bluuebunny/crossref_metadata_2025 huggingface dataset:
Children of Twins Design
Authors: D'Onofrio Brian M.
Published: September 2005

Because 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

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

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

Test 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.
Analysis of Variance: Classification
Authors: Kirk Roger E.
Published: September 2005

The nomenclature and acronyms for analysis of variance (ANOVA) designs are described. The presentation focuses on four characteristics of the designs: layout of the designs, partition of the total sum of squares and degrees of freedom, hypotheses that can be tested, and advantages and disadvantages of the designs.
Clinical Psychology
Authors: Treat Teresa A. , Weersing V. Robin
Published: September 2005

Rapid 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

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.
Binomial Confidence Interval
Authors: Lunneborg Clifford E.
Published: September 2005

The binomial parameterp, the proportion of successes in a population, has as its point estimator the proportion of successes observed in a random sample from that population,p* = s/n. A confidence interval for the binomial parameter broadens that point estimate out, reflecting the uncertainty associated with the limited size of the sample.
Cluster Analysis: Overview
Authors: Manton Kenneth G. , Lowrimore Gene , Yashin Anatoli , Kovtun Mikhail
Published: September 2005

This 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

Hierarchical 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

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

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

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

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.
Cohen, Jacob
Authors: Cohen Patricia
Published: September 2005

Jacob Cohen's contributions to data analysis in the behavioral sciences include identifying the problem of low statistical power of much research, proposing power analysis methods and rough effect size norms to be used in planning research, development of kappa to assess chance‐corrected agreement, and promotion of multiple regression as a flexible general analytic system.
Cohort Sequential Design
Authors: Prinzie Peter , Onghena Patrick
Published: September 2005

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

Cohort 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.
Coincidences
Authors: Everitt Brian S.
Published: September 2005

This article examines what we mean by coincidence and points to the fact that coincidences do happen, and rare events do occur.
Combinatorics for Categorical Variables
Authors: Indurkhya Alka
Published: September 2005

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

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.
Community Intervention Studies
Authors: Murray David M.
Published: September 2005

Community intervention trials randomize whole communities to conditions and observe residents of those communities to assess the effects of an intervention. Community intervention trials face special problems of design and analysis that must be considered to ensure adequate power and valid results. This article provides a brief review of these issues.
Compensatory Equalization
Authors: Onghena Patrick
Published: September 2005

Compensatory equalization is a threat to the treatment construct validity in intervention studies, in which comparison groups not obtaining the preferred treatment are provided with compensations that make the comparison groups more equal than originally planned. Compensatory equalization can seriously bias the estimation of treatment effects and should be avoided whenever possible, for example, by social isolation or masking of the comparison groups. If compensatory equalization cannot be avoided, then broadening the treatment effect construct seems the most viable option.
Compensatory Rivalry
Authors: Conrad Karen M. , Conrad Kendon J.
Published: September 2005

Compensatory rivalry is a potential threat to the construct validity of the cause in intervention studies. Compensatory rivalry exists when the study group not receiving the experimental treatment (i.e., intervention) feels disadvantaged, disappointed, or left out and decides to obtain a similar intervention on its own. It may or may not involve intentional competition or rivalry with the experimental group. While we are not likely to prevent compensatory rivalry from operating, we should be aware of its possibility, measure it, and if possible, statistically adjust for it. Minimally, we would want to consider its possibility in interpreting the study findings.
Completely Randomized Design
Authors: Maxwell Scott E.
Published: September 2005

The completely randomized designCompletely Randomized Design (CRD) is the simplest type of experimental design. Three characteristics define this design: (1) each individual is randomly assigned to a single treatment condition, (2) each individual has the same probability of being assigned to any specific treatment condition, and (3) each individual is independently assigned to treatment conditions.
Computational Models
Authors: Ployhart Robert E. , Harold Crystal M.
Published: September 2005

