bluuebunny/crossref_metadata_2025 huggingface dataset:
Item Bias Detection: Classical Approaches
Authors: Mellenbergh Gideon J.
Published: September 2005

Under the assumptions of Classical Test Theory (CTT), a person's observed test score is an estimate of his (her) true test score. Therefore, CTT‐based methods to detect differentially functioning items use the test score to equate members of different groups. An item is considered to be differentially functioning between two groups when item responses differ between members of the two groups at the same test score. Five methods for the detection of differentially functioning dichotomous item responses and their generalization to ordinal‐polytomous item responses are discussed.
Classical Test Models
Authors: Muñiz José
Published: September 2005

The term ‘Classical Test Theory’ covers an entire set of psychometric models and procedures whose main objective is to solve the psychometric problems arising in the measurement of variables in the social sciences. Classical test theory permits us to estimate the psychometric properties of the tests, questionnaires, and scales used in social science measurement, guaranteeing that measurements are made with the appropriate scientific and technical rigor. The first work in this area appeared at the beginning of the twentieth century, and by the 1960s, the core of the classical approach was well established. The classical model assumes that a person's empirical score in a test is made up of two additive components, the true score corresponding to the assessed person in that test, and a certain measurement error. From this simple model, and with the addition of some assumptions and the definition of parallel tests, we obtain the principal classical formulas that allow the estimation of the psychometric properties of tests, such as reliability and validity.
Collinearity
Authors: Chen Gilad
Published: September 2005

Collinearity reflects situations in which two or more independent variables are perfectly or nearly perfectly correlated. In the context of multiple regression, collinearity violates an important statistical assumption and results in uninterpretable and biased parameter estimates and inflated standard errors. Regression diagnostics such as
variance inflation factor
(VIF) and
tolerance
can help detect collinearly, and several remedies exist for dealing with collinearity‐related problems.
Comorbidity
Authors: Rhee S. H. , Hewitt John K. , Corley R. P. , Stallings M. C.
Published: September 2005

Comorbidity between psychiatric disorders often exceeds the rate expected by chance alone. Increased knowledge regarding the causes of comorbidity between two psychiatric disorders may have a significant impact on research regarding the classification, treatment, and etiology of both of disorders. We examined the validity of common methods used to test alternative comorbidity models.
Correlation
Authors: Kornbrot Diana
Published: September 2005

Correlation describes whether two variables ‘go together’. Correlation is a general term, covering various different kinds of association or relationship between two variables. Correlation does not imply causality. Correlations may be positive or negative, linear (looking like a straight line) or nonlinear (curved), and strong or weak. There are several different measures of correlation. Correlation measures range from +1, indicating perfect positive agreement to −1, indicating perfect negative agreement. The most appropriate measure depends on the type of measurement scale and distribution of both variables and the shape of the relationship between them.
Number of Matches and Magnitude of Correlation
Authors: Rovine Michael J.
Published: September 2005

A definition of the correlation as the proportion of matches between two continuous variables is described. This definition is compared to other coefficients; in particular, coefficients that are used to describe the association in a 2 × 2 contingency. These include Yule's Q, Peirce's coefficient, the ϕ‐coefficient, and the Binomial Effect Size Display (BESD).
Cross‐Sectional Design
Authors: Busk Patricia L.
Published: September 2005

Cohorts of individuals are measured at the same time in order to research temporal or age differences. By taking a cross section of a population, researchers avoid the disadvantages of longitudinal research, specifically loss of subjects over time.
Cross‐Validation
Authors: Stuetzle Werner
Published: September 2005

Cross‐validation is a method for estimating the error of a prediction rule. It is commonly used for model selection in regression and classification problems. Cross‐validation is similar in spirit to other computer intensive methods like the Bootstrap and permutation tests, in that it substitutes computing for mathematical analysis. It is easy to understand and trivial to implement.
Cultural Transmission
Authors: Hershberger Scott L.
Published: September 2005

Cultural transmission refers to the transfer of the knowledge, values, and ideas within a population. It is also a nongenetic form of natural selection in which behavioral adaptations that arise from cultural influences are passed from one generation to the next. Importantly, cultural transmission occurs between an individual and the individual's conspecifics, both between generations and within generations. ‘Cultural transmission’ is not synonymous with ‘environmental influence’ – only ‘individuals’ are the relevant part of the environment critical to cultural transmission. The transfer of information is based on social learning specifically, and not on other types of learning such as behavioral reinforcement. Mathematical models of cultural transmission have been developed that emphasize either the similarities or the differences among individuals within a population. Cultural transmission may also be an important cause of correlated genotypes and environments.
De
F
ries–
F
ulker Analysis
Authors: Rende Richard , Slomkowski Cheryl
Published: September 2005

