bluuebunny/crossref_metadata_2025_split huggingface dataset:
L
indley's Paradox
Authors: Shafer Glenn 
Published: September 2014

Abstract

A test of significance can disagree strongly with a Bayesian analysis when the Bayesian analysis assigns a substantial probability to the point hypothesis and distributes the remaining probability diffusely. The disagreement is sometimes called
Lindley's paradox
. If the diffuse distribution under the alternative hypothesis is based on evidence, the Bayesian analysis is convincing, but if the distribution is diffuse only because of ignorance, the test of significance may be more convincing.
Loss Function
Authors: Tritchler D. 
Published: September 2014

Abstract

In decision theory, the loss function expresses the consequences of a specific decision when a particular state of nature holds. Negative loss is called
gain or utility
. The aim in Bayesian theory is to minimize the expected loss, integrating over the prior distribution. In frequentist theory, various restrictive conditions may be imposed, or a minimax solution may be sought. Statistical procedures such as hypothesis testing and estimation may be interpreted in terms of loss functions. Practical applications include the design of clinical trials and screening procedures.
Minimum Variance Unbiased (
MVU
) Estimator
Authors: Bethel J. 
Published: September 2014

Abstract
Determining the minimum variance of an unbiased estimator constitutes a fundamental topic in mathematical statistics. Two primary results are the Cramér–Rao inequality, which gives a lower bound on the variance of an unbiased estimator, and the Rao–Blackwell theorem, which supplies a method for improving the variance of unbiased estimators that are not functions of sufficient statistics. The strongest results are available for sufficient statistics from complete exponential families. However, any functions of sufficient statistics will attain the Cramér–Rao lower bound for sufficiently large sample sizes.
Paired

t

Test
Authors: Hsu Henry , Lachenbruch Peter A. 
Published: September 2014

Abstract

This is used to compare mean differences between treatments when the observations have been obtained in pairs. The difference between the paired values is assumed to be normally distributed, and the null hypothesis that the expectation is zero is tested by Student's
t
test. The robustness properties are discussed, as is the asymptotic relative efficiency of nonparametric alternatives.
Pitman Efficiency
Authors: Zacks S. 
Published: September 2014

Abstract
The Pitman efficiency is an index for comparing test procedures or estimators. It is especially important for comparing procedures in large samples. If procedure P1 requires n1 observations to attain a certain power of a test, or a specified mean squared error, and procedure P2 requires n2 observations to achieve the same precision, the Pitman relative efficiency of P1 against P2 is n2/n1. Accordingly, if the mean squared error of an estimator E1 is v1/n + o(1/n), and if that of another estimator, E2, is v2/n + o(1/n), then the asymptotic (large sample) relative efficiency of E1 against E2 is v2/v1. Under smoothness regularity conditions, the variance of an unbiased estimator, in the one‐parameter case, is bounded below by the Cramer–Rao (CR) lower bound. Accordingly, the ratio of the CR‐lower bound to the variance of the estimator is defined as the efficiency index of the unbiased estimator. This is the Pitman relative efficiency of the estimator against the best possible one. Moreover, the CR‐lower bound contains the Fisher information function as a factor, and the inverse of the Fisher information function is the asymptotic variance of the maximum likelihood estimator (bf MLE). Therefore, the efficiency of an unbiased estimator is measured relative to the asymptotic variance of the maximum likelihood estimator.

The Pitman relative efficiency of consistent and asymptotically normal test statistics is defined as the ratio of their corresponding
efficacy ratios
. The asymptotic efficacy relates the rate of change of the mean function of the statistic to its asymptotic standard deviation. For further information, see the article.
Simultaneous Confidence Intervals
Authors: Chen Tuhao , Hoppe Fred M. 
Published: September 2014

AbstractThese provide a confidence region for a multivariate parameter, comprising individual intervals for the separate components of the parameter. There is a specified confidence level of the simultaneous correctness of all the statements. The approach is useful for multiple comparisons of treatment means. The methods of Bonferroni, Tukey, Scheffé and Duncan are described, with examples.
Statistical Dependence and Independence
Authors: Wermuth Nanny , Cox D. R. 
Published: September 2014

AbstractStatistical dependence is a type of relation between different characteristics measured on the same units. At one extreme is deterministic dependence; at the other is statistical independence, where the distribution of one variable is the same for all levels of the other. With more than two variables, an important distinction is between marginal and conditional dependence. In many contexts, the degree of dependence may be summarized by a suitable measure of association, perhaps as part of a general model. Reference is made to graphical models.
Randomized complete blocks designs
Authors: Murray L. 
Published: September 2014