Computational models provide a powerful methodology useful for answering many statistical and substantive questions. We address the topic from two perspectives. The first considers computational modeling as a methodology for answering substantive questions. The second considers statistical ‘Monte Carlo simulations’ as a special case of computational models.
Computer‐Based Test Designs
Authors: Zenisky April L.
Published: September 2005

Among the decisions to be made in implementing a computer‐based test, the choice of test design is one of the most important. A test design is the manner by which individual items are selected for presentation to examinees during administration. The importance of evaluating test design options is critical because it not only concerns test administration but also basic activities in the test development process and the quality and precision of scores to be obtained for a specified testing purpose. Essentially, conceptualizing the test design options for computerized testing first hinges on the property of being adaptive or not, and then there are varied approaches within each of those two groupings. The purpose of this entry is to provide an overview of selected test designs, adaptive and otherwise, while highlighting certain measurement advantages and concerns associated with each.
Software for Behavioral Genetics
Authors: Neale Michael C.
Published: September 2005

Algorithms for computing heritability and other statistics of interest to quantitative geneticists have been available for almost 100 years. In the past 20 years there has been considerable growth in software development for behavior genetic studies, which was largely motivated by a desire to obtain maximum likelihood estimates and to compare how well alternative models or hypotheses fit the data. Initially these methods were implemented in purpose‐built programs of very limited utility, which were difficult to use and to modify. LISREL overcame these problems by providing a more general modeling interface, but this was also found to be limited for the analysis of data collected from relatives. Mx was developed to reduce or eliminate these shortcomings; having a matrix algebra interpreter it permits specification of complex models for both traditional genetic epidemiology such as twin studies, as well as for linkage and association studies, and permits specification of mixture distributions and alternate model fitting methods.
Computer‐Adaptive Testing
Authors: Luecht Richard M.
Published: September 2005

This entry presents an overview of computer‐adaptive testing (CAT). The basic CAT algorithm is introduced, followed by a discussion of item response theory (IRT) test information functions and their role in adaptive testing. Issues such as test efficiency and security risks under CAT are also discussed. The entry concludes with a description of four promising CAT variants, including CAT shadow tests, a‐stratified CAT, testlet‐based CAT, and computer‐adaptive multistage testing.
Concordance Rates
Authors: van den Oord Edwin J. C. G.
Published: September 2005

In genetic studies of medical conditions, pairwise or probandwise concordance rates are often calculated to study the relative importance of genes and environment.
Confidence Intervals
Authors: Dracup Chris
Published: September 2005

In estimating a population parameter from sample data, it is more informative to provide a range of ‘plausible’ parameter values rather than a one‐point estimate. A 95% confidence interval contains those values of the population parameter that would not be rejected at the 0.05 significance level by a statistical test applied to the sample data. In the long run, such intervals should provide 95% ‘coverage,’ with 95% of them including their true population value (assuming the data meet any distribution assumptions). Topics covered include the construction of confidence intervals for means, proportions, and mean differences; the effects of discrete and nonsymmetrical sampling distributions; central and noncentral intervals; bootstrapped intervals and the Bayesian approach.
Confidence Intervals: Nonparametric
Authors: Garthwaite Paul H.
Published: September 2005

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.
Configural Frequency Analysis
Authors: von Eye Alexander
Published: September 2005

Configural 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.
Factor Analysis: Confirmatory
Authors: Byrne Barbara M.
Published: September 2005

The intent of this article is to present an introductory overview of the basic concepts and testing procedures associated with confirmatory factor analysis (CFA). Working from a hypothesized four‐factor structure of a nonacademic self‐concept (SC), as measured by 32 items from the Self Description Questionnaire, readers are introduced to both a graphical and a structural equation specification of this CFA model, followed by a review of the related procedures involved in its testing, estimation, and evaluation, together with the interpretation of results. Important issues and caveats associated with the testing of CFA models are also briefly addressed.
Confounding in the Analysis of Variance
Authors: Bogartz Richard S.
Published: September 2005

