached 1037 times. Descriptive statistical methods were the most commonly used, followed distantly by predictive statistical methods. Frequency distributions and percentages were used in most quantitative studies. While t-test and ANOVA were the most parametric methods used, Chi-squared was the most non-parametric method used. Most of the studied variables influence the Arab researchers' choice of the category of statistical methods used in their research in LIS. Besides, the author's characteristics are the most influential variables in the use of statistical methods, followed by the research methodology, while the effect of article characteristics is less.

Most studies of estimating overlapping coefficients assume two specific parametric models for population densities. The methods that used such of this assumption are called parametric methods, whic...

In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.

Different probability models are used to model survival data. However, it is important to know which model describe best the data because if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret and helps in predictions. This article presents the Bayesian censored data modeling assuming Gumbel, double exponential, exponentially modified Gaussian, Weibull, and lognormal distributions as sampling models. In particular, a historical Leukemia data set is used to show the comparison among different models. Markov Chain Monte Carlo (MCMC) methods are used to compute the posterior summaries. Different model selection criteria, like, Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), Leave-one-out Cross-Validation (LOOCV), and Watanabe-Akaike Information Criterion (WAIC) are used for model selection. It is observed from the comparative study that the lognormal model has the minimum values of different model selection criteria and considered to be the best for this Leukemia data.

N-Nitrosamines have recently been the subject of intense regulatory scrutiny, including the setting of low exposure limits (18 ng/day) (European Medicines Agency (EMA), 2020). This paper evaluates different methodologies to determine statistically robust bounds on the carcinogenic potency of chemical classes, using historic TD50 data (Peto et al., 1984; Thresher et al., 2019) and exemplified for N-nitrosamines. Initially, the distribution of TD50 values (TD50s) for N-nitrosamines of known potency was characterised. From this, it is possible to compare parametric and non-parametric methods to obtain percentiles of interest from the distribution of TD50s, which are shown to be robust to uncertainty in the initial TD50 estimates. These methods may then be applied to different chemical subclasses. The values obtained may be of use in refining acceptable intakes for N-nitrosamines and their subclasses.

The aim of time-varying heart rate variability spectral analysis is to detect and quantify changes in the heart rate variability spectrum components during nonstationary events. Of the methods available, the nonparametric short-time Fourier Transform and parametric time-varying autoregressive modeling are the most commonly employed. The current study (1) compares short-time Fourier Transform and autoregressive modeling methods influence on heart rate variability spectral characteristics over time and during an experimental ozone exposure in mature adult spontaneously hypertensive rats, (2) evaluates the agreement between short-time Fourier Transform and autoregressive modeling method results, and (3) describes the advantages and disadvantages of each method. Although similar trends were detected during ozone exposure, statistical comparisons identified significant differences between short-time Fourier Transform and autoregressive modeling analysis results. Significant differences were observed between methods for LF power (p ≤ 0.014); HF power (p ≤ 0.011); total power (p ≤ 0.027); and normalized HF power (p = 0.05). Furthermore, inconsistencies between exposure-related observations accentuated the lack of agreement between short-time Fourier Transform and autoregressive modeling overall. Thus, the short-time Fourier Transform and autoregressive modeling methods for time-varying heart rate variability analysis could not be considered interchangeable for evaluations with or without interventions that are known to affect cardio-autonomic activity.

When statistically comparing outcomes between two groups, researchers have to decide whether to use parametric methods, such as the t-test, or non-parametric methods, like the Mann–Whitney test. In endocrinology, for example, many studies compare hormone levels between groups, or at different points in time. Many papers apply non-parametric tests to compare groups. We will explain that non-parametric tests have clear drawbacks in medical research, and, that’s the good news, they are often not necessary.

This review article presents an assessment of trends in statistical methods and an evaluation of their appropriateness in articles published in the Archives of Plastic Surgery (APS) from 2012 to 2017. We reviewed 388 original articles published in APS between 2012 and 2017. We categorized the articles that used statistical methods according to the type of statistical method, the number of statistical methods, and the type of statistical software used. We checked whether there were errors in the description of statistical methods and results. A total of 230 articles (59.3%) published in APS between 2012 and 2017 used one or more statistical method. Within these articles, there were 261 applications of statistical methods with continuous or ordinal outcomes, and 139 applications of statistical methods with categorical outcome. The Pearson chi-square test (17.4%) and the Mann-Whitney U test (14.4%) were the most frequently used methods. Errors in describing statistical methods and results were found in 133 of the 230 articles (57.8%). Inadequate description of P-values was the most common error (39.1%). Among the 230 articles that used statistical methods, 71.7% provided details about the statistical software programs used for the analyses. SPSS was predominantly used in the articles that presented statistical analyses. We found that the use of statistical methods in APS has increased over the last 6 years. It seems that researchers have been paying more attention to the proper use of statistics in recent years. It is expected that these positive trends will continue in APS.

