bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bayesian Statistics
Authors: Phillips Lawrence D. 
Published: September 2005

Abstract
Bayesian statistics is based on the interpretation of a probability as a degree of belief held by an individual about some hypothesis, event, or uncertain quantity. These ‘prior’ degrees of belief are revised in light of new information by the application of Bayes's theorem, a simple consequence of the addition and multiplication laws of probability, thereby resulting in a ‘posterior’ probability distribution. Bayesian statistical inferences are based on this posterior distribution, usually in the form of probability statements about the hypotheses, events, or uncertain quantities of interest, sometimes giving different inferences from classical statistical methods even though they are both based on the same data.
Binomial Effect Size Display
Authors: Rosenthal Robert 
Published: September 2005

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%.
Biplot
Authors: Gower John 
Published: September 2005

Abstract
Biplots give graphical displays of approximations to the values of two‐way arrays. Variants allow for multivariate data matrices, two‐way tables, correlation, covariance, and (dis)similarity matrices and for quantitative, nominal, and ordered categorical variables. Plotting devices include points to represent cases or samples, calibrated axes, possibly curvilinear, to represent quantitative variables, and convex regions to represent categorical variables.
Block Random Assignment
Authors: Berger Vance W. 
Published: September 2005

Abstract
The validity of the comparison between any two treatment groups is predicated on the comparability of these two treatment groups in all relevant respects other than the treatments under study. Without this condition, any observed differences in the outcomes across the treatment groups can be attributed to either the treatments or the underlying differences having nothing to do with the treatments. To definitively attribute observed differences to the treatments themselves (the intended conclusion), all competing potential attributions must be falsified. Randomization is used to create comparable comparison groups, but the extent to which it does so depends on the specifics of how it is implemented. If at some point during the study there exists an imbalance across treatment groups in the number of subjects allocated, and this imbalance is subsequently corrected, then time effects are confounded with treatment effects, and the comparison groups may not be comparable. To ensure that this chronological bias does not occur, block randomized assignment may be used. This ensures that at no point in time will the imbalance ever become larger than some specified threshold. One drawback to block randomized assignment is that it can lead to predictable allocations. If the allocation sequence is predictable, then selection bias could interfere with the comparability of the comparison groups. The trade‐off between chronological bias and selection bias has implications for the selection of the block size, or the use of alternative procedures.
Bradley–Terry Model
Authors: Marden John I. 
Published: September 2005

AbstractIn a paired comparison experiment, several judges compare several objects. Each judge performs a number of paired comparisons, that is, considers a pair of the objects, and indicates which of the two is preferred. The Bradley–Terry model is a simple but powerful model in which each object is equipped with a measure of overall strength, and the chance that one object is preferred to another depends on only their relative strengths. The model is useful not only for preference data but also for competitions, for example, among sports teams.
Canonical Correlation Analysis
Authors: Thompson Bruce 
Published: September 2005

Abstract
Canonical correlation analysis is a statistical method employed to investigate relationships among two or more variable sets, each consisting of at least two variables. Canonical correlation analysis is the multivariate form of the general linear model, which presumes that all analyses are correlational, derive estimates by applying weights to measured variables, and yield variance‐accounted‐for effect sizes. As is the case throughout the GLM, noteworthy functions must be interpreted by consulting both standardized weights and structure coefficients in concert with each other.
Case Studies
Authors: Onghena Patrick 
Published: September 2005

Abstract
A case study is an intensive and rigorous empirical investigation of a contemporary phenomenon, usually referring to a single individual, within its real‐life context. Valid inferences from case studies are possible by connecting closely to theory, collecting systematic and objective data, using continuous assessment or observations during an extended period of time, looking at multiple cases to test tentative hypotheses, and applying formal data‐analytic techniques. Case studies may involve unique, critical, or revelatory cases, and may differ on several dimensions: from more quantitative to more qualitative, more or less descriptive, exploratory, or explanatory, involving one or multiple cases, and involving no or multiple subunits of analysis. Some common pitfalls in conducting case study research are described and references to good examples are given.
Case–Control Studies
Authors: Berger Vance W. , Zhang Jialu 
Published: September 2005

Abstract
A case–control study is an observational study that is generally retrospective in nature. In case–control studies, investigators sample subjects with and without some trait (possibly a disease), and then look back in time to assess the antecedent risk factors. In the case–control study, the margin of disease is fixed. This means that we cannot directly calculate the relative risk. However, when the prevalence of the disease is low, the relative risk can be approximated by the odds ratio, which can always be computed regardless of whether the study is retrospective or prospective.
Catastrophe Theory
Authors: Wagenmakers E.‐J. , van der Maas H. L. J. , Molenaar P. C. M. 
Published: September 2005