Unintentional and intentional confounding in the analysis of variance is discussed. Some different kinds of unintentional confounding that can occur in between‐subject designs, within‐subject designs, and mixed designs are considered. The usefulness of losing information to conserve resources by intentionally confounding variables gives rise to split‐plot, confounded factorial, and fractional replication designs. An example from infancy research is provided.
Confounding Variable
Authors: Onghena Patrick , van den Noortgate Wim
Published: September 2005

A confounding variable is a variable that is related to an explanatory variable and at the same time has an effect on a response variable that is entangled with a possible effect of the explanatory variable, possibly leading to wrong conclusions about the latter. Confounding may also occur in situations involving more than one explanatory or response variable, and more than one confounding variable may be present. Observational studies, quasi‐experiments, as well as randomized experiments might be affected by confounding. If confounding variables cannot be avoided or ruled out by design, a final option is to model them as covariates.
Contingency Tables
Authors: Everitt Brian S.
Published: September 2005

Contingency table arise from cross‐classifying a sample of observation with respect to a number of categorical variables. Each cell of such a table contains a count of the observation falling in the cell. In the most common type of contingency table arising from two categorical variables, interest generally centers on whether the two variables are independent. The relevant test statistic has, for large sample size, a chi‐squared distribution. Tables involving more than two variables are usually analyzed with log‐linear models.
Nuisance Variables
Authors: Mitchell Dayton C.
Published: September 2005

Extraneous variation in a dependent variable can be controlled using selection, stratification, and/or statistical adjustment. In experimental studies, control is used to increase statistical power, whereas in nonexperimental studies, control is used in an effort to reduce confounding effects of preexisting differences among groups.
Correlation and Covariance Matrices
Authors: Macdonald Ranald R.
Published: September 2005

A covariance matrix measures the shared variability within a set of variables assuming that all the relationships between them are linear. The correlation matrix is the covariance matrix of a set of variables after they have been standardized. Standardization means that the measures of association are scale independent.
Correlation Issues in Genetics Research
Authors: Cherny Stacey S.
Published: September 2005

Correlation is of central importance in behavioral genetic research. A basic goal of behavioral genetic research is to partition variance in a trait into variance due to genetic differences among people (commonly referred to as
heritability
(or
h
2
), variance because of environmental influences shared among family members (shared environmental variance, or
c
2
), and nonshared environmental variance as a result of unique individual experiences (
e
2
) (
see
ACE Model
). This is accomplished by analyzing correlational structure within different familial relationships. Although in practice we perform
maximum‐likelihood
model‐fitting analyses on raw data and partition (unstandardized) covariance structure, examining familial correlations directly is the best way of quickly getting an idea of what is going on in the data.
Correspondence Analysis
Authors: Greenacre Michael
Published: September 2005

Correspondence analysis is a method of multivariate analysis applicable to categorical data. In its simple form it is used to visualize the relationship between two categorical variables, but can be extended to multiple correspondence analysis to visualize the relationship among several variables. These methods are explained from a correlational and geometric viewpoint and are illustrated by cross‐national survey data on sexual attitudes.
Co‐twin Control Methods
Authors: Goldberg Jack , Fischer Mary
Published: September 2005

The co‐twin control method is an elegant research design that uses differences within twin pairs to examine the association between a putative environmental risk factor and an outcome variable. The design is extremely efficient for examining risk factor–outcome associations compared to unmatched designs. This is especially true when using monozygotic (MZ) twins who share 100% of their genetic material. Co‐twin control studies can be used in both the experimental and observational settings. Statistical analysis for continuously distributed outcome variables focuses on the within‐pair mean difference, while for dichotomous outcomes, the matched pair odds ratio is used. Whenever possible, it is informative to examine differences in the relationship between the risk factor–outcome association by zygosity; findings that are only present in dizygotic (DZ) pairs suggest that the observed association may be due to genetic influence on both the risk factor and outcome. We present an illustration of the analysis of a co‐twin control study, looking at the association between military service in Vietnam and posttraumatic stress disorder, with data from the Vietnam Era Twin Registry. A wide range of new regression modeling methods, which account for nonindependent observations, can be readily adapted for co‐twin control studies.
Counternull Value of an Effect Size
Authors: Rosenthal Robert
Published: September 2005

