bluuebunny/crossref_metadata_2025 huggingface dataset:
Least Squares Estimation
Authors: van de Geer Sara A.
Published: September 2005

The method of least squares is about estimating parameters by minimizing the squared discrepancies between observed data on the one hand, and their expected values on the other. It is commonly used in the context of a regression model, where one observes pairs of variables (
X
,
Y
), with
X
a covariable and
Y
a response variable. The expectation of the response variable
Y
given the covariable
X
is modeled as a function
f
β
(
X
) depending on parameters β.

We present an explicit expression for the least squares estimator

of β in the linear regression model, and also give its covariance matrix. The calculations are illustrated with a numerical example. The F statistic for testing linear hypotheses on β is also given. We conclude with some extensions.
Maximum Likelihood Estimation
Authors: Enders Craig K.
Published: September 2005

Maximum likelihood estimation identifies the population parameter values most likely to have produced a particular sample of data. Estimation involves the computation of a log likelihood, a value that quantifies the probability that the sample originated from a normally distributed population with a given set of parameters. Standard errors are obtained as a by‐product of estimation, and can be used to conduct significance tests. Differences between full and restricted maximum likelihood are discussed.
Ethics in Research
Authors: Miller Richard
Published: September 2005

This review of research ethics provides a history of the regulation of research ethics and a summary of ethical issues including the recruitment of human participants, informed consent, debriefing, deception, avoiding harm, confidentiality, risk/benefit assessment, vulnerable populations, methodological issues, the use of animals, and ethical publication standards.
Exact Methods for Categorical Data
Authors: Hershberger Scott L.
Published: September 2005

Exact tests evaluate the significance of a test statistic by using the test statistic's empirically derived sampling distribution instead of a theoretical sampling distribution. Preference for exact tests may occur in situations in which the sample size is small, or when the data have distributional deficiencies. Two well‐known exact tests, Pitman's test and Fisher's test, are described.
Expectancy Effect by Experimenters
Authors: Rosenthal Robert
Published: September 2005

Experimenter expectancy effect is the term referring to the unintended effect of experimenters' expectations or hypotheses on the results obtained from their research participants. Experimentally induced expectations have been shown to influence the behavior of psychological experimenters so as to increase the likelihood that their research participants will respond so as to confirm the experimenters' hypotheses or expectations. Experimental evidence for the operation of this phenomenon is described, and strategies for the control of experimenter expectancy effects are outlined.
Expectation
Authors: Walwyn Rebecca
Published: September 2005

The expectation of a random variable with a particular probability distribution is its theoretical mean or average value. Expectations can also be calculated for functions of random variables.
Experimental Design
Authors: Delaney Harold D.
Published: September 2005

Experimental design is concerned with procedures for evaluating the effects of treatments. The crucial role of random assignment to conditions for making causal inferences is stressed. Distinctions are made between quasi‐experiments and randomized experiments, crossed and nested factors, and between‐subject and within‐subject designs.
Factor Analysis: Exploratory
Authors: Pruzek Robert
Published: September 2005

Exploratory factor analysis (EFA) provides a way to account for intercorrelations or covariances among all pairs of variables in a battery using a relatively small number of latent variables called common factors. The method can be especially helpful for analyzing structural relationships in situations where observed variables are approximately linearly related to one another, and when individual‐level observations are fallible, that is, subject to errors of measurement. Exploratory factor analysis has gained prominence in many fields over many years, and it has been the subject of much praise as well as criticism. Psychometric and statistical practice has not fully caught up with contemporary appreciations of factor analytic and related methods, but past and recent developments suggest notable promise for continued applications in applied sciences.
Principal Components and Extensions
Authors: Michailidis George
Published: September 2005

In this paper, we discuss some extensions of principal components analysis. We focus in particular on extensions that deal with categorical multivariate data. We also briefly discuss various approaches that try to enable the techniques that handle nonlinearities in the data.
External Validity
Authors: Howell David C.
Published: September 2005

External validity refers to the degree to which any relationship that is found between an independent and a dependent variable can be generalized across people, settings, and times.
Face‐to‐Face Surveys
Authors: Doyle James K.
Published: September 2005

In a face‐to‐face survey, an interviewer is physically present to ask the survey questions and to assist the respondent in answering them. This survey delivery mode can offer many advantages over mail and telephone surveys in terms of the complexity and quality of the data collected. However, because these advantages come with significantly increased logistical costs as well as additional potential sources of response bias, face‐to‐face surveys are typically conducted only when there are compelling reasons to opt out of other survey delivery modes.
Facet Theory
Authors: Borg Ingwer
Published: September 2005

