bluuebunny/crossref_metadata_2025 huggingface dataset:
Scaling of Preferential Choice
Authors: Böckenholt Ulf
Published: September 2005

Scaling models for preferential choice data serve the dual purpose to summarize choice data and to facilitate the forecasting of choices by decision makers facing possibly new or different variants of the choice options. The summary representation obtained by scaling methods can provide useful information for identifying both option characteristics that influence choice and systematic sources of individual differences in the evaluation of these option characteristics. Many scaling models are based on Thurstone's random‐utility approach and allow the analysis of different types of both revealed and stated choice data.
Scatterplots
Authors: Williams Siân E. , Wright Daniel B.
Published: September 2005

Scatterplots display the relationship between two variables. Most statistical and graphics packages allow a number of extra options to be added to provide more information about the bivariate relationship, the univariate information, and the characteristics of individual cases.
Second Order Factor Analysis: Confirmatory
Authors: Tisak John , Tisak Marie S.
Published: September 2005

Confirmatory second‐order factor analysis may be conceptualized as a further factor analyzing of the results of an initial factor analysis of some observed variables. Specifically, the initial or first‐order factor means, variances, and covariances are re‐analyzed into more general or abstracted variables. For pedagogical reasons, this approached is initially developed via a first and second‐order multivariate multiple regression analysis using measured or observed variables. Next by analogy, the approach is extended to latent variates or unobserved factors. Throughout an illustration is presented using Thurstone's Primary Mental Abilities, Horn and Cattell's Fluid and Crystallized Intelligences, and Spearmen's General Intelligence.
Selection Study (Mouse Genetics)
Authors: Henderson Norman
Published: September 2005

Artificial selection for the high and low expression of behavioral traits has long