The counternull value of an effect size is the nonnull magnitude of effect size that is supported by exactly the same amount of evidence as supports the null value of the effect size. That is, if the counternull value were taken as the null hypothesis, the resulting
P
value would be the same as the obtained
P
value for the actual null hypothesis. Reporting the counternull, in addition to the
P
value, virtually eliminates the common error of equating failure to reject the null with the estimation of the effect size as equal to zero.
Counterbalancing
Authors: DePuy Venita , Berger Vance W.
Published: September 2005

When subjects are consecutively given more than one treatment in an experiment, including for crossover design, earlier treatments may affect the results observed during later treatments. To counteract this, the treatment order may be varied between different subjects, or counterbalanced. While complete counterbalancing often requires large numbers of participants, partial counterbalancing, often through the use of a Latin squares design, can provide a reasonable alternative.
Counterfactual Reasoning
Authors: Holland Paul W.
Published: September 2005

Counterfactual conditional statements underlie definitions of causation. The substitution of factual, observed data in control groups for counterfactual information about treatment groups is the basis of causal inference in randomized experiments and observational studies. Formal models that give causal interpretations to statistical calculations and that involve counterfactual quantities were introduced as early as 1923.
Covariance
Authors: Kornbrot Diana
Published: September 2005

Covariance is a descriptive measure of the extent to which two variables vary together. It depends on the unit of measurement of both variables. The covariance may be positive, where both variables go up together; or negative where one goes down as the other goes up. Covariance does not imply causality.
Analysis of Covariance: Nonparametric
Authors: Berger Vance W.
Published: September 2005

There are numerous benefits in adjusting an analysis for one or several covariates, but often these benefits come at the price of having to make additional assumptions, such as distributional assumptions or assumptions regarding the relationship between a covariate and a response variable. For example, the validity of the popular analysis of covariance model is predicated on a variety of assumptions. Clearly, the need to make assumptions, or to restrict the results so that they apply only when these assumptions are true, is a weakness, and it would be preferable to reap the benefits of covariate adjustment without having to rely on unreasonable assumptions. There is a body of nonparametric covariate adjustment techniques that aim to allow for this. Specific techniques depend on the nature of the covariate (e.g., binary or continuous).
Covariance Structure Models
Authors: Thum Y. M.
Published: September 2005

As originally formulated by Bock and by Bock and Bargmann, covariance structure analysis is a statistical method for the structural analysis of the sample variance–covariance matrix of respondent scores on a test battery aimed at validating the constructs making up the battery. A generalization of the mixed‐effects model, we examine some of its applications beyond tests and testing. We provide revised results for the data analyzed by Wiley, Schmidt, and Bramble. We note its formal equivalence with a confirmatory factor analysis with known factor loading and note some of its connections to other statistical models for multivariate outcomes.
Covariance/Variance/Correlation
Authors: Rodgers Joseph Lee
Published: September 2005

In this entry, I describe the covariance, variance, and correlation, each in a common framework that allows their interrelationships to be apparent. Specifically, the covariance is the uniting concept, within which the variance and correlation are special cases. Following separate treatments, I present a formula that explicitly shows the relationships between the three indices. Finally, I briefly describe the role of each in Structural Equations Modeling (SEM).
Calculating Covariance
Authors: Chen Gilad
Published: September 2005