Facet theory (FT) is a methodology for designing and analyzing observations. A facet classifies objects of interest in one particular way. Several facets can be linked in a mapping sentence to yield schemes for the construction of multifaceted observations. Such designs also serve to predict certain structures for its data. To check these structures, FT has developed particular data analytic methods such as multidimensional scalogram analysis (MSA) or partial order structuple analysis with coordinates (POSAC), or suggests to use main‐stream techniques such as multidimensional scaling (MDS) in particular ways.
Factor Analysis of Personality Measures
Authors: Chaplin William F.
Published: September 2005

Factor analysis refers to a broad array of statistical models and techniques that have the general goal of describing underlying patterns in relational data. A common application of factor analysis is to items that assess personality, with the goal of identifying the major dimensions of human personality. These dimensions may be viewed as descriptive or causal depending upon the views of the investigator, and different numbers and types of dimensions have been proposed. Subjective decisions about the items to include in the analysis, the method of factor identification (principle components or principle factors), the number of factors, the rotation of the factors, and the interpretation of the factors all contribute to the diversity of the results obtained with different factor analyses. The goal of factor analysis is generally to simplify the complex structure of human personality, not to fully model that complexity. Thus, recent results from the application of confirmatory factor analysis to personality data that indicate that established factor models do not adequately model all the covariation among personality measures are neither surprising nor particularly relevant.
Factor Analysis: Multitrait–Multimethod
Authors: Wothke Werner
Published: September 2005

Confirmatory factor analysis is the preferred multivariate model for describing multitrait–multimethod matrices. Trait‐only factor analysis assumes that all common variation is due to shared traits. An expanded trait‐method factor model allows for additional variation due to shared methods. Experience shows that the trait‐only model fits few empirical matrices but that the more general trait‐method model is usually plagued by estimation problems. Reasons for the model failure are referenced.
History of Factor Analysis: A Psychological Perspective
Authors: Thorndike Robert M.
Published: September 2005

The history of unrestricted (exploratory) factor analysis is briefly reviewed from the perspective of its contribution to psychological theory, particularly models of mental abilities. Attention is focused on the contributions of Spearman and Thurstone. Various means of judging the quality of a factor solution are described. The logic of factor analysis as a means of identifying meaningful psychological constructs from a matrix of correlations is introduced from the algebraic and geometric perspectives.
Family History Versus Family Study Methods in Genetics
Authors: Burke Ailbhe , McGuffin Peter
Published: September 2005

Family history methods, where the familiality of a trait or disorder is explored by taking a history from one or more informants, are less costly and time‐consuming than family studies where a direct interview and examination of all available relatives of an index case is carried out. However family studies have a higher sensitivity. Studies based on families alone cannot distinguish between the effects of shared genes and shared environment.
Heuristics: Fast and Frugal
Authors: Hoffrage Ulrich
Published: September 2005

Fast and frugal heuristics can be used to make cue‐based inferences about an uncertain world. They are models of bounded rationality in the sense that they continue to yield a good performance even under conditions of limited time, limited knowledge, and limited computational complexity. They are specified in terms of search rules, stopping rules, and decision rules. They are robust and can outperform more complex strategies, because and not in spite of their simplicity.
F
echner,
G
ustav
T
Authors: Ross Helen
Published: September 2005

Fechner was a physicist who turned to psychophysics and philosophy. He was famous for Fechner's law ‐ that sensation increases with the logarithm of the stimulus intensity. His main contribution to statistics lay in the development of probabilistic procedures for measuring thresholds.
Field Experiment
Authors: Busk Patricia L.
Published: September 2005

An experiment conducted in a natural setting to show a causal relationship. These studies attempt to control the influence of environmental constraints on the relationship between the independent and dependent variables. They do not rely exclusively on natural conditions of the environment in that the independent variables are manipulated by the experimenter. Field experiments typically have less rigorous control features than laboratory experiments.
Finite Mixture Distributions
Authors: Everitt Brian S.
Published: September 2005

Finite mixture distribution are a particular class of probability distributions that are particularly useful for modeling data thought to contain relatively distinct subgroups of clusters of observations. They can be used as the basis of a cluster analysis of the data via estimation of both, the number of component distributions in the mixture and the parameters of these distributions.
Fisherian Tradition in Behavioral Genetics
Authors: Dickins David
Published: September 2005