DeFries‐Fulker (DF) analysis involves a series of models that provide traditional estimates of genetic and environmental parameters for individual differences on a trait, along with unique parameters specific to the etiology of extreme levels of a trait. These models are presented along with reference to a new model‐fitting implementation of the DF approach.
Differential Item Functioning
Authors: Rogers H. Jane
Published: September 2005

Differential item functioning (DIF) occurs when individuals at the same level on the trait(s) or construct(s) being assessed but from different subpopulations have unequal probabilities of attaining a given score on the item. Methods for investigating DIF have been developed for both dichotomously and polytomously scored items. These methods may be classified by whether they condition on an unobserved or observed variable. Item response theory, logistic regression, Mantel–Haenszel, and SIBTEST procedures for dichotomously scored responses and their extensions to polytomous responses are currently the most widely used methods for detecting DIF.
Causal‐Comparative Study
Authors: Busk Patricia L.
Published: September 2005

A nonexperimental design that is employed to explore cause‐and‐effect relationships is called
ex post facto
or causal‐comparative. The title
ex post facto
is applied to studies in which data are gathered retrospectively, whereas causal‐comparative is used when data are gathered from groups and the independent variable is not manipulated as in an experiment.
Discriminant Analysis
Authors: Huberty Carl J.
Published: September 2005

The basic notions of descriptive and predictive discriminant analysis (DDA and PDA) are discussed. Descriptions of conductiong a DDA and PDA are given, with implications for reporting results of these two analyses. Distinctions betweeen DDA and PDA are emphasized.
Distribution‐Free Inference, an Overview
Authors: Lunneborg Clifford E.
Published: September 2005

Distribution‐free or nonparametric techniques provide a basis for statistical inference where parametric assumptions cannot be justified. In particular, such techniques are essential where the scale of measurement is not interval or, if interval, observations are not likely to follow a Normal law. Standard and more recent distribution‐free techniques are surveyed here.
Ecological Fallacy
Authors: Kreft Ita G. G.
Published: September 2005

Before the invention of multilevel data analysis, researchers have struggled with the question how to analyze data that consist of observations in natural occurring groups. The choice is to analyze individuals irrespective of group membership, or analyze groups, and ignore individual differences within groups. A mistake, called ecological fallacy, may appear when inferences are made for individuals based on group data analysis and vice versa. The following examples show some dramatic fallacies and explain the reason why cross‐level inferences can lead to a wrong interpretation of the data.
Exploratory Data Analysis
Authors: Lovie Sandy
Published: September 2005

Exploratory Data Analysis (EDA) is one of the most influential recent developments in statistics. Led by John Tukey, EDA offered a new inductive orientation to the discovery of knowledge. In detail, this meant the invention of new graphical methods, the development of robust, outlier resistant measurements, and the modernization of regression analysis and related linear model approaches.
Eigenvalue/Eigenvector
Authors: Jolliffe Ian
Published: September 2005

The words eigenvalue and eigenvector often appear in computer output for multivariate statistical techniques. An explanation is given of what is meant by these terms for some specific techniques and more generally.
Eta and Eta Squared
Authors: Field Andy P.
Published: September 2005

Eta squared (η
2
) is an elegant and simple way to express an effect size (typically the effect of manipulations across several groups). Put simply, it is the ratio of variability explained by the manipulations (the group means) to the total variability. It is an accurate measure for the sample, but is a biased estimate of the effect in the population.
Event History Analysis
Authors: Vermunt Jeroen K. , Moors Guy
Published: September 2005

The purpose of event history analysis is to explain why certain individuals are at a higher risk of experiencing the event(s) of interest than others. This can be accomplished by using special types of methods which are usually referred to as hazard models. Two special features of hazard models are that they can deal with censored observations and with covariates that change their values during the observation period.
Factor Analysis: Multiple Groups
Authors: Little Todd D. , Slegers David W.
Published: September 2005