Understanding dose–response relationship is a crucial step in drug development. There are a few parametric methods to estimate dose–response curves, such as the Emax model and the logistic model. These parametric models are easy to interpret and, hence, are widely used. However, these models often require the inclusion of patients on high-dose levels; otherwise, the model parameters cannot be reliably estimated. To have robust estimation, nonparametric models are used. However, these models are not able to estimate certain important clinical parameters, such as ED50 and Emax. Furthermore, in many therapeutic areas, dose–response curves can be assumed as nondecreasing functions. This creates an additional challenge for nonparametric methods. In this paper, we propose a new Bayesian isotonic regression dose–response (BIRD) which features advantages from both parametric and nonparametric models. The ED50 and Emax can be derived from this model. Simulations are provided to evaluate the BIRD model perf...

The distribution of earthquake magnitudes plays a crucial role in the estimation of seismic hazard parameters. Due to the complexity of earthquake magnitude distribution, non-parametric approaches are recommended over classical parametric methods. The main deficiency of the non-parametric approach is the lack of complete magnitude data in almost all cases. This study aims to introduce an imputation procedure for completing earthquake catalog data that will allow the catalog to be used for non-parametric density estimation. Using a Monte Carlo simulation, the efficiency of introduced approach is investigated. This study indicates that when a magnitude catalog is incomplete, the imputation procedure can provide an appropriate tool for seismic hazard assessment. As an illustration, the imputation procedure was applied to estimate earthquake magnitude distribution in Tehran, the capital city of Iran.

The time-dependent-asymmetric-linear parsimony is an ancestral state reconstruction method which extends the standard linear parsimony (a.k.a. Wagner parsimony) approach by taking into account both branch lengths and asymmetric evolutionary costs for reconstructing quantitative characters (asymmetric costs amount to assuming an evolutionary trend toward the direction with the lowest cost).A formal study of the influence of the asymmetry parameter shows that the time-dependent-asymmetric-linear parsimony infers states which are all taken among the known states, except for some degenerate cases corresponding to special values of the asymmetry parameter. This remarkable property holds in particular for the Wagner parsimony.This study leads to a polynomial algorithm which determines, and provides a compact representation of, the parametric reconstruction of a phylogenetic tree, that is for all the unknown nodes, the set of all the possible reconstructed states associated to the asymmetry parameters leading to them. The time-dependent-asymmetric-linear parsimony is finally illustrated with the parametric reconstruction of the body size of cetaceans.

In this study, the performance of various methods for generating quantitative parametric images of dynamic C-11-phenytoin PET studies was evaluated. Methods: Double-baseline 60-min dynamic C-11-phenytoin PET studies, including online arterial sampling, were acquired for 6 healthy subjects. Parametric images were generated using Logan plot analysis, a basis function method, and spectral analysis. Parametric distribution volume (V-T) and influx rate (K-1) were compared with those obtained from nonlinear regression analysis of time-activity curves. In addition, global and regional testretest (TRT) variability was determined for parametric K-1 and V-T values. Results: Biases in V-T observed with all parametric methods were less than 5%. For K-1, spectral analysis showed a negative bias of 16%. The mean TRT variabilities of V-T and K-1 were less than 10% for all methods. Shortening the scan duration to 45 min provided similar V-T and K-1 with comparable TRT performance compared with 60-min data. Conclusion: Among the various parametric methods tested, the basis function method provided parametric V-T and K-1 values with the least bias compared with nonlinear regression data and showed TRT variabilities lower than 5%, also for smaller volumeof- interest sizes (i.e., higher noise levels) and shorter scan duration.

Receiver Operating Characteristics (ROC) curve serves as a statistical tool to measure the quality of Biomarker in assessing the accuracy of any diagnostic test. This paper portrays the historical background of ROC curve and reviews various parametric methods adopted for fitting the ROC curve till date. The parametric ROC models that are considered in this paper are Bi-Normal, Bi-Gamma, Bi-Lomax, Bi-Weibull, Bi-Rayleigh, Bi-Beta, Bi-Triangular, Bi-Uniform and Bi-Exponential ROC models.