R.A. Fisher did much to bring about the ‘Modern Synthesis’ of Mendelian genetics with Darwinian natural selection into a theory of evolution that worked. This was the fruit of his dual talent as a mathematician (particularly, but not exclusively, as a statistician) and a biologist. Though his training also in physics would have led him to welcome the subsequent transformation of parts of biology to ‘hard science’ status in the field of molecular and developmental genetics, his insights were in the domain of transmission genetics, acting in populations, from which he derived a cluster of fecund hypotheses that have been particularly influential in the field of behavioral biology/evolutionary psychology.
Fixed Effect Models
Authors: Vandenberg Robert J.
Published: September 2005

A term associated with the application of analysis of variance in experimental designs, fixed‐effect refers to a type of independent variable or factor. Most researchers exploying experimental designs use fixed‐effects in that the levels of the independent variables are finite, known, and in most cases, manipulated by the researcher to be reasonable different to detect a difference on the dependent variable.
F
riedman's Test
Authors: Sawilowsky Shlomo , Fahoome Gail
Published: September 2005

The nonparametric Friedman test expands the Sign (
S
) test to
k
related samples. The null hypothesis is that the samples come from the same population, which is tested against the alternative that at least one of the samples comes from a different population.
Functional Data Analysis
Authors: Ramsay James
Published: September 2005

Functional data analysis (FDA) models data using functions or functional parameters. The complexity of the functions is not assumed to be known in advance, so that methods are used for approximating these with as much flexibility as the data require.
Fuzzy Cluster Analysis
Authors: Manton Kenneth G. , Lowrimore Gene , Yashin Anatoli , Kovtun Mikhail
Published: September 2005

Usually in cluster analysis, an object is a member of one and only one cluster, a property described as ‘crisp’ membership. Fuzzy cluster analysis allows an object to have partial membership in more than one cluster. Selecting a good membership function is important to the success of the methods. The Grade of Membership model – which has a long history of usage in other contexts – is proposed as a straightforward way of performing fuzzy cluster analysis. The Grade of Membership model is illustrated by an example involving gene expression data.
Game Theory
Authors: Colman Andrew M.
Published: September 2005

Game theory models interactive decision making in terms of players, strategies, and payoffs. Conventional (individual) decision theory cannot prescribe rational choice in games, because a player cannot maximize expected utility without knowing how the coplayer(s) will act. Game theory, therefore, incorporates assumptions of common knowledge in addition to rationality. Rational players choose dominant strategies whenever possible, but many games lack such strategies. Every finite game has a Nash equilibrium, and this is the key solution concept of game theory, but the theory is indeterminate, because many games have multiple equilibria. Various criteria for equilibrium selection have been proposed. Experimental games provide information about the strategic behavior of human decision makers with bounded rationality. Evolutionary game theory helps to explain the evolution of cooperation and altruism and adaptive learning in repeated games.
Gene‐Environment Correlation
Authors: Dick Danielle M.
Published: September 2005

Genetic and environmental effects are not independent sources of influence on behavior, but rather, genotype can influence an individual's exposure to certain environments, how that individual experiences the environment, and the degree of influence that certain environments exert. This phenomenon is called
gene‐environment correlation
. Three types of gene‐environment correlation are discussed: passive, evocative, and active. Examples of each type of gene‐environment correlation, and support for these effects from the literature are presented.
Gene‐Environment Interaction
Authors: Jacobson Kristen C.
Published: September 2005

Gene‐environment interaction, or GxE, as it is commonly called in behavioral genetic literature, is the acknowledgement that genetic and environmental influences on variation in behaviors and traits may not act additively and independently, but may instead be dependent upon one another. There are three main strategies for assessing GxE interactions in behavioral genetic research, primarily through the use of adoption studies, twin studies, and studies of genotyped individuals. Each method has its relative strengths and weaknesses.
Generalizability
Authors: Berger Vance W.
Published: September 2005

Researchers generally study a phenomenon in a specific setting, and then try to generalize the obtained results to other settings. The degree to which the results of a study can be generalized from one setting to other settings is referred to as ‘generalizability’. Generalizing information from observations is essential for synthesis of knowledge, and there are some commonly accepted general rules for making generalizations. Here, we will first present a set of such commonly accepted rules and discuss the applications of these rules in behavioral sciences. We will then argue that generalization is not a mechanistic or statistical process, but rather that it requires abstract thinking. Therefore, any set of rules for generalizing information is subject to many exceptions.
Generalizability Theory: Basics
Authors: Boulet John R.
Published: September 2005