Abstract

Catastrophe theory describes how small, continuous changes in control parameters (i.e., independent variables that influence the state of a system) can have sudden, discontinuous effects on dependent variables. Such discontinuous, jumplike changes are called
phase‐transitions
or
catastrophes
. Examples include the sudden collapse of a bridge under slowly mounting pressure, and the freezing of water when temperature is gradually decreased. This entry expands on the ideas inherent in catastrophe models.
Categorizing Data
Authors: Durkalski Valerie , Berger Vance W. 
Published: September 2005

AbstractIn epidemiology and clinical studies, it is common to categorize continuous outcomes and/or prognostic variables with the goal of simplifying both the interpretation of results and the statistical methods. However, the implications of categorization and the trade‐off between statistical power and simplicity should be understood before taking on this approach, because information, and hence power, can be lost in the process.
Analysis of Variance: Cell Means Approach
Authors: Kirk Roger E. , Bekele B. Nebiyou 
Published: September 2005

Abstract
The two forms of the cell means model are described: the unrestricted model and the restricted model. Computational procedures are presented for a completely randomized design, randomized block design, and completely randomized factorial design. Computational procedures also are presented for a completely randomized analysis of covariance (ANCOVA) design. The relative merits of the cell means model and the classical analysis of variance (ANOVA) model approaches to analysis of variance are discussed.
Censored Observations
Authors: Berger Vance W. 
Published: September 2005

AbstractObservations are referred to ascensoredwhen the variable of interest is not completely observed but some information on the value is available. For example, in oncology clinical trials, one is interested in patients' survival time, measured as the time from entry (or randomization) until death. But owing to budget and other practical constraints, trials cannot be run until all patients have experienced the event (be it death or some other endpoint). The ‘time to death’ is not observed for any patient who is still alive at the end of the trial, but it would not be accurate to state that no information is available. It is known that their time to death is at least as long as the time from enrollment until the end of the observation period of the trial. We call the observation censored or, more precisely, right censored. Observations can also be left censored, for example when an assay has a detection limit. It is also possible for an observation to be interval censored, such as when repeated screening for breast cancer reveals that cancer developed between two consecutive screenings. Special methods of analysis are required for censored data, to account for what is known and what is not known.
Centering in Linear Multilevel Models
Authors: de Leeuw Jan 
Published: September 2005

Abstract
This entry considers the effects of centering the predictors in a multilevel regression analysis. It is shown that grand mean centering of first‐level predictors does not change the model or the fit, and merely leads to a different parametrization. Within‐group centering of first‐level predictors does lead to an essentially different model, and not to a simple reexpression of the same model.
Central Limit Theory
Authors: Miles Jeremy 
Published: September 2005

Abstract
The central limit theorem underlies a wide range of statistical tests – it is one of the most important theorems in statistics. It states that the sampling distribution of the mean will approach normal, as the sample size increases, whatever the shape of the distribution in the population. It is easy to demonstrate by considering the distribution of dice rolls. There are occasions when the central limit theorem does not apply, for example, when the distribution of the measurement is made up of a mixture of distributions.
Children of Twins Design
Authors: D'Onofrio Brian M. 
Published: September 2005

AbstractBecause parents provide the environmental context for the family and transmit genetic makeup to their offspring, the genetic and environmental processes responsible for associations between family risk factors and offspring adjustment are confounded. Social scientists typically use statistical controls to account for ‘third’ variables that influence both characteristics, but family studies cannot account for unmeasured genetic or environmental confounds. The Children of Twins (CoT) Design can separate co‐occurring genetic and environmental developmental mechanisms because the design utilizes control groups that vary in genetic and environmental risk. As a result, the design can delineate intergenerational associations into (a) environmental processes specifically related to the risk factor, (b) genetic factors that influence the risk factor and offspring characteristic, and (c) common environmental factors that vary between families. The CoT approach offers advantages over traditional family studies that assume genetic factors are not important; rather, the genetically informed design explores the manner in which genetic and environment processes act to influence offspring adjustment.
Chi‐Square Decomposition
Authors: Rindskopf David 
Published: September 2005