In clinical research, sample size determination is one of the most important things. There are parametric method using t-test and non-parametric method suggested by Kim and Kim (2007) based on Wilcoxon`s rank sum test for determining sample size in non-inferiority trials. In this paper, we propose sample size calculation method based on placements method suggested by Orban and Wolfe (1982) and using the power calculated by Kim (1994) in non-inferiority trials. We also compare proposed sample size with that using Kim and Kim (2007)`s formula and that of t-test for parametric methods. As the result, sample size calculated by proposed method based on placements is the smallest. Therefore, proposed method based on placements is better than parametric methods in case that it`s hard to assume specific distribution function for population and also more efficient in terms of time and cost than method based on Wilcoxon`s rank sum test.

The authors present a method for predicting the long-term deformation of materials based on the base diagram concept. The long-term strength calculation of steels 18Cr–12Ni–Mo and 21Cr–32Ni–Ti–Al for different specified stress and temperature values showed the efficiency of its defining relations. The advantage this approach has over the most common parametric methods such as the Larson–Miller, Orr–Sherby–Dorn, Manson–Sakkop, and Trunin parameters is shown.

Analysis of variance (ANOVA) is used to compare the means of various samples. Parametric ANOVA approaches assume normally distributed error terms within subsamples. Permutation tests like synchronized permutation tests are computationally intensive and distribution free procedures. Hence they overcome the limitations of parametric methods. Unbalanced designs with differing subsample sizes are quite frequent in various disciplines. There is a broad literature about unbalanced designs and parametric testing. For permutation tests this topic received some attention recently. This paper extends the synchronized permutation method to unbalanced two-level ANOVA designs. A simulation study investigates the behavior of different procedures for various types of unbalanced designs. It compares the results to other permutation approaches. The synchronized permutation method yields comparable results to the best performing competing permutation approaches. However the approach is limited to certain kinds of unbalanced designs.

Continuous data arise in most areas of medicine. Familiar clinical examples include blood pressure, ejection fraction, forced expiratory volume in 1 second (FEV1), serum cholesterol, and anthropometric measurements. Methods for analysing continuous data fall into two classes, distinguished by whether or not they make assumptions about the distribution of the data. Theoretical distributions are described by quantities called parameters, notably the mean and standard deviation.1 Methods that use distributional assumptions are called parametric methods, because we estimate the parameters of the distribution assumed for the data. Frequently used parametric methods include t tests and analysis of variance for comparing groups, and least squares regression and correlation for studying the relation between variables. All of the common parametric methods (“ t methods”) assume that …

The aim of this study was to undertake the theoretical derivations of non-parametric methods, which use linear regressions based on rank order, for stability analyses. These methods were extension different parametric methods used for stability analyses and the result was compared with a standard non-parametric method. Intensive computational methods (e.g., bootstrap and permutation) were applied, and data from the plant-breeding program of the Biology Department of UFLA (Minas Gerais, Brazil) were used to illustrate and compare the tests. The non-parametric stability methods were effective for the evaluation of phenotypic stability. In the presence of variance heterogeneity, the non-parametric methods exhibited greater power of discrimination when determining the phenotypic stability of genotypes. The aim of this study was to undertake the theoretical derivations of non-parametric methods, which use linear regressions based on rank order, for stability analyses. These methods were extension different parametric methods used for stability analyses and the result was compared with a standard non-parametric method. Intensive computational methods (e.g., bootstrap and permutation) were applied, and data from the plant-breeding program of the Biology Department of UFLA (Minas Gerais, Brazil) were used to illustrate and compare the tests. The non-parametric stability methods were effective for the evaluation of phenotypic stability. In the presence of variance heterogeneity, the non-parametric methods exhibited greater power of discrimination when determining the phenotypic stability of genotypes.

A variety of nonparametric and parametric methods have been used to estimate the mean cumulative function (MCF) for the recurrence data collected from the counting process. When the recurrence histories of some units are available in disconnected observation windows with gaps in between, Zuo et al. (2008) showed that both the nonparametric and parametric methods can be extended to estimate the MCF. In this article, we establish some asymptotic properties of the MCF estimators for the window-observation recurrence data.