Generalizability (G) theory can be thought of as a comprehensive extension of classical test theory (CTT). The focus of G theory is on isolating and estimating the relative magnitude of specific sources of measurement error. This information can be used to optimize the sampling of measurement conditions in future studies. The major concepts underlying G theory, including the relevant terminology and nomenclature, are presented in this entry. The use of G theory is illustrated through data obtained from an assessment of the clinical skills of physicians. On the basis of these data, variance components are estimated, interpreted, and used to calculate reliability‐like coefficients. In addition, various Decision (D) studies are undertaken to provide a basic understanding of how a simple generalizability scenario can be extended to more complex designs, including those in which some sources of unwanted variation in the observations may be considered to be random, fixed, or nested. These studies demonstrate how an investigator can concentrate on targeting and minimizing measurement conditions that contribute the largest amounts of error, thereby increasing generalizability. Generalizability theory provides models and methods that allow an investigator to disentangle multiple sources of error. As a result, it is an important tool for producing reliable, valid, and comparable assessments.
Generalizability Theory: Estimation
Authors: Sanders Piet F.
Published: September 2005

Generalizability theory is a conceptual and statistical framework for the analysis and construction of measurement instruments. Among the most important concepts of generalizability discussed in the first section of this entry are the universe of admissible observations, universe and observed scores, random and fixed facets, crossed and nested designs, variance components, generalizability studies, decision studies, and generalizability coefficients. A discussion of the results of a generalizability study and a decision study of a crossed one‐facet random effects design and of a two‐facet crossed one‐facet random effects design is presented in the two following sections. A number of other designs that illustrate the versatility of generalizability theory are presented in the final section.
Generalized Additive Model
Authors: Everitt Brian S.
Published: September 2005

Generalized additive models (GAM) provide an extension to generalized linear models by allowing the explanatory variables in the model to be represented by smoothed functions, for example, locally weighted regression fits suggested by the empirical relationship between the response and each explanatory variable.
Generalized Estimating Equations (GEE)
Authors: Hardin James W.
Published: September 2005

Correlated datasets arise from repeated measures studies where multiple observations are collected from a specific sampling unit (a specific patient's status over time), or from grouped orclustered datawhere observations are grouped based on sharing some common characteristic (animals in a specific litter). When measurements are collected over time, the term longitudinal or panel data is preferred. Generalized estimating equations provide a framework for analyzing correlated data. This framework extends the generalized linear models methodology, which assumes independent data. We discuss the estimation of model parameters and associated variances via generalized estimating equation methodology.
Genotype
Authors: Elston Robert C.
Published: September 2005

The genotype of an organism is its genetic make‐up, as opposed to its phenotype, or outward appearance. If the two alleles at a locus are the same, the genotype is homozygous; otherwise it is heterozygous. If a heterozygote has the same phenotypic distribution as one of the corresponding homozygotes, the allele in that heterozygote is dominant and the other allele is recessive with respect to that phenotype. A multilocus genotype is made up of two haplotypes. In the case of a quantitative trait, dominance corresponds to intralocus interaction, epistasis to interlocus interaction.
Goodness of Fit
Authors: Mulaik Stanley A.
Published: September 2005

Goodness of fit is assessed by tests of exact fit and indices of approximation. The chi squared statistic is a test of exact fit. Many indices of approximation are based on estimates of the normalized noncentrality parameter, which is a measure of the degree of lack of fit for the model to the data that is invariant of sample size. Discussed are commonly used indices such as the CFI, the RMSEA, the GFI index, and Steiger's Γ1.
Goodness of Fit for Categorical Variables
Authors: von Eye Alexander , Bogat G. Anne , von Weber Stefan
Published: September 2005

The examination of frequency distributions of categorical variables often involves an evaluation of the appropriateness of probability models.Goodness‐of‐fitstatistics are suitable for this task. These statistics assess the discrepancy between the data and a probability model. Applications focus on (1) overall goodness‐of‐fit and (2) individual residuals. This entry describes the most frequently used goodness‐of‐fit statistics and presents an application in the context of logistic regression.
Graphical Chain Models
Authors: Wermuth Nanny
Published: September 2005

This article reviews the early twentieth century origins of graphical models and outlines the subsequent major developments from path analysis and conditional independence to the use of graphical models in representing relations among random variables, and, more recently, chains of such multivariate relations.
Graphical Methods Pre‐20th Century
Authors: Smith Laurence D.
Published: September 2005