AbstractThis article discusses the general need for blocking when experimental units are not homogeneous. Complete, generalized, and incomplete block designs are discussed, together with issues of randomization, missing cells, and the usual assumption of “no interaction”. Two specific cases of the Randomized Complete Block Design are considered: the fixed case (treatments and blocks are both fixed) and the mixed case (treatments are fixed, blocks are random). For each case, the scalar linear models are defined in full‐rank and non‐full‐rank versions, together with necessary assumptions. Point estimates and standard errors are given for main‐effect means and cell means, and for variance components. The analysis of variance table is given, with expected mean squares, for testing hypotheses.
Grouped Survival Times
Authors: Zhang Mei‐Jie 
Published: September 2014

AbstractThe grouped survival data consists of occurrence and exposure data over given time intervals and possible covariate strata. Grouping data from such large sample sizes into tabular presentations (life tables) often provides a convenient format for presenting and summarizing life information. Grouped survival data can involve censored data (right censoring, left censoring, or double censoring) and/or truncated data. Moreover, the exact censoring or truncation times may be unknown for grouped data. In this article, we provide the literature on analyzing grouped survival data, and discuss the estimating procedure for the hazard function and survival function under nonparametric or parametric models, test statistics for comparing the survival probabilities among different population groups, and large sample properties for these estimators and test statistics.
Influence Function in Survival Analysis
Authors: Reid N. 
Published: September 2014

AbstractThe influence function of a statistic is a type of derivative that indicates how perturbations in the data affect the statistic. If the influence function is bounded, then the effect of outliers on the statistic is limited. Influence functions can be used in deriving the limiting distribution of a statistic, and can also be used to develop diagnostics for regression models. This latter application has been useful in proportional hazards regression.
Joint modelling of longitudinal and event time data
Authors: Henderson Robin 
Published: September 2014

Abstract
The relationship between the development over time of a quantitative response variable and a parallel process recording events in time can be investigated through a joint model for the two outcome types. Interest in this topic arose from two separate backgrounds: the possibility and consequences of informative dropout in longitudinal trials, and measurement error problems for survival studies with time‐varying covariates. Modeling strategies include combining a marginal distribution for one response type with a conditional distribution for the other, or adopting a correlated random effects model with otherwise conditional independence. Naive methods can lead to significant bias, yet more sophisticated modeling approaches are often sensitive to assumptions, some of which cannot be checked from observable data. When simple summaries such as treatment effect estimators are of interest, sensitivity analyses can bring some reassurance as to whether important conclusions are maintained as assumptions are allowed to change. Overall, the topic is relatively new and research is continuing in many directions.
Measurement Error in Survival Analysis
Authors: Prentice Ross L. 
Published: September 2014

AbstractThis entry describes various approaches to estimating the regression coefficient in the Cox failure time regression model when some of the regression variables are poorly measured. Regression parameter estimation may be considered if there is a validation subsample within which the “true” regression variable is available, or if there is a reliability subsample within which multiple estimates of the regression variable having independent measurement errors are available. The former context is closely connected to corresponding missing data estimation problems. Simplead hocestimators are reviewed, along with effective but inconsistent regression calibration estimators, and more complex nonparametric maximum likelihood and augmented inverse probability weighted estimators. With only a reliability sample available, estimation procedures include regression calibration and an extended risk set regression calibration approach, along with corrected score estimation procedures. Some comments on procedures for measurement error accommodation in an additive hazards model are also provided. This rapidly developing measurement error research area has implications for the analysis of follow‐up studies in a number of important application areas.
Smoothing Hazard Rates
Authors: Wang Jane‐Ling 
Published: September 2014

AbstractThe nonparametric approach to estimate hazard rates for lifetime data is flexible, model‐free, and data‐driven. No shape assumption is imposed other than that the hazard function is a smooth function. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. We describe methods for grouped lifetime data observed at certain time intervals and for continuously observed lifetime data. There are some intrinsic differences between the smoothing approaches for these two types of data. More specifically, smoothing an initial hazard estimate based on the life table is adopted for grouped lifetime data; while for continuous data, smoothing is employed to increments of the Nelson–Aalen cumulative hazard estimate aiming at the derivative of the cumulative hazard function. A few nonparametric hazard regression methods are also discussed.
Truncated Survival Times
Authors: Gruttola Victor , Liao Q. 
Published: September 2014

AbstractTruncation of survival data arises when observation can only occur if the failure time (survival time) lies within a certain interval (l,r) wherelorrmay be infinite. When the failure time is outside the truncation interval, no information about the subject is available, so the subject is “sampled from a conditional distribution”. This feature distinguishes truncation from censoring. Left truncation (delayed entry) is relatively easily handled by minor modification of hazard‐based survival analysis methods. Right truncation has been extensively studied in connection with latency times from HIV infection to onset of clinical AIDS.
Standardization Methods
Authors: Inskip Hazel 
Published: September 2014