In the literature, some semiparametric statistical methods were recently developed under density ratio models, and these methods are usually more robust than parametric methods and more effective than nonparametric methods. In this paper, we propose a semiparametric hypothesis testing method on the difference of two population means under a semiparametric density ratio model. This method is essentially built upon semiparametric estimation of the difference of two population means. Some theoretical results as well as simulation results are provided, which suggest that our proposed method is slightly superior to some commonly used parametric and nonparametric methods when data are normal, and is significantly better than them when data are not normal. We also apply our proposed method to analysis to two real examples.

To make inferences concerning a population, parametric methods are traditionally used for sample data analysis assuming that these come from ordinary populations, which not always happens. Most of the times such assumption leads to inadequate conclusions and decisions, especially when the data are distributed asymmetrically. It was aimed on this work to adjust some plausible models for this type of data, aiming to compare eggs productions in quails of different lines through frequentist and Bayesian methods. In the analyzed data it could be verified that the parametric and non-parametric frequentist procedures were, in general, equally conclusive. The Bayesian procedure was the only one which detected difference between the yellow and red lines, regarding the preconized energy diet, and between the blue and yellow for the second eclosion group. By the frequentist methods differences between the blue and red lines were not found; however, given a Poisson distribution for the eggs production, through multiple comparisons between the posterior mean under the Bayesian focus, differences were found between all lines. For being more sensitive, besides flexible, such procedure detected differences not observed by the traditional methods between the yellow and red lines, in the higher energy diet; between the blue and the red one in the second eclosion group and in general. It was concluded that quails of the yellow line showed bigger eggs production, regardless of the eclosion group and diet. Such results raise the discussion on the appropriate use of methods and procedures for statistical data analysis.

Summary As new diagnostic tests are developed and marketed, it is very important to be able to compare the accuracy of a given two continuous-scale diagnostic tests. An effective method to evaluate the difference between the diagnostic accuracy of two tests is to compare partial areas under the receiver operating characteristic curves (AUCs). In this paper, we review existing parametric methods. Then, we propose a new semiparametric method and a new nonparametric method to investigate the difference between two partial AUCs. For the difference between two partial AUCs under each method, we derive a normal approximation, define an empirical log-likelihood ratio, and show that the empirical log-likelihood ratio follows a scaled chi-square distribution. We construct five confidence intervals for the difference based on normal approximation, bootstrap, and empirical likelihood methods. Finally, extensive simulation studies are conducted to compare the finite-sample performances of these intervals, and a real example is used as an application of our recommended intervals. The simulation results indicate that the proposed hybrid bootstrap and empirical likelihood intervals outperform other existing intervals in most cases.

Assessment of yield stability is an important issue for maize (Zea mays L.) cultivar evaluation and recommendation. Many parametric procedures are available for stability analysis, each of them allowing for different interpretations. The objective of the present study was to assess yield stability of maize hybrids evaluated in the National Maize Cultivar Regional Trials in southwestern China using 20 parametric stability statistics proposed by various authors at different times, and to investigate their interrelationships. Two yield datasets were obtained from the 2003 and 2004 national maize cultivar regional trials in southwestern China. A combined analysis of variance, stability statistics, and rank correlations among these stability statistics were determined. Effects of location, cultivar, and cultivar by location interaction were highly significant (P

In this paper, a nonparametric method is proposed for the estimation of decreasing mean residual life with type II censored data. This method is based on the comparison between two estimators of the reliability function: the Kaplan-Meier estimator, and an estimator derived from the empirical MRL function. Simulation results indicate that the new approach is able to give good performance, and can outperform some existing parametric methods when censoring is heavy.

Establishing measurement equivalence is important because inaccurate assessment may lead to incorrect estimates of effects in research, and to suboptimal decisions at the individual, clinical level. Examination of differential item functioning (DIF) is a method for studying measurement equivalence. An item (i.e., one question in a longer scale) exhibits DIF if the item response differs across groups (e.g., gender, race), controlling for an estimate of the construct being measured. A distinction between applications in health, as contrasted with other settings such as educational and aptitude testing, is that there are many health-related constructs and multiple measures of each, few of which have received much critical evaluation. Discussed in this article are several methods for detection of differential item functioning (DIF), including non-parametric and parametric methods such as logistic regression, and those based on item response theory. Basic definitions and criteria for DIF detection are provided, as are steps in performing the analyses. Recommendations are presented and future directions discussed.