Despite their utility for analyzing and presenting data, the use of graphs in science is a relatively late development and their emergence through history has been uneven and contested. Modern statistical graphics date largely to the pioneering work of William Playfair in the late eighteenth century. The gradual spread of graphical methods in the early nineteenth century was slowed by various antigraph prejudices, but eventually culminated in their enthusiastic reception during the second half of that century. During the Golden Age of graphics, graphs were used extensively in fields ranging from demography to laboratory physiology. Hailed as the universal language of science, graphs underwent a proliferation of novel formats, and they figured crucially in a number of scientific discoveries. The behavioral scientists of that period – including many of psychology's founding figures – made sophisticated applications of graphical methods, but such methods would be eclipsed by the rise of inferential statistics in the behavioral sciences after 1900.
Graphical Presentation of Longitudinal Data
Authors: Wainer Howard , Spence Ian
Published: September 2005

There are some ideas that are so ubiquitous that we cannot imagine the world without them: language and numbers come to mind as immediate examples. Data‐based graphics provide a third example. The graphical representation and communication of data is such a simple and clear process that it is no easier to think of a world before graphs than a world before arithmetic. Yet, graphs were invented and, moreover, invented relatively recently. The very first plots were graphs of longitudinal data. In this essay, we will trace some of the development of graphs for the display of longitudinal data.
Hawthorne Effect
Authors: Gottfredson Gary D.
Published: September 2005

The term
Hawthorne effect
has come to refer mistakenly to an increase in worker performance resulting merely from research or managerial attention to a work group. References to a Hawthorne effect in describing research have also come to connote flawed research. The remarkable improvements in worker productivity in the Hawthorne relay‐assembly experiment probably occurred because workers (a) began to receive pay contingent on the number of relays assembled, (b) set personal goals of increasing their assembly rate, and (c) attended to information about their productivity. The separation of the experimental workers from other assemblers also removed a social obstacle to improved productivity. This led workers to learn to assemble more relays per hour. The Hawthorne researchers intended to study the influence of arrangements that reduced fatigue on productivity, but the study design failed to rule out learning as the mechanism leading to improved performance.
Heteroscedasticity and Complex Variation
Authors: Goldstein Harvey
Published: September 2005

In the standard generalized linear model, the residual variance is assumed to be a constant or a well‐defined function of the linear predictor. In many applications, however, this assumption may not hold and interest will often focus on modeling the residual variation as a function of further explanatory variables, such as gender or age. The article shows how to formulate such models and provides extensions to the multilevel case and to the modeling of a full covariance matrix.
Hierarchical Models
Authors: Ployhart Robert E.
Published: September 2005

This chapter provides a brief and relatively nontechnical introduction to hierarchical linear models. The purpose of such models is first explained in graphical terms. This is followed by a description of the model and then an empirical example. Numerous primary sources are provided for readers to learn the more technical details.
Hill's Criteria of Causation
Authors: Goodman Karen J. , Phillips Carl V.
Published: September 2005

The term
criteria of causation
(or
causal criteria
) is often applied to Sir Austin Bradford Hill's (8) list of factors to consider before inferring causation from an observed association. This list is widely taught and cited, despite widespread cautions about the limitations of the list, by Hill and others, and despite lack of evidence that invoking such criteria is useful. This entry describes Hill's views on assessing causation and what others have since said on the subject of causal criteria.
Historical Controls
Authors: Berger Vance W. , Shafran Randi
Published: September 2005

Randomized trials, in which a single group of units is randomly allocated to two or more treatment conditions and then studied in parallel over time, is the gold standard methodology for reducing biases. Yet not every comparison is amenable to a randomized trial. For example, one cannot randomize subjects to their genders or races. Furthermore, even some comparisons that could theoretically be amenable to study with a randomized trial would not be, for ethical reasons. This would include studies of tobacco. Nonrandomized studies may still be parallel over time, in that all treatment groups are treated and studied over the same time interval. In some cases, though, one needs to use historical controls, and perform a before‐and‐after comparison. Strong conditions are required for such comparisons to be reliable.
History of Analysis of Variance
Authors: Tweney Ryan D.
Published: September 2005

First used by behavioral scientists in the 1930s, use of Analysis of Variance (ANOVA) grew quickly after World War II, and exactly paralleled incorporation of statistical significance testing in general. Detailed consideration of this history suggests several reasons for the pattern of slow growth, followed by rapid institutionalization. In particular, ANOVA stood duty as a warrant of scientific legitimacy among behavioral scientists, a fact that may also be relevant to understanding recent critiques by psychologists of its overuse and misuse.
History of Behavioral Statistics
Authors: Lovie Sandy
Published: September 2005

This article covers the growth of psychological statistics and the background to it from the nineteenth century to the twentieth. The general theme is that the nineteenth century was a time when statistics took up the challenge of a fundamentally uncertain world by embracing probability theory and providing an array of structuring principles to reduce the uncertainty.
History of Discrimination and Clustering
Authors: Hershberger Scott L.
Published: September 2005