Covariance is a measure of association, or covariability, between two variables (e.g., variables
X
and
Y
). A positive covariance indicates positive association between
X
and
Y
, whereas a negative covariance indicates a negative association between
X
and
Y
. However, the magnitude of covariance is heavily dependent on the unit of measurement used to measure
X
and
Y
C
ramér–
von
M
ises Test
Authors: Lunneborg Clifford E.
Published: September 2005

The Cramér–von Mises test assesses whether two independent samples could have been drawn from the same or equivalent distributions.
Criterion‐Referenced Assessment
Authors: Hambleton Ronald K. , Li Shuhong
Published: September 2005

This entry provides an introduction to criterion‐referenced testing and approaches for resolving several technical problems. Several of the important differences between norm‐referenced testing and criterion‐referenced testing will be introduced first. Next, the challenge of setting performance standards on criterion‐referenced tests and several of the methods will be discussed. Finally, approaches for estimating decision consistency and decision accuracy from single and double test administrations are described.
Critical Region
Authors: Nickerson Raymond S.
Published: September 2005

Fundamental to statistical hypothesis testing, especially as advocated by Neyman and Pearson, is the identification of a
critical region
of a decision space, which is defined as a region of a theoretical probability distribution. The conclusion to be drawn from a test is determined by whether the statistic of interest falls within the critical region.
Cross‐Lagged Panel Design
Authors: Kenny David A.
Published: September 2005

The minimal cross‐lagged panel design is two variables measured at two times. Multiple regression analyses, in which the time two measures are regressed on the time one measures, have become the standard method of analyzing the design. Currently, methods to rule out third‐variable causation are little used. Several analysts have argued that two waves are insufficient to obtain much information about how processes unfold over time.
Cross‐Classified and Multiple Membership Models
Authors: Rasbash Jon
Published: September 2005

This paper proposes a notation and some diagrammatic tools for describing cross‐classified and multiple‐membership multilevel models. Example structures and analyses are given from the areas of education, psychology, medicine, and veterinary epidemiology.
Crossover Design
Authors: Kenward Michael G.
Published: September 2005

In a crossover trial, each subject is randomly allocated to one of several possible sequences of treatments. The sequences are chosen to provide some form of balance of treatments among periods. The main aim of such a design is to increase precision of treatment comparisons through the use of within‐subject information.
Deductive Reasoning and Statistical Inference
Authors: Cussens James
Published: September 2005

Connections and contrasts between deductive reasoning and statistical inference are given. Bayesian statistical inference is analyzed, including an account of its relation to deductive logic and the status of prior distributions. Classical statistical inference is investigated with a focus on hypothesis testing.
Demand Characteristics
Authors: de Munter Agnes
Published: September 2005

Demand characteristics come into being when research data are collected through exchange of information between human participants. It is this complex of unintended or unverifiable indications in the research situation that make the respondent believe he or she can guess the researcher's hypotheses or objectives. They are systematic errors, which form a threat to validity. In research, they can be traced by means of ‘quasi‐control’ strategies. It is hoped that this form of bias can be neutralized by restricting the interaction between researcher and respondent.
Design Effects
Authors: Klar Neil , Donner Allan
Published: September 2005

The purpose of this article is to review the concept of design effect as originally defined in the context of survey sampling, but also to demonstrate its strong relevance to broader areas of scientific interest. A worked example is provided illustrating its application of this concept to the planning of sample size requirements for a school‐based cluster randomization trial.
Development of Statistical Theory in the 20th Century
Authors: Lee Peter M.
Published: September 2005

This article covers the three most important approaches to statistical inference in the twentieth century: Fisher's fiducial inference, Neyman and Egon Pearson's null and alternative hypothesis testing, and the application and extension of Bayes theorem by Savage and de Finetti.
Two‐mode Clustering
Authors: Mechelen Iven Van , Bock Hans‐Hermann , de Boeck Paul
Published: September 2005