The general factor model, when extended to include mean‐level information, is a very powerful tool for cross‐group and longitudinal comparisons. The multiple‐group mean and covariance structures (MACS) approach is particularly useful for making cross‐group (or cross‐time) comparisons because it allows for (a) simultaneous estimation of all parameters in each group (or at each occasion) and (b) direct statistical comparisons of the estimated parameters across the groups (or occasions). Because the means of measured indicators are included explicitly in the analyses, they provide a basis to make a very strong test of the validity of construct comparisons (i.e., measurement equivalence) across groups and across time. Specifically, strong factorial invariance indicates that constructs are fundamentally similar in each group or across time (i.e., comparable) and hypotheses about the nature of possible group‐ or time‐related influences can be meaningfully tested on any of the constructs' basic moments (means, variances, or covariances) across time or across each group whether the groups are defined on the basis of culture, gender, or any other grouping criteria.
Factorial Designs
Authors: Ramsey Philip H.
Published: September 2005

Factorial designs are described and illustrated with an example. The example is used to show how one might properly evaluate the statistical significance of the various effects in the design.
Fixed and Random Effects
Authors: Snijders Tom A. B.
Published: September 2005

In performing a multilevel analysis, what is a level? And when should a variable have a random slope? This depends on whether the units in the design should be regarded as being representative of a population and on whether the researcher wishes to draw conclusions primarily about the observed units or primarily about the population.
Focus Group Techniques
Authors: Rodabough Tillman , Wiggins Lacey
Published: September 2005

Frequently misunderstood as a simple discussion group, weak by scientific standards and producing little valid data, focus groups, in fact, make contributions whether combined with more traditional research methods or standing alone as a unique technique.
Generalized Linear Mixed Models
Authors: Hedeker Donald
Published: September 2005

Generalized linear models (GLMs); represent a class of regression models for several types of dependent variables where the linear predictor includes only fixed effects. Incorporation of random effects into GLMs yields the class of models known as generalized linear mixed models (GLMMs). Random effects are typically included for analysis of clustered and/or longitudinal data to account for the correlation of the data. GLMMs are especially useful for analysis of correlated nonnormal data, and the term GLMMs often refers to models for these kinds of data.
Growth Curve Modeling
Authors: Singer Judith D. , Willett John B.
Published: September 2005

We demonstrate the conceptual underpinnings and practical use of growth curve models (also known asindividual growth modelsandmultilevel models for change), which describe how a continuous outcome changes systematically over time.
Histogram
Authors: Everitt Brian S.
Published: September 2005

A histogram is a graphical display of the frequency distribution of a set of continuous data that has been grouped into classes or categories. The height of a vertical bar spanning each class interval represents the frequency of observations in that category.
History of Correlational Measurement
Authors: Cowles Michael
Published: September 2005

The beginnings of attempts to index the relationship between two or more variables began in the nineteenth century. A number of mathematicians produced theoretical underpinnings that lead to the concept of correlation, but none appreciated the practical applications of the method. Galton looked at correlation in the context of heredity with the aim of providing objective mathematical descriptions that would bolster his belief in, and demonstrate the truth of the social philosophy of planned heredity that he named
eugenics
. Pearson, a mathematician and also a eugenist, arrived at the best formula for the coefficient of correlation and it was named after him. Later, the methods of partial and multiple correlation followed. The methods of factor analysis were introduced and techniques for handling relationships among ordinal and nominal data added to the growing collection of statistical methods in the behavioral and biological sciences.
Industrial/Organizational Psychology
Authors: Landis Ronald S. , Kaplan Seth A.
Published: September 2005

Industrial and organizational (IO) psychologists utilize a variety of statistical techniques in their research. A nine‐year review of two leading journals (
Journal of Applied Psychology
and
Personnel Psychology
) in the field reveals that correlational techniques appear in the largest percentage of studies. More complex methods such as structural equation modeling (SEM) and hierarchical linear modeling (HLM) appear in proportionally fewer studies. Representative examples of how various statistical techniques are used in IO research are provided, and possible reasons for the observed results are presented. In addition, IO psychologists' contributions to statistics and the role of statistics in IO theory development are discussed.
Information Matrix
Authors: Myung Jay I. , Navarro Daniel J.
Published: September 2005

Fisher information essentially describes the amount of information data provide about an unknown parameter. It has applications in finding the variance of an estimator, as well as in the asymptotic behavior of maximum likelihood estimates, and in Bayesian inference.
Interquartile Range
Authors: Clark‐Carter David
Published: September 2005

The interquartile range is a measure of spread (or dispersion). It is defined as the difference between the upper and lower quartiles in a set of ordered data. It is an important feature in a box plot.
J
onckheere–Terpstra Test
Authors: Lunneborg Clifford E.
Published: September 2005