The history of discrimination and clustering is primarily defined by the development of two quantitative procedures, discriminant analysis, and cluster analysis. Although they have different goals, the procedures address complimentary problems in classification, and thus are frequently used together.
History of Factor Analysis: A Statistical Perspective
Authors: Bartholomew David J.
Published: September 2005

This article provides a brief, semi‐technical history of factor analysis from 1904 to recent times. It begins with the pioneering work of Charles Spearman and finishes with the modern approach of covariance structure modeling, which has incorporated factor analysis into a larger statistical setting.
History of Multivariate Analysis of Variance
Authors: Hershberger Scott L.
Published: September 2005

Multivariate analysis of variance (MANOVA) can be thought of as a multivariate generalization of analysis of variance (ANOVA), in which more than one dependent variable is used to evaluate group differences. Wilks introduced lambda (Λ) in 1932 as a statistical test of the equality of group centroids. Wilks's Λ was derived from the likelihood ratio of the null and non‐null hypotheses usually specified in MANOVA. Subsequently, other MANOVA test criteria were developed, although all share with Λ the difficulty of unusually complex sampling distributions. Instead of using Λ directly, either an approximate chi‐square orFratio transformation of Λ is preferred.
History of Mathematical Learning Theory
Authors: Lovie Sandy
Published: September 2005

The article outlines the story of modern mathematical learning theory from 1950. In particular, the account provides a brief comparison of the earlier work by Hull with the newer approaches by Estes, Bush and Mosteller, and Luce. It is noted that the latter were thoroughgoing probabilists in that they argued that all learning could only be modeled by stochastic mechanisms.
History of Psychometrics
Authors: Buchanan Roderick D. , Finch Susan J.
Published: September 2005

Psychometrics developed as a means for measuring psychological abilities and attributes, usually via a standardized psychological test. Its emergence as a specialized area of psychology combined entrenched social policy assumptions, existing educational practices, contemporary evolutionary thinking, and novel statistical techniques. Psychometrics came to offer a pragmatic, scientific approach that both fulfilled and encouraged the need to rank, classify, and select people.
History of Surveys of Sexual Behavior
Authors: Everitt Brian S.
Published: September 2005

According to psychiatrist Anthony Storr, ’sexual intercourse is one of the most natural and certainly the most rewarding and the most life‐enhancing of all human experiences'. Few of us would argue with that, but although sex plays a vital part in our lives, it has for long periods been associated with guilt and shame, rather than enjoyment. Perhaps this explains why it is only in the last hundred years or so that psychologists, biologists, and others have tried to discover the truth about human sexual behavior in a scientific and objective manner. One of the main tools used in such investigations has been the sample survey, and this paper presents a brief (and therefore necessarily incomplete) history of surveys about sex.
History of the Control Group
Authors: Dehue Trudy
Published: September 2005

In contemporary behavioral and social research, scientific experimentation means comparing experimental groups to control groups and establishing the statistical significance of the resulting averages. Yet, this design is of a rather recent date. From the early nineteenth century, scientific experimentation with human beings has been a much debated topic. The rule of comparing groups, however, did not appear in methodological manuals until the second decade of the twentieth century. This article presents a history of the control group. It first discusses nineteenth‐century methodological views on human science experimentation, and explains why the notion of the control group could not be conceived at the time. Next, it describes and explains the introduction of control groups in the course of the twentieth century. By analyzing the nineteenth‐century values that excluded group comparison, it aims to identify the twentieth‐century principles endorsing it.
Hodges–Lehman Estimator
Authors: Lunneborg Clifford E.
Published: September 2005

The Hodges–Lehmann one‐sample procedure provides an efficient alternative to the sample median as an estimator of the location of a population, while the two‐sample procedure estimates the location shift parameter linking two populations.
Horseshoe Pattern
Authors: Everitt Brian S.
Published: September 2005

When applying multidimensional scaling to data that has an inherent one‐dimensional structure, for example, in a chronological study, the two‐dimensional scaling solution may often arrange the points in a ‘horseshoe’ shape, which is a consequence of the ‘blurring’ of the larger distances.
Inbred Strain Study
Authors: Wade Claire
Published: September 2005