Abstract
When analyzing a contingency table, the most frequently used procedure is to test the association between variables using a chi‐square test of independence. If the variables are not independent, no further testing is typically done. However, the chi‐square can be decomposed, or partitioned, into components to test hypotheses concerning the nature of the differences among categories of the variables. One can determine which categories of one variable are (and are not) the same in their relation to the other variable.
C
holesky Decomposition
Authors: Cherny Stacey S. 
Published: September 2005

Abstract
The Cholesky decomposition is probably the most commonly used model in behavior genetic analysis. Referring to it as a model, however, is somewhat misleading, since it is, in fact, primarily a method for estimating a covariance structure under the constraint that the estimated covariance matrix is positive semidefinite. The specific parameter estimates of the decomposition are of less interest than the expected covariance matrix it implies.
Classical Test Score Equating
Authors: Kolen Michael J. , Tong Ye 
Published: September 2005

AbstractTest equating procedures are statistical score adjustment procedures that are used when alternate forms of educational and psychological tests are constructed to a common set of content and statistical specifications. Alternate forms enhance the security of tests and allow for examinees to be tested more than one time with a different set of test questions. Even though efforts are made by test developers for the alternate forms to be equivalent, such forms differ somewhat in difficulty. A data collection design is necessary for conducting equating. Equating also involves application of statistical methodology. Traditional equating methods equate score distributions. In this entry, equating designs and traditional equating methods are described. Error in equating is considered. Selected practical issues are also discussed.
Clinical Psychology
Authors: Treat Teresa A. , Weersing V. Robin 
Published: September 2005

AbstractRapid advancement in the understanding and amelioration of complex clinical phenomena places heavy demands on clinical scientists for thoughtful articulation of theoretical models, methodological expertise, and statistical rigor. This article provides a descriptive and prescriptive overview of the use of statistics in clinical psychology. Five classes of research questions that clinical psychologists commonly address are described: the definition and measurement of constructs, the evaluation of group differences, the prediction of group membership, the examination of a network of constructs, and the evaluation of research questions across studies or data sets. A set of four principles that underlie the use of statistics in clinical research are described: the importance of theory to the rapid advancement of clinical science; the centrality of model specification, evaluation, and comparison to clinical research; the need for researchers to master research design and the mechanics of statistical techniques; and the limitations of null‐hypothesis statistical testing (NHST).
Clinical Trials and Intervention Studies
Authors: Lesaffre Emmanuel , Verbeke Geert 
Published: September 2005

Abstract
Intervention studies are experimental studies that evaluate the effect of an intervention on humans. There are many different types of intervention, including medical, social, psychological, and so on. In all of these cases, interventions seek to improve the condition of the individual. In an epidemiological context, an intervention study is a specific type of a cohort study. When a medical intervention is involved, one speaks of a clinical trial. Clinical trials take a prominent place in clinical research, as they are pivotal for the registration of new medical treatments.
We give a brief overview of the types of intervention studies, but special attention will be paid to clinical trials. Aspects of designing and analyzing an intervention study will be presented.
Cluster Analysis: Overview
Authors: Manton Kenneth G. , Lowrimore Gene , Yashin Anatoli , Kovtun Mikhail 
Published: September 2005

AbstractThis article discusses analysis techniques for clustering objects into hopefully meaningful sets. Hierarchical methods are presented for clustering both variables and cases. Examples are presented for variations on the methods. A nonhierarchical method, k‐means, is discussed for continuous data. Finally, an example comparing the results of k‐means clustering to an ad hoc method using principal components analysis is given.
Hierarchical Clustering
Authors: Leese Morven 
Published: September 2005

AbstractHierarchical cluster analysis is contrasted with optimization methods. Different ways of defining similarity or distance between cases and between clusters are given. The hierarchical clustering process is illustrated using single linkage and average linkage on a small data set, and a number of other standard agglomerative and divisive techniques are listed. The role of the dendrogram in illustrating the clustering process and the cophenetic correlation is described, as are methods for the interpretation of clusters and for deciding on the number of clusters. Some potential problems of standard methods are highlighted and model‐based methods are mentioned as an alternative approach.
k

‐means Analysis
Authors: Wishart David 
Published: September 2005

Abstract

Optimization methods for cluster analysis are described, in particular,
k
‐means analysis. It is shown that the original naïve
k
‐means algorithm will not always converge, whereas an exact assignment test for
k
‐means analysis converges to an optimal solution for the Euclidean sum of squares in finite time. A general optimization method is defined for use with any criterion function, for example, an information content statistic or sum of squared distances. The general optimization method also converges provided that the selected criterion function has a theoretical lower bound. The use of random trials to search for the global optimal solution is developed, and the reproducibility of different
k
‐means solutions is discussed. Outlier deletion in
k
‐means analysis helps to tighten a descriptive classification, and a dendrogram for
k
‐means analysis is developed to illustrate the data structure.
C
ochran's
C
Test
Authors: Mair Patrick , von Eye Alexander 
Published: September 2005