For the one‐way design, the Jonckheere‐Terpstra procedure tests the null hypothesis of no difference in response magnitude across treatments against an ordered alternative, that response magnitude increases over a pre‐specified ordering of the
treatments. Where the treatment levels can be ordered according to expected response magnitude (e.g., drug dosages, stimulus intensities, and hours of practice), the Jonckheere–Terpstra test (1954) employs a more coherent, directional alternative hypothesis, that is, the response magnitude does not decrease for any treatment level increase and actually increases for one or more treatment level increases.
K
endall's
T
au‐τ
Authors: Kornbrot Diana
Published: September 2005

Kendall's tau, τ, is a correlation measure of association based on ranks of scores rather than raw scores. It is based on the number of swaps needed to put the second variable into exactly the same or exactly the opposite order to the first variable. It is applicable if either or both variables are direct rankings, or only
ordinal
. It is also applicable when both variables are metric but not
normally distributed
, or when the relation between the variables is monotonic, but nonlinear. Methods for calculating τ and procedures for hypothesis testing are provided. Kendall's τ is compared with Spearman's ρ and Pearson's
r
.
Data Mining
Authors: Hand David J.
Published: September 2005

Data mining is the discovery of structures and patterns in large data sets. There are two aspects to data mining: model building and pattern detection. Model building in data mining is very similar to statistical modeling, although new problems do arise because of the large sizes of the data sets and the fact that data mining is secondary data analysis. Pattern detection seeks anomalies or small local structures in data, with the vast mass of the data being irrelevant. Although some subdisciplines of statistics have examined special cases of this problem, the bulk of the work on pattern detection to date has been computational, with an emphasis on algorithms.
Latent Transition Models
Authors: van de Pol Frank , Langeheine Rolf
Published: September 2005

Flows between states for discrete periods of time can be described with a Markov chain, a process without memory. More realistic for social science data is a heterogeneous mixture of Markov chains, of movers and stayers. Alternatively, or in conjunction with heterogeneity in the tendency to change, one can take measurement unreliability into account, using latent or indirectly measured Markov models. The basic model variants are explained with data examples. References to overview papers are given.
Longitudinal Designs in Genetic Research
Authors: Price Thomas S.
Published: September 2005

A brief introduction to longitudinal designs in genetic research, covering aspects of experimental design and the theory and interpretation of longitudinal behavioral genetic models. The Cholesky decomposition and the simplex model are used as examples.
Multivariate Analysis of Variance
Authors: Hartung Joachim , Knapp Guido
Published: September 2005

Multivariate analysis of variance (MANOVA) techniques are used to analyze simultaneously the influence of qualitative factors on more than one quantitative variable. MANOVA allows testing the null hypothesis that the mean responses of the quantitative variables are the same across all the levels of a factor averaged over all the other factors against the alternative hypotheses that there are at least two factor levels that have different mean responses. We describe the four test statistics commonly used for hypothesis testing in MANOVA and frequently implemented in statistical software packages.
Marginal Models for Clustered Data
Authors: Fitzmaurice Garrett M.
Published: September 2005

Clustered data commonly arise in studies in the behavioral sciences. For example, clustered data arise when observations are obtained on children nested within schools. Longitudinal and repeated measures studies also give rise to clustered data. Marginal models provide a broad class of regression models that are suitable for analyzing diverse types of clustered data (e.g., continuous, binary, and count data). The distinctive feature of marginal models is that they focus on each response within the cluster separately, allowing dependence of the mean response on covariates but not on any random effects or other responses within the same cluster. By focusing on the population mean response, averaged over all clusters, the regression coefficients relating the mean response to covariates are said to have
population‐averaged
interpretations.
M
axwell,
A
lbert
E
rnest
Authors: Bartholomew David J.
Published: September 2005

A.E. Maxwell (1916–1996) spent most of his career at the Institute of Psychiatry, University of London, latterly as head of the Biometrics Unit. He is best known for his co‐authorship (with D.N. Lawley) of the book
Factor Analysis as a Statistical Method
. This established factor analysis as a branch of statistical methodology. His other publications include several books on psychological statistics and he also engaged in extensive consulting and advisory work.
Markov ChainMonteCarlo andBayesian Statistics
Authors: Congdon Peter
Published: September 2005

Bayesian estimation via repeated sampling algorithms has opened new possibilities in analyzing complex statistical models and data sets. Such algorithms are now the standard for estimating parameters, making other inferences (e.g., posterior probabilities on hypotheses relating to parameters), and in model choice. A set of methods collectively known as Monte Carlo Markov Chain algorithms is discussed as well as issues in their practical implementation.
Measures of Association
Authors: Hershberger Scott L. , Fisher Dennis G.
Published: September 2005