Two‐mode clustering methods provide a simultaneous clustering of the rows and columns of a rectangular data matrix. By the simultaneity of the methods they may reveal the value, interaction or dependence information as implied by the data.
Direct and Indirect Effects
Authors: Muller Dominique , Judd Charles M.
Published: September 2005

A three‐variable model with one independent variable (

X

), one dependent variable (

Y

), and a possible mediator (or suppressor) can be decomposed into three different types of effects. The first one is the indirect effect which is the portion of the relationship between

X

and

Y

that goes through the mediator. The second one is the direct effect which is the portion of the relationship between

X

and

Y

that does not go through the mediator. And, finally, the total effect is the sum of both the direct and the indirect effects.
Direct Maximum Likelihood Estimation
Authors: Enders Craig K.
Published: September 2005

Direct maximum likelihood (ML) is used to estimate models with missing data. Direct ML has theoretical advantages, and is unbiased and efficient when data are missing at random. The EM algorithm is one widely‐used method for obtaining ML parameter estimates with missing data.
Dominance
Authors: Evans David M.
Published: September 2005

Dominance refers to the nonlinear interaction between alleles at the same locus. In the case of a discrete trait, if one allele masks the effect of the other allele at the same locus, we say that the first allele displays dominance over the second allele. In the case of a quantitative trait, the amount of dominance at a locus may be quantified by the dominance parameter
d
, which equals the deviation of the heterozygote's phenotypic value from the midpoint of the two homozygotes' phenotypic values. In the case of a single biallelic locus in Hardy–Weinberg equilibrium, the dominance variance is given by the formula (2
pqd
)
2
where
p
and
q
are the allele frequencies at the locus. The amount of dominance variance affecting a trait can be estimated using the classical twin design.
Dot Chart
Authors: Everitt Brian S.
Published: September 2005

A dot chart is a graphical representation of data values associated with each class of a categorical variable. The value for each category is indicated by the position of a dot along a horizontal line. It has some similarities to a bar chart but can be used in a wider variety of situations.
Dropouts in Longitudinal Data
Authors: de Leeuw Edith D.
Published: September 2005

Different types of nonresponse threaten the validity of longitudinal studies: First, the initial nonresponse during the recruitment in the base‐line survey; Second, successive dropout at each time point. In this entry, specific attention is given to dropout and strategies to limit the problem. Dropout in longitudinal surveys has three separate sources: failure to locate research participants, failure to contact research participants, and failure to achieve cooperation. Effective measures are described to reduce nonresponse. To limit nonresponse, a total design approach is advocated with specific attention to each source. That is to limit both noncontact (i.e., failure to locate and subsequent failure to contact a located research participant), and noncooperation.
Dropouts in Longitudinal Studies: Methods of Analysis
Authors: Little Roderick J.
Published: September 2005

The statistical analysis of repeated‐measures data when some participants drop out prior to the end of the study has been reviewed. Methods considered include complete‐case analysis, where only the cases that are followed to the end of the study, are analyzed; imputation methods that fill in values after drop out, and multiple imputation, a refinement that accounts for imputation uncertainty; and methods that can be applied to the nonrectangular data set that arises from the missing data, including maximum likelihood for linear and nonlinear mixed models. Methods of analysis when the missing data are not missing at random are also reviewed.
Dummy Variables
Authors: Cortina Jose
Published: September 2005

Dummy variables are used to represent the various distinctions that exist in categorical variables. The term has a specific meaning but is often used to describe any coded variable that represents a part of a categorical variable. Dummy coding and its manifestations are described.
Educational Psychology: Measuring Change Over Time
Authors: Kulikowich Jonna M.
Published: September 2005

Educational psychologists use repeated measures analyses to study changes over time that reflect academic, cognitive, emotional, and social development of students. The purpose of this chapter is to review the basic principles and procedures of repeated measures in statistics, and, based on these principles and procedures, to describe important considerations of educational psychologists as they attempt to answer research questions. Testing of assumptions, estimating effect sizes and power, and current statistical advances in the study of how individuals' affect, behavior, and cognition change are discussed.
Effect Size Measures
Authors: Kirk Roger E.
Published: September 2005