To predict long-term creep life from short-term creep life data, various parametric methods such as Larson-Mille. (L-M), Orr-Sherby-Dorn (O-S-D), Manson-Haferd (M-H) parameters, and a Minimum Commitment Method (MCM) were suggested. A number of the creep data were collected through literature surveys and experimental data produced in KAERI. The polynomial equations for type 316LN SS were obtained by the time-temperature parameters (TTP) and the MCM. Standard error (SE) and standard error of mean (SEM) values were obtained and compared with the each method for various temperatures. The TTP methods showed good creep-life prediction, but the MCM was much superior to the TTP ones at and . It was found that the MCM were lower in the SE values when compared to the TTP methods.

The accuracy of classifying bogue (Boops boops) according to the fishery from which it was harvested was evaluated by applying several statistical classification techniques to fish parasite abundances. Bogue captured in 2001 in two fisheries off the Atlantic coast of Spain were compared with one off the Spanish Mediterranean coast. One hundred bogue were classified to each harvest location (fishery) using different numbers of parasite species chosen as predictors by a best subset method. Two parametric methods of classification (linear and quadratic discriminant analysis) were compared with two non-parametric approaches (k-nearest neighbour classification and feed-forward neural network) and the cross-validated correct classification rate determined in each case. The best results were achieved for k-nearest neighbour classification with 96% of fish being correctly assigned to their fishery. That result was based on five predictor parasite species, namely Aphanurus stossichii, Bacciger israelensis, Hemiurus communis, Microcotyle erythrini and Lecithocladium excisum. The optimal classification for a feed-forward neural network was very similar to that achieved with linear discriminant analysis at 94% correct classification rate for only four predictor species. Quadratic discriminant analysis performed worst of the four classification methods examined. Classification accuracies for all four statistical approaches were, however, remarkably similar and were quite accurate with only between 4 and 8% of fish incorrectly classified regardless of the method used. With greater temporal and spatial resolution of sampling effort, this technique holds promise as a cost-effective method of distinguishing harvest locations of bogue that can readily be adapted to other fish species.

Pashardes (1991) and Banks et al. (1994) use parametric methods to estimate lifetime equivalence scales. Their approaches put parametric restrictions on the differences in within-period expenditure needs across household types, the intertemporal allocation of expenditure, and the shapes of commodity demand equations. This paper puts parametric structure only on the differences in within-period expenditure needs across household types. This implies structure on the intertemporal allocation of expenditure, but leaves the shapes of commodity demand equations unrestricted. Semiparametric methods are used to estimate within-period and lifetime equivalence scales with Canadian expenditure data, and to test the restrictions imposed on within-period expenditure functions. Estimated lifetime equivalence scales are similar in size to those estimated by Banks et al. (1994) and exhibit equal lifetime costs for first and second children. Copyright © 2005 John Wiley & Sons, Ltd.

The objective of the this work is to verify the applicability of parametric methods that measure the cost efficiency of Brazilian electricity distributors. We estimate total cost functions, derived from a Cobb-Douglas production function. The frontier cost model is estimated using GLS (Variance Components – Random Effects) and pooled least square (Fixed Effects) methods. We apply these methods to a sample of 25 Brazilian power distribution companies over a period of 12 years, from 1990 through 2001. The results indicate that in the period studied all the companies were equally efficient in controlling their costs.

Some specific transformation functions are introduced in this paper to transform probability distributions commonly used for parametric modeling in survival analysis in order to make the analysis more flexible and prevent possible overestimation in longer survival times. The developed distributions were used to model the survival functions for two different data sets that contain information about patients suffering from breast cancer and colorectal carcinoma. The results are compared with the standard approach using Akaike´s information criterion.

We present simple parametric methods that overcome major limitations of the literature on joint/marginal density estimation. In doing so, we do not assume any form of marginal or joint distribution. Furthermore, using our method, a multivariate density can be easily estimated if we know only one of the marginal densities. We apply our methods to financial data.

Interval estimation of the x th effective dose (ED x ), where x is a prespecified percentage, has been the focus of interest of a number of recent studies, the majority of which have considered the case in which a logistic dose-response curve is correctly assumed. In this paper, we focus our attention upon the 90% effective dose (ED 90 ) and consider the situation in which the assumption of a logistic dose-response curve is incorrect. Specifically, we consider three classes of true model: the probit, the cubic logistic and the asymmetric Aranda-Ordaz models. We investigate the robustness of four large sample parametric methods of interval construction and four methods based upon bootstrap resampling.