Measures of association are numerical estimates of the magnitude of the statistical dependence between two variables. A multitude of such measures have been proposed; we review some of the most commonly used ones, dividing them into two types. The first is suitable for nominal scale data, and includes measures based on the odds ratio, measures based on Pearson's χ2, and measures of predictive association. The second type is suitable for ordinal scale data, and includes measures of concordance‐discordance, and measures based on derived scores.
Model Selection
Authors: Cortina Lilia M.
Published: September 2005

Given the complexity inherent in behavioral phenomena, there are typically multiple plausible models that can account for any set of observations. The task, then, is to select the model that shows superior qualities in terms of fit, parsimony, interpretability, and consistency with theory. Even then, the researcher cannot claim to have identified the one ‘true’ model, because selection of an excellent model could artifactually result from failure to consider every possible alternative.
Moments
Authors: Walwyn Rebecca
Published: September 2005

Moments are expectations that are used to describe the probability distributions of random variables. The mean and variance of a random variable are the two most important examples of moments.
Multigraph Modeling
Authors: Khamis Harry J.
Published: September 2005

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.
Multiple Linear Regression
Authors: West Stephen G. , Aiken Leona S.
Published: September 2005

Multiple regression represents the relationship between a dependent variable and a weighted linear combination of a set of independent variables. Multiple regression can be used to model a wide variety of forms of relationships and types of independent variables. Diagnostic procedures can be used to identify violations of assumptions and outlying data points which adversely affect its performance. Multiple regression can be used to describe relationships, predict future scores on the dependent variable, and test specific hypotheses.
Nonequivalent Group Design
Authors: Reichardt Charles S.
Published: September 2005

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.
T
ype
I
,
T
ype
II
and
T
ype
III
Sums of Squares
Authors: Hershberger Scott L.
Published: September 2005

Whenever factorial designs have equal cell frequencies, the factors are orthogonal. Although orthogonal factors are not required, orthogonal factors permit a unique decomposition of the variance in the dependent variable. If cell frequencies vary, or there are empty cells, the factors are nonorthogonal: The variance decomposition of the dependent variable differs depending on which of Type I, II, III, or IV sums of squares is used for the analysis.
Normal Scores and Expected Order Statistics
Authors: Lunneborg Clifford E.
Published: September 2005

Rank tests replace raw scores with their ranks prior to computing a test statistic and its reference distribution. This use of ranks is advocated where the normality of the raw score observations is in doubt. An alternative approach is to replace the raw scores with values that resemble observations from a normal distribution more closely than do the integer‐spaced ranks, while taking the order of the raw scores into account. Permutation tests that are carried out following such a rank‐preserving transformation of the data is called a normal scores test.
Observational Study
Authors: Rosenbaum Paul R.
Published: September 2005

An observational study is an empiric investigation that attempts to estimate the effects caused by a treatment when it is not possible to perform an experiment. Random assignment of subjects to treatment or control in an experiment ensures that comparable groups of subjects are compared under alternative treatments. Without random assignment, in an observational study, the treatment and control groups may not be comparable prior to treatment, so that differing outcomes after treatment may not be effects caused by the treatment. Pretreatment differences that have been accurately measured are calledovert biases; they may often be controlled using analytical adjustments, such as matching, stratification, or covariance adjustment. Pretreatment differences that were not recorded are called hidden biases, and they pose substantial problems that must be addressed by other means. A well designed observational study permits detection of one or two of the most plausible hidden biases. The analysis of an observational study can measure the degree of sensitivity of conclusions to hidden biases of plausible magnitudes. Design strategies involving pattern specificity, such as Campbell's ‘multiple operationalism’ or Hill's dose‐response, may reduce sensitivity to hidden bias, and this possibility may be appraised using the design sensitivity of competing designs.
Ordinal Regression Models
Authors: Hershberger Scott L.
Published: September 2005

Regression models for ordinal data have been developed based upon the cumulative probabilities for the categories of response variable. One of the most frequently used ordinal regression model is the ordinal logistic model, a member of the family of generalized linear models.
Parsimony/Occham's Razor
Authors: Mulaik Stanley A.
Published: September 2005

In modeling data, parsimony is the fewness of model parameters estimated relative to the number of data points fit by the model. The more parsimonious a model, the more degrees of freedom by which the model can fail to fit the data, thus making the model more potentially disconfirmable and more strongly supported when the model fits.
Placebo Effect
Authors: Onghena Patrick
Published: September 2005