Abstract
Standardization methods are used to adjust for the effects of age and sex, and possibly other factors, in the comparison of mortality or disease rates between two or more populations. Such methods have a long history, particularly for the comparison of mortality rates. The two methods that are most widely used are known as direct and indirect standardization and the mortality ratios that are derived from these are known respectively as the Comparative Mortality Figure and the Standardized Mortality Ratio. When the populations at risk are hard to define, methods involving the proportions of deaths from specific causes can be used. More recently, different approaches involving modeling have been developed to adjust rates for the effects of age and other confounding factors.
Age–Period–Cohort Analysis
Authors: Holford Theodore R. 
Published: September 2014

Abstract
Age–period–cohort analysis refers to the interpretation of temporal trends in disease incidence or mortality rates in terms of the three time scales, age, calendar date (period), and year of birth (cohort). We present graphical and analytic methods for understanding trends in disease rates. A fundamental issue of identifiability arises in some models because of a linear constraint on these time scales: year of birth plus age equals the current calendar year. We review parametric and nonparametric approaches to estimate identifiable aspects of the data, such as the curvature of temporal trends.
Subjective Probability and Human Judgement
Authors: Ayton Peter 
Published: September 2014

AbstractPsychological research on Subjective Probability has used a variety of strategies to investigate how reliable people are at judging probabilities. The issue is of considerable practical importance as all sorts of critical decisions depend on assessment of the likelihood of events for which there is neither a method for mathematically computing its probability nor actuarial data for measuring it empirically. Since the development of Decision theory, a plethora of management technologies have emerged that can take advantage of likelihood information for decision support. While the concept of subjective probability remains a theoretically contentious notion for some, people can and do express and request judgments of the likelihood of uncertain events. Here, research investigating the validity of subjective probabilities – judged likelihood – is reviewed.
Configural Frequency Analysis
Authors: Eye Alexander 
Published: September 2014

AbstractConfigural Frequency Analysis (CFA) is a method for the analysis of cross‐classifications of categorical variables. Using CFA, one examines individual cells or groups of cells of cross‐classifications with the goal of determining whether they contain more or fewer cases than expected based on some chance model. The specification of the chance model determines the interpretation of results. Depending on chance model, cells with more or fewer cases than expected can be interpreted as indicative of local associations, but also of predictor‐criterion relationships; they allow one to distinguish between groups, or they reflect typical and atypical patterns of change over time.
Multigraph Modeling
Authors: Khamis Harry J. 
Published: September 2014

Abstract
Multigraph modeling makes use of mathematical graph theory to analyze and interpret hierarchical loglinear models. For a given such model, a multigraph is constructed, and from the multigraph, decomposability is determined from a simple combinatorial identity; factorization of the joint distribution is based on a maximum spanning tree; and the conditional independence interpretation comes from the edge cutsets.
Simulation Methods for Categorical Variables
Authors: Weber Stefan , Eye Alexander 
Published: September 2014

Abstract
The results of a simulation study on the performance of measures for the analysis of 2 × 2 tables are reported. The simulations included 11 measures for 2 × 2 tables: Pearson's?, the standard normal z, the log‐odds ratio, the log‐linear interaction, Goodman's (1991) weighted log‐linear interaction, Vogel's z, the binomial test, Lehmacher's (1981) asymptotic hypergeometric test, Perli, Hommel, and Lehmacher's (1985) asymptotic test, Lindner's (1984) exact hypergeometric test, and Lausch and von Weber's (2002) adaptation of Dunkl and von Eye's (1990) test. The factors varied in the simulations were (1) type of sampling distribution, (2) sample size, (3) strength of association in the 2 × 2 table, (4) the symmetry of the distribution in the 2 × 2 table, and (5) the nominal a. Results suggest that the distribution of these 11 tests is very near the normal under all conditions. Of the five factors, only the type of the sampling distribution has no strong effects on the ß‐curves of the 11 measures. Finally, it was found that the 11 measures respond differently to the five factors such that the rank order of performance varies with the simulated conditions.
Optimization Methods
Authors: Lewis Robert Michael , Trosset Michael W. 
Published: September 2014

Abstract
Optimization is concerned with identifying the best element in a set of competing possibilities. Except in special circumstances, one must use numerical methods to search for solutions iteratively. If one's problem is well‐behaved, for example, the objective to be minimized is smooth and the feasible possibilities are smoothly defined by finite numbers of equality and inequality constraints, then one can use a number of sophisticated methods to identify local solutions, that is, possibilities that are as good or better than any other nearby possibilities. However, finding global solutions is much harder.
Linear Models: Permutation Methods
Authors: Cade Brian S. 
Published: September 2014