A method to determine the relative difference in capture efficiency between two aquatic sampling gears is presented. The principle is to perform a number of paired comparisons between two gears by conducting catching operations at the same time and place. It is argued here that the median of the efficiency ratios from the paired comparisons is an appropriate estimator of the true difference in gear efficiency, and that non-parametric methods are suitable for statistical analysis of the results. The presented method is applied, together with two parametric methods, to data from two different comparison experiments; a comparison between two research vessels and a comparison of two different longlines. Estimates of relative differences in gear efficiencies between aquatic sampling gears can be used to improve density measurements of organisms, investigate differences in gear selection properties and analyse differences in economic effectiveness of commercial fishing gears.

These procedures for forming confidence intervals are attractive because they require weaker assumptions than parametric methods. Several of the procedures exploit the relationship between hypothesis tests and confidence intervals and these require hypotheses to be found that give specified P values. Finding the appropriate hypotheses can be computationally demanding, but for some problems there are efficient search techniques. Keywords: bootstrap; Mann–Whitney test; nonparametric confidence intervals; permutation tests; randomization tests; resampling; Robbins–Monro process; Mann–Whitney test

Carryover of stimuli in sequential judgments was studied for a visual assessment task involving estimation of the percentage cover of black circles on a white image. Seven image types with different levels of cover density were arranged in a sequentially balanced design in which each image type was preceded the same number of times by all image types. In the absence of carryover, when images were preceded by images with the same cover density, the response scores were well fitted by a power function of percentage cover with a mean exponent of 0.73 over subjects. Carryover took the form of an assimilation, so that the cover estimate for a target image was generally higher when preceded by an image with higher cover, and lower when preceded by an image with lower cover. However, the magnitude of the carryover effect showed little evidence of increasing with difference in cover between successive images. Nonparametric and parametric methods for testing for carryover are presented. The need for development of psychological models to explain the proposed statistical models is discussed.

A ranking exists in electoral systems research of different electoral formulas—the mathematical functions governing the conversion of votes into legislative seats—in terms of both proportionality of seats and votes and favorability to the largest party. I reexamine this issue with new methods and new evidence, attempting to cross-validate previous rankings using a larger and more controlled data set and more precise parametric methods than have been applied previously. The results by and large confirm previous knowledge but also illuminate several important new facets obscured in previous investigations. For example, at common ranges of district magnitude (from 5 to 15 seats), it is shown that electoral formula may matter at least as much as district magnitude in shaping proportionality.

We examine bootstrap approaches to the analysis of the sensitivity of quantitative diagnostic test data. Methods exist for inference concerning the sensitivity of one or more tests for fixed levels of specificity, taking into account the variability in the sensitivity due to variability in the test values for normal subjects. However, parametric methods do not adequately account for error, particularly when the data are non-normally distributed, and non-parametric methods have low power. We implement bootstrap methods for confidence limits for the sensitivity of a test for a fixed specificity and demonstrate that under certain circumstances the bootstrap method gives more accurate confidence intervals than do other methods, while it performs at least as well as other methods in many standard situations.

A number of recent studies have looked at the coverage probabilities of various common parametric methods of interval estimation of the median effective dose (ED 50 ) for a logistic dose-response curve. There has been comparatively little work done on more extreme effective doses. In this paper, the interval estimation of the 90% effective dose (ED 90 ) will be of principal interest. We provide a comparison of four parametric methods of interval construction with four methods based on bootstrap resampling.

This paper proposes an alternative bootstrap method for constructing prediction intervals for an ARMA process, when its innovations are represented by a linear GARCH model. The potential of this bootstrap method is assessed through a study which compares the proposed technique with a standard one.

Two statistical methods are described and discussed for preparing data from continuous toxicity studies with standard experimental design to be analyzed statistically by parametric methods. Both methods are intended to bring consistency to thepreclinical area of drug development by standardizing thestatistical methods used to assess the results. The first method is a Box-Cox transformation method in which responses are transformed to achieve homoscedasticity; the second method is a power-of-the-mean modeling of the variance. The two methods are comparable regarding homoscedasticity and homogeneity across studies. However, they have different advantages and drawbacks. The most important advantage of the power-of-the-mean model compared with the Box-Cox transformation is that results from theanalyses areon thesamescaleas theoriginal measurements. Hence, the comparability of results from different studies is facilitated. Empirical analyses have been performed for different studies and responses to compare an...