A 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.
Quantiles
Authors: Lovie Pat
Published: September 2005

A quantile is defined as a value that cuts off a certain proportion
p
of the area under a probability distribution function (a theoretical quantile) or of the distribution of a set of data (empirical quantile). Quantile is a general name for a class of statistics, which include familiar measures such as the median, quartiles, and percentiles.
Epistasis
Authors: Evans David M.
Published: September 2005

Biologically speaking, epistasis refers to the interaction between genes at different loci to produce effects which are different from that expected from the individual loci themselves. In quantitative genetic terms, epistasis refers to a deviation from additivity in the effect of alleles and genotypes at different loci with respect to their contribution to a quantitative phenotype. The proportion of variance due to epistasis may be estimated using careful breeding experiments in experimental organisms, but cannot be estimated using the classical twin design. It is possible to model epistasis explicitly in linkage and association analyses.
Empirical Quantile–Quantile Plots
Authors: Lovie Sandy
Published: September 2005

An empirical quantile–quantile plot is an instance of added value scatterplots, which allows the analyst to perform a simultaneous graphical comparison between the measures of location and spread of two equal‐sized samples.
Equivalence Trials
Authors: Hatch John P.
Published: September 2005

Statistical significance testing is inappropriate for determining whether treatments have equivalent effects. Equivalence testing and noninferiority testing, which are based on testing whether the confidence interval of the mean difference falls entirely within clinically defined equivalence margins, are designed for this purpose.
Error Rates
Authors: Thompson Bruce
Published: September 2005

Error rate refers to the probability of making one or more incorrect decisions regarding null hypotheses. The most commonly recognized forms of errors are Type I errors (i.e., rejecting a null that actually is true) and Type II errors (i.e., failing to reject a null that actually is false). Researchers also distinguish between making a Type I error on a given hypothesis test (called a
testwise Type I error
) and making one or more Type I errors in a set of hypothesis tests (called
experimentwise Type I error
).
Conditional Standard Errors of Measurement
Authors: Tong Ye , Kolen Michael J.
Published: September 2005

Errors of measurement for test scores generally are viewed as random and unpredictable. Conditional standard errors of measurement (SEMs) index the amount of error in the measurement process and are required to be reported for tests. Methods of estimating conditional SEMs, based on both classical test theory and generalizability theory, are described in this entry. These methods are based on differing assumptions, but the conditional SEMs estimates obtained from these methods are commonly highly related for educational achievement tests.

Conditional SEMs vary by score level. Conditional SEMs typically have high values for extreme scores and have low values for middle scores on the raw score scale. However, a nonlinear transformation of the raw scores to scale scores can lead to conditional SEMs that have other patterns across score levels.
Misclassification Rates
Authors: Krzanowski Wojtek J.
Published: September 2005

This article surveys the ways in which the error rate incurred by a classifier, that is, the proportion of future incorrect classifications, can be estimated. Theoretically derived rates depend heavily on distributional assumptions; so, in practice, data‐based estimates are generally preferred. Methods based on resubstitution, test‐set estimation, cross‐validation, jackknifing, and bootstrapping are described. The phenomenon of tuning the classifier by using one of these methods to optimize its performance is also explained, and the dangers of overoptimism in assessing error rates of a tuned classifier are highlighted. Interval estimation of error rates is briefly discussed, and an illustrative example is provided.
Estimation
Authors: van de Geer Sara A.
Published: September 2005

This paper is concerned with the relationship between sample data and the probability distribution (
P
), which is supposed to have generated it. The estimation of
P
using an empirically derived distribution is discussed along with specific estimators such as the sample mean, the sample median, and a histogram. Estimation by the method of moments and minimum chi‐square estimation are explained, as are the concepts of bias, mean square error, and sufficiency.