Abstract
Permutation tests of hypotheses about parameters in linear models derive their validity from exchangeability of the errors in the null model. These errors are unobservable but differ from the observable residuals by a constant for any hypothesis that posits a null, reduced parameter model with just an intercept term. For these hypotheses, exact permutation inferences are possible for iid error distributions of any form. Other hypotheses on subsets of parameters in multiple regression models are not exact because the residuals are not exchangeable with equal probability. Several options to improve exchangeability for these hypotheses have been developed and are presented for permutation tests on quantile regression estimates of the linear model.
Balanced Incomplete Block Designs
Authors: Cotton John W. 
Published: September 2014

AbstractBalanced incomplete block designs (BIBD) are experimental designs that can be described by a labeled, fully filled rectangular array or by a larger equivalent rectangular display with some empty cells. A cell in the rectangle identifies one treatment in a given block. The number of different treatments for a given block (individual) is less than the total number of treatments; this precludes having each treatment appear once in every block. Hence, the design is anincompleteblock design. Without some constraints on the number of occurrences of certain treatments in different rows, the average performance in different parts of the design can be biased. This bias yields different averages for two treatments, for example, because of differences in the cells in which those treatments were employed. To eliminate the bias, a special form of balance is employed in which every possible pair of treatments appears in an equal number of blocks. Accordingly, there also is balance in the total number of times each treatment occurs. Analysis methods are discussed for general linear fixed, mixed, and Bayesian models. I discuss a special case of a BIBD design, Youden squares, that permits but does not require the assessment of one more independent variable than other BIBDs. In the behavioral sciences, the rows of Youden squares can be different blocks, typically different people or animals, and the columns can be different observation occasions that permit the assessment of so‐called period effects.
Single‐Case Designs
Authors: Onghena Patrick 
Published: September 2014

Abstract
A single‐case design is an experimental design for a study in which one entity is observed repeatedly during a certain period under different levels of at least one independent variable. Single‐case designs have a long tradition and growing impact in behavioral science. They are the designs of first choice if demonstration of an effect in a single case is aimed at or if a test of a theory in a single case is sufficient (or the only possibility), and they are most compatible with clinical practice. The systematic and purposive planning of interventions in single‐case research represents the main difference with both observational time series research and qualitative case study research. In addition, single‐case research can gain internal and statistical‐conclusion validity by including randomization in the design. Two types of randomized single‐case designs are presented: randomized alternation designs and randomized phase designs. Finally, external validity of single‐case results can be demonstrated or tested by simultaneous or sequential replication and the corresponding simultaneous randomization tests and meta‐analytic procedures.
Nonequivalent Group Design
Authors: Reichardt Charles S. 
Published: September 2014

Abstract
A nonequivalent group design is a quasi‐experiment used to assess the relative effects of treatments that have been assigned to groups of participants nonrandomly. Because the participants have been assigned to treatments nonrandomly, differences in the composition of the treatment groups can bias the estimates of the treatment effects. A variety of statistical methods are available for taking account of this selection bias. Each method imposes different assumptions about the nature of the selection effects, but it can be difficult to determine which set of assumptions is most appropriate in a given research setting. Researchers are advised to minimize selection differences by using groups of participants that are initially as similar as possible.
Alternating Treatment Designs
Authors: Herrera Gina Coffee , Kratochwill Thomas R. 
Published: September 2014

Abstract
The alternating treatments design (ATD) is a type of single‐participant design that is commonly used to determine the effectiveness of two or more treatments. Conditions in the ATD are alternated rapidly and randomly/semirandomly, and effects can by analyzed statistically (e.g., randomization tests) and/or by visual inspection. Using the ATD can be advantageous because treatment effects can be found rather quickly and a withdrawal phase and baseline data are not required.
Effect Size Measures
Authors: Kirk Roger E. 
Published: September 2014

AbstractA variety of measures of effect magnitude are described. Many of the measures can be classified as either measures of effect size (typically, standardized mean differences) or measures of strength of association. There also is a large group of statistics that do not fit into either category. Measures of effect magnitude are used for a variety of purposes: (a) to estimate the sample size required to achieve an acceptable power, (b) to integrate the results of empirical research studies in meta‐analyses, (c) to supplement the information provided by null hypothesis significance tests, and (d) to determine whether research results are practically significant.
Binomial Effect Size Display
Authors: Rosenthal Robert 
Published: September 2014

Abstract

The binomial effect size display (BESD) was designed to indicate the practical importance of any particular effect size estimate. The BESD displays the difference between two proportions such as the difference between the success rate of a new intervention and the success rate of the standard intervention. For example, an
r
of 0.20 is said to account for ‘only 4% of the variance’, but the BESD shows that this proportion of variance accounted for is equivalent to increasing the success rate (e.g., survival rate, improvement rate, etc.) from 40 to 60%.