Genetic contributions in complex trait analyses can be controlled or removed by the use of inbred strains as the test subjects. To be regarded as inbred strains, the mammals concerned must have been subjected to at least 20 generations of full‐sib mating (the expected inbreeding coefficient will be 98.6% or greater). Variation in the test scores observed within inbred strains will be of either environmental (treatment) origin or otherwise caused by random experimental error, since genetic variation is largely absent.
Incidence
Authors: Grietens Hans
Published: September 2005

Incidence is determined as the number of new cases of a disease in a population at a specified interval of time. Incidence rates provide information about the number of new cases or cases added to the sick population. Incidence studies are part of epidemiological research. They are conducted in medicine, psychiatry, and behavioral science. By means of an incidence study, one can truly identify individuals at risk for a disease, or risk factors. There is a dynamic relationship between prevalence and incidence, since prevalence rates are a function of both the incidence and the duration of a disease.
Incompleteness of Probability Models
Authors: Macdonald Ranald R.
Published: September 2005

Probabilities are unable to incorporate all the uncertainty that there is about anything that happens in the world because the world has to be packaged by someone before a probability model can apply. As a result, all probabilities and inferences from them are subjective and open to challenge.
Independent Component Analysis
Authors: Stone James V.
Published: September 2005

Independent component analysis (ICA) extracts statistically independent variables from a set of measured variables, where each measured variable is affected by a number of underlying physical causes. Extracting such variables is desirable because independent variables are usually generated by different physical processes. Thus, by extracting independent variables, ICA can effectively extract the underlying physical causes for a given set of measured variables.
Independent 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 2 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 models
or psychometric models. Common genetic and environmental factors influence all observed variables via a single psychometric factor, or underlying latent liability. The second class of models is referred to as independent pathway or biometric models. 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 do not necessarily cause similar groupings. This means that different clusters of variables can be identified for shared genetic and environmental effects. For this reason biometric models can yield different results compared to higher order phenotypic factor models, which implicitly assume identical groupings for genetic and environmental effects.
Influential Observations
Authors: Pettit Lawrence
Published: September 2005

An influential observation is one that has a large effect on our inferences. To measure the influence of an observation, we often compare the inferences we would make with all the data to those made excluding one observation at a time. This paper discusses several diagnostic measures of influence.
Information Theory
Authors: Mair Patrick , von Eye Alexander
Published: September 2005

Communication and information theory were founded by Shannon (1948). Shannon and Weaver (1949) developed the classical system of communication and the mathematical bases of communication. Information theory is concerned with measuring the degree to which a message provides one with knowledge one did not possess before. The broadest understanding of information theory includes all problems for which it is sensible to use the word
information
in its usual sense. The amount of information that is transmitted is scaled in units of
entropy
. Information theory allows one to analyze and assess a situation in which a signal that was selected from an
a priori
specified set is transmitted through a channel with limited capacity. The output of the channel is not determined by the input. Modern applications of information theory can be found in electronics and in the social sciences.
Intention‐to‐Treat
Authors: Molenberghs Geert
Published: September 2005

The randomized clinical trial paradigm is sketched, as well as the foundations on which its validity is based. Issues that jeopardize this validity, such as patient noncompliance and early withdrawal, are discussed. Intention to treat, being an important historical answer to this problem, is introduced, together with a set of criticisms and an indication of alternative approaches.
Interaction Effects
Authors: Aiken Leona S. , West Stephen G.
Published: September 2005

Interaction effects refer to the effects of particular unique combinations of variables on an outcome that would not be expected from their average effects. When two variables interact, the conditional effect of one variable at a particular value of the other variable depends on the specific value of the other variable. One variable moderates the effect of the other variable. When variables interact, the effects of the two variables in combination are nonadditive; their simultaneous effect is not the sum of their individual effects. Continuous and categorical variables may interact; a variety of patterns of interactions are possible.
Interaction Plot
Authors: Lovie Pat
Published: September 2005

An interaction plot is a simple line graph for examining interactions between variables in factorial designs. For a two‐factor design, the cell means on the response variable for each level of one factor are plotted over all the levels of the second. The resulting profiles are parallel when there is no interaction and nonparallel when interaction is present.
Internal Consistency
Authors: Schmitt Neal
Published: September 2005

The internal consistency of a measure refers to the degree to which items in the measure assess the same underlying construct. Coefficient alpha is widely used as an index of internal consistency though it has limitations in that regard. Limitations and other possibilities are discussed.
Internal Validity
Authors: Howell David C.
Published: September 2005

Internal validity refers to the degree to which any effect that is found for an experiment can be attributed to the action of the manipulated independent variable. This entry discusses 14 threats to internal validity and, in some cases, techniques for dealing with those threats.
Internet Research Methods
Authors: Stewart David W.
Published: September 2005