Abstract
Cochran's C test is used to test the assumption of variance homogeneity of the residuals in the analysis of variance. The test statistic is a ratio that relates the largest empirical variance of a particular treatment to the sum of the variances of the remaining treatments. The theoretical distribution with the corresponding critical values can be specified.
Coefficient of Variation
Authors: Lovie Pat 
Published: September 2005

Abstract
The coefficient of variation is a measure of dispersion of data relative to the mean. It is defined as the standard deviation divided by the mean. Since the coefficient of variation is independent of the units of measurement and of the magnitude of the data, it is useful for comparing the variability of two or more samples of data from different variables or from the same variables when the means are very different.
Item Response Theory (
IRT
): Cognitive Models
Authors: Hendrickson Amy B. , Mislevy Robert J. 
Published: September 2005

Abstract
Advances in cognitively based assessments have increased the need for inferences that can address complex task performance and instructionally useful information. These assessments integrate empirically based models of student learning and cognition with methods for designing tasks and observing student performance, with procedures for interpreting the meaning of those observations. Several psychometric models have been introduced to handle claims cast in such information‐processing terms, explicitly modeling performance in terms of theory‐based predictions of performance. Cognitively based item response theory (IRT) models incorporate features of items that influence persons' responses, and relate these features to response probabilities. Examples of IRT models that incorporate cognitively motivated structures are presented, including the Linear Logistic Test Model, multidimensional cognitive IRT models, and latent class models.
Cohort Sequential Design
Authors: Prinzie Peter , Onghena Patrick 
Published: September 2005

Abstract
Cohort‐sequential designs or accelerated longitudinal designs are designs in which adjacent segments consisting of limited longitudinal data on a specific age cohort can be linked together with similar segments from other temporally related age cohorts to determine the existence of a common developmental trend. These designs enable researchers to study individual development over a long interval of the life course by limited repeated measurements of independent age cohorts, resulting in temporally overlapping measurements of the various age groups. Such designs create possibilities not available in standard longitudinal designs for separating age effects from cohort and period effects.
Cohort Studies
Authors: Prentice Ross L. 
Published: September 2005

AbstractCohort studies are fundamental to epidemiologic research, whether in behavioral or biologic areas. The role of cohort studies relative to case‐control studies and intervention trials is briefly described. Some important issues for, and approaches to, cohort study data collection and analysis are outlined. A cohort study and a companion intervention trial among postmenopausal women in the United States provides illustration.
Combinatorics for Categorical Variables
Authors: Indurkhya Alka 
Published: September 2005

Abstract
This chapter provides an overview of categorical variables and rudimentary combinatorics. Datasets gathered in the behavioral, social, and biomedical sciences using survey instruments tend to consist of categorical responses. A categorical variable is defined as a variable that has two or more mutually exclusive groups (or categories) that may or may not have an intrinsic order. There are two types of categorical variables, namely, nominal and ordinal. The distribution of a categorical variable in a population is described using counts (or percentage). Counting rules are defined and illustrated to compute the total possible counts under different scenarios. The empirical binomial distribution is derived using counting rules.
Common Pathway Model
Authors: Rijsdijk Frühling 
Published: September 2005

Abstract

While traditional multivariate statistical methods can describe correlational patterns of a set of variables (e.g., psychiatric symptoms or problem behaviors in children), they cannot provide insight into why certain symptoms or behaviors tend to co‐occur in a population. This can be achieved using methods of
multivariate genetic analysis
. In multivariate genetic models, two main classes can be distinguished, which differ in the way the common factors are assumed to influence the different observed variables. The way unique factors influence the observed variables is the same in both classes. The first class of models is referred to as common pathway or psychometric models. Common genetic and environmental factors influence all observed variables via a single psychometric factor, or underlying latent liability. This factor is identical to the factor derived from higher order phenotypic factor analyses, with the difference that twin data allows estimation of the relative importance of genetic and environmental effects of this factor. The second class of models is referred to as
independent pathway models
or biometric models, where the common genetic and environmental factors influence the observed variables directly, without an intermediate higher order factor. As a result, the common genetic and environmental factors do not necessarily cause similar groupings of variables.