A placebo effect is conceptually defined as the beneficial effect associated with an intervention that does not include the presumed active ingredients. It can be operationally defined as the positive difference between the results of a placebo condition and a no‐treatment condition in a randomized trial. Placebos play a crucial role as a control in clinical medication trials, but discussion remains regarding their effect sizes and possible working mechanisms. As a confounding factor, a placebo effect is considered as a specific type of reactivity effect that should be distinguished from other confounding factors like history, spontaneous recovery, or statistical regression.
Population Stratification
Authors: van den Oord Edwin J. C. G.
Published: September 2005

In case‐control studies, population stratification can cause associations between marker alleles and disease status. These associations are ‘spurious’ because the marker is not informative about the location of a disease mutation. Family‐based tests are an important tool to avoid such spurious findings but the extent to which these tests are really needed is a topic of debate.
Prospective and Retrospective Studies
Authors: Dykacz Janice Marie
Published: September 2005

Prospective and retrospective studies differ in whether the explanatory variable or the outcome variable is used to select the individuals in the study. The relative risk is frequently used to measure association for a prospective study. The odds ratio is frequently used to measure association for a retrospective study.
PValues
Authors: Dracup Chris
Published: September 2005

The advantages of reporting exactPvalues rather than using conventional significance levels are outlined. WhilePvalues do not represent the probability of truth of the null hypothesis, they do provide an index of the strength of evidence against that hypothesis. ThePvalue depends on whether the alternative hypothesis is one‐tailed or two‐tailed, with the two‐tailedPvalue generally being twice the one‐tailedPvalue. There is considerable debate about howPvalues for statistics with discrete distributions should be computed. In situations where the null hypothesis is known to be false,Pvalues provide useful information about the probability of error in the establishment of the direction of the true effect.
Qualitative Research
Authors: Patton Michael Quinn
Published: September 2005

Qualitative research analyzes data from direct fieldwork observations, in‐depth, open‐ended interviews, and written documents. Qualitative researchers engage in naturalistic inquiry, studying real‐world settings inductively to generate rich narrative descriptions and construct case studies. Inductive analysis across cases yields patterns and themes, the fruit of qualitative research.
Quartiles
Authors: Clark‐Carter David
Published: September 2005

Quartiles are the result of partitioning an ordered set of numbers into quarters. They can contribute to measures of dispersion such as the interquartile range and are used in box plots.
Randomization Based Tests
Authors: Ludbrook John
Published: September 2005

I argue that when an experiment in behavioral psychology is designed, it almost always involves taking a nonrandom sample and, by a process of randomization, dividing it into two or more ‘treatment’ groups. This places such experiments within the randomization model of inference, not the better‐known population model. The appropriate tests of significance under the randomization model are permutation (randomization) tests.
Randomized Block Designs
Authors: Maxwell Scott E.
Published: September 2005

The randomized block design (RBD) is a standard design used primarily to control for a nuisance variable. The advantage of controlling for an important nuisance variable is increased power and precision relative to a nonblocked, completely randomized design.
Rank Based Inference
Authors: Hettmansperger T. P. , McKean J. W. , Sheather S. J.
Published: September 2005

The use of ranks has a long history stretching back to 1945 with the seminal work of Wilcoxon. Early nonparametric rank tests were developed for the basic one‐ and two‐sample designs and then extended to the one‐ and two‐way layouts. These tests are popular because of their nonparametric property along with their good efficiency and robust properties. In this entry, we describe and illustrate how to extend rank‐based methods to the general linear model including regression, analysis of variance, and analysis of covariance. We also describe a coefficient of determination that is useful when assessing the fit of a model to the data.
R
asch Modeling
Authors: Fischer Gerhard H.
Published: September 2005

The Rasch Model is an item response model for ability or achievement tests with dichotomous item response format. Basic properties of the model are sufficiency of the raw score with respect to the person parameter and the so‐called ‘
specific objectivity
’ of comparisons between items and between persons. The model guarantees measurements with interval scale properties, except for very special cases where the scale becomes an ordered metric scale. The best‐founded approach to the estimation of the parameters of the model and to testing of fit or of other hypotheses about the parameters is the conditional likelihood method. Extensions of the model allow, for instance, to formalize structural hypotheses about the item parameters, to measure and test hypotheses about change, and to deal with scales composed of items with more than two ordered response categories.
Rater Agreement – Kappa
Authors: Mun Eun Young
Published: September 2005

Whether there is agreement or consensus among raters or observers on their evaluation of the objects of interest is one of the key questions in the behavioral sciences. One way to measure rater agreement is to have two raters make independent observations on the same group of objects, to classify them into a limited number of categories, and then to see to what extent the raters' evaluations overlap. Of all measures, Cohen's kappa (κ, 1960) is one of the best known and most frequently used measures to assess the extent of agreement by raters in a summary statement for entire observations.
Rater Agreement – Weighted Kappa
Authors: Mun Eun Young
Published: September 2005

One of the characteristics of Cohen's kappa (κ) is that any discrepancy between raters is equally weighted as zero. On the other hand, any agreement means
absolute agreement
between raters, and is equally weighted as one. Thus, the distinction between agreement and disagreement is categorical. For example, Table 1 from the Cohen's kappa section shows three agreement cells and six disagreement cells. In deriving Cohen's kappa, all six disagreement cells are treated equally. However, there could be situations in which the discrepancy between adjacent categories such as Categories 1 and 2 can be considered as partial agreement as opposed to complete disagreement. In those situations, Cohen's weighted kappa can be used to reflect the magnitude of agreement.
Reactivity
Authors: Onghena Patrick
Published: September 2005

Reactivity is a threat to the outcomes or treatments construct validity of observational and intervention studies that refers to the unintended reaction of participants on being observed or on being in a study. It is a threat to the
outcomes construct validity
if participants behave differently because they are aware that some aspect of their functioning is being observed or measured. It is a threat to the
treatments construct validity
if participants behave differently because they interpret the research or treatment setting in a way that makes the actual treatment different from the treatment as planned by the researcher. Because of the inevitable tendency of human participants to interact and give meaning to settings and their own and other's behavior, reactivity is a considerable risk to invalidity of both quasi‐ and randomized experiments in behavioral science.
Recursive Models
Authors: Cortina Lilia M.
Published: September 2005

Recursive statistical models only include unidirectional effects – that is, causality flows in only one direction. These models do not permit reciprocal causation or feedback loops, nor do they allow variables that are linked in a causal chain to have correlated disturbance terms. If all criteria for being recursive are met, then the model is identified.
Resistant Line Fit
Authors: Lovie Pat
Published: September 2005

Resistant line fitting is a simple method, developed within the exploratory data analysis framework, for representing a linear relationship between two variables. It is based on a robust measure, the median, and is especially useful as an alternative to least squares when data contain outliers.
Reversal Design
Authors: Ferron John
Published: September 2005

Reversal designs are used to study the effect of a treatment on the behavior of a single participant. The participant is observed repeatedly prior to treatment to establish a baseline level of behavior. The treatment is then administered and repeated observations are made to assess whether the behavior improves during treatment. The treatment is then removed and repeated observations are made to see if the behavior reverses toward baseline levels.
Robust Statistics for Multivariate Methods
Authors: Victoria‐Feser Maria‐Pia
Published: September 2005

Robust statistics deals with slightly misspecified models. When the data have not been generated exactly from the assumed models, robust procedures are by definition not (or very little) influenced by these model deviations. This is, in general, not the case with classical procedures such as least squares, maximum likelihood, and so on. Numerous multivariate models are based on the multivariate normal distribution, for which a relatively large number of robust procedures have been proposed. Most of the robust estimators are based on weighted means and covariances, and the weights are decreasing functions of the Mahalanobis distances. For nonnormal multivariate models, weights are more difficult to define, and more research is needed to develop robust procedures in these cases.
Receiver Operating Characteristics Curves
Authors: Wright Daniel B.
Published: September 2005

The receiver operating characteristic (ROC) curve is the principal graphical device for signal detection theory (SDT). It is generally used when there is a right or a wrong answer and participants provide some measure of confidence in their responses. The ROC is a scatterplot between the hit rate and the false alarm rate. Exploring this space allows the researcher to consider the differential value of hits and correct rejections (or of misses and false alarms). This is where ROCs have a big advantage over the alternatives. The main alternative,
logistic regression
, is based on similar mathematics. Historically, SDT/ROCs assumed normal distributions, but this is very similar to the logistic distributions, and most statistical packages allow either. The choice of approach rests largely on the form of graphical communication the researcher wants to use. While logistic regression focuses on discrimination, in SDT the researcher explicitly differentiates two types of accuracy: sensitivity and specificity. The ROC curve is an excellent tool for comparing these.
Sample Size and Power Calculation
Authors: Murphy Kevin R.
Published: September 2005

The precision with which sample statistics estimate population parameters is strongly influenced by the number of observations. Statistical power analysis provides a method of determining the sample sizes needed to control for errors in hypothesis testing. Power is largest when the effects being studied are large and the sample is large.
History of Path Analysis
Authors: Mulaik Stanley A.
Published: September 2005

Sewell Wright was a geneticist who originated the method of path analysis for studying causal hypotheses with correlations and partical correlations and who struggled to get it accepted in a climate of British and logical expiricism that was hostile to the concept of causality. The method subsequently developed into the modern method of structural equation modeling.
Structural Equation Modeling: Categorical Variables
Authors: Skrondal Anders , Rabe‐Hesketh Sophia
Published: September 2005

In the behavioral sciences, response variables are often noncontinuous, common types being dichotomous, ordinal or nominal variables, counts and durations. Conventional structural equation models (SEMs) have thus been generalized to accommodate different kinds of responses.
Sensitivity Analysis
Authors: Wakefield Jon
Published: September 2005

In an observational study, there is always the possibility of bias due to unmeasured variables, measurement error in explanatory variables and/or selection bias; and randomized studies are also not immune to at least some of these biases. A sensitivity analysis provides a means of asking a series of ‘what if?’ questions, in order to determine the robustness of the observed association to sources of bias.
Sign Test
Authors: Sawilowsky Shlomo
Published: September 2005

Arguably the oldest distribution‐free test, the Sign test is used either in the one‐sample context to test a hypothesis about a population median or in the paired sample context to test a hypothesis about the equality of two population medians.
Single‐Case Designs
Authors: Onghena Patrick
Published: September 2005

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.
Social Psychology
Authors: Judd Charles M. , Muller Dominique
Published: September 2005

In part due to the wide array of their theoretical interests, social psychologists use, and sometimes develop, a similarly wide array of statistical tools. These tools range from basic analysis of variance, with factors either between and/or within participants, to more integrative general linear models, and from multilevel modeling procedures to structural equation modeling.
State Dependence
Authors: Skrondal Anders , Rabe‐Hesketh Sophia
Published: September 2005

State dependence occurs if the current outcome of a dynamic process depends on prior outcomes. It is crucial to distinguish between true and spurious state dependence.
Software for Statistical Analyses
Authors: Silver N. Clayton
Published: September 2005

This article describes general purpose statistical software packages and special purpose packages for hierarchical linear modeling, meta‐analysis, power analyses, qualitative data, structural equation modeling, and confidence intervals for effect size indexes. The packages are compared and problems identified. Additional sources of statistical software are listed and future improvements in statistical software are addressed.
Survey Sampling Procedures
Authors: Moore Kris K.
Published: September 2005

Survey sampling provides procedures to estimate characteristics of a population based on a sample. Questionnaire design, collection of sample information, sampling methods, and sample size are discussed.
Symmetry: Distribution Free Tests for
Authors: Lunneborg Clifford E.
Published: September 2005

Nonparametric tests for the median of a distribution and the related estimation of confidence intervals for that parameter assume that the distribution sampled is symmetric about the median. To avoid obtaining misleading results, a preliminary test for distribution symmetry is advisable.
Symmetry Plot
Authors: Lovie Sandy
Published: September 2005

Like EQQ plots, symmetry plots are another instance of added value scatterplots, which, in this case, allows the analyst to perform a graphical test as to the equality of the shape of a sample about a central value.
Reliability: Definitions and Estimation
Authors: Mead Alan D.
Published: September 2005

Reliability, ρ

XX
′

, is the degree to which test scores are precise and free from error. Classical test theory defines reliability as the ratio of true score variance to observed score variance:

. This article provides a comprehensive definition of reliability and then describes the methods by which reliability is commonly estimated, including their limitations. The article then discusses several closely‐related topics: the standard error of measurement; reliability in subpopulations; the Spearman‐Brown prophesy formula; true score correlations; reliability of speeded tests; and the relationship between classical reliability and item response theory information.
Covariance Matrices: Testing Equality of
Authors: Krzanowski Wojtek J.
Published: September 2005

Parametric multivariate inferential techniques make distributional assumptions about the data, and a common assumption in multisample problems is that dispersion matrices are equal in all the populations from which the samples have come. There is therefore need for a hypothesis test that can check on the adequacy of this assumption. In this article, we provide an appropriate test statistic, give its approximate (large sample) null distribution, illustrate its use on a small data set, and provide some cautionary comments about interpretation.
Tolerance and Variance Inflation Factor
Authors: Miles Jeremy
Published: September 2005

The variance inflation factor (VIF) and tolerance are two closely related statistics for diagnosing collinearity in multiple regression. They are based on the
R
‐squared value obtained by regressing a predictor on all of the other predictors in the analysis. Tolerance is the reciprocal of VIF.