This article provides an introduction to the use of the Internet as a research tool. Methods for searching the Internet for secondary sources of information are explained and representative search tools and information resources are identified. The use of the Internet as a tool for gathering primary data is also discussed. Issues related to the evaluation of information obtained from the Internet are identified.
Interrupted Time Series Design
Authors: Ferron John , Rendina‐Gobioff Gianna
Published: September 2005

Interrupted time‐series designs allow researchers to examine the effect of an intervention. Multiple observations are obtained prior to the intervention to establish a baseline. Multiple observations are also obtained after the intervention. Effects are demonstrated when the observations after the intervention deviate from expectations derived from baseline projections.
Intraclass Correlation
Authors: Field Andy P.
Published: September 2005

Intraclass correlations are used to assess the consistency between measures of the same class (i.e., measures of the same thing). Two common uses are in comparing paired data (such as twins) on the same measure and assessing the consistency between judges' ratings of a set of objects. There are different conceptualizations of the intraclass correlation and the variance components used to calculate them in these different models. There is an important distinction between the cases when the measures are a single score or an average of multiple scores, and when a measure of consistency or a measure of absolute agreement is required.
Intrinsic Linearity
Authors: Goldsmith L. Jane , Berger Vance W.
Published: September 2005

In some cases in which a response variable is related to one or more predictor variables through a nonlinear relationship, suitable transformations of the response variable, predictor variables, parameters, or various combinations can lead to a linear model, thereby enabling the use of the powerful and efficient theory of linear models for estimation and prediction. Care must be taken with the use of such transformations to ensure that the resulting linear model has an error term of the appropriate, additive form.
INUSConditions
Authors: Horsten Leon , Weber Erik
Published: September 2005

We give a concise summary of Mackie's theory of causation, which can be seen as a sophisticated variant of the analysis of the notion of causation in terms of necessary and sufficient conditions. Special emphasis is placed on the notion ‘INUS condition’, which occupies a central place in Mackie's account.
Item Response Theory (
IRT
) Models for Polytomous Response Data
Authors: Keller Lisa A.
Published: September 2005

Many measurement tools are constructed of items that can be scored in several categories. For example, essay items, or other constructed response items, or personality and attitude inventories composed of Likert‐type items. Several item response models have been developed to deal with items of this type. The models are extensions of the dichotomous items presented in this volume. The five models discussed are the Graded Response Model, the Rating Scale Model, the Partial Credit Model, the Generalized Partial Credit Model, and the Nominal Response Model. Descriptions of the models are provided, along with graphical representations, and descriptions of how to interpret the parameters. The entry concludes with a list of articles that have applied these models in different contexts.
Item Response Theory (IRT) Models for Rating Scale Data
Authors: Engelhard George
Published: September 2005

The purpose of this entry is to provide a brief description of several IRT models that can be used to analyze rating scale data. Rating scale data are defined as responses scored in two or more ordered categories. Rating scale data represent the most common formats for collecting information from examinees or raters. The basic idea that motivates the use of IRT models for rating scale data is that the scoring ofm + 1 ordered categories with ordered integers (0, 1, …,m) using the assumption that there are equal intervals between the categories may not be justified. IRT models provide a framework to explicitly examine this assumption, and parameterize the categories without this assumption. The specific IRT models that are described in this entry are direct models (Partial Credit Model, Generalized Partial Credit, and Rating Scale Model) and indirect models (Graded Response Model and Modified Graded Response Model). Graphical procedures are used to illustrate various aspects of these IRT models.
Item Analysis
Authors: Luecht Richard M.
Published: September 2005

This entry presents a general database framework for scoring and analysis many types of selected‐response and constructed‐response item types. Specific item analysis methods and reporting techniques, including conditional statistics and discrimination indices, are presented within the context of this framework. A brief discussion of item response theory (IRT) item analysis methods is included.
Item Exposure
Authors: Robin Frederic
Published: September 2005

Often necessary in practice, the reuse of items over administrations is a threat to the validity of test scores. This entry briefly describes the nature of that threat and shows how item exposure can be used as a means for continuously evaluating, managing and monitoring it. This entry also outlines major strategies and methodologies for controlling item exposure within levels that testing programs can find acceptable.
Jackknife
Authors: Rodgers Joseph Lee
Published: September 2005

The jackknife is a resampling method that can be used to do hypothesis testing, to estimate standard errors, to define confidence intervals, and to estimate bias. This entry treats the history of the development of the jackknife, organizes the jackknife procedure in relation to other resampling procedures, and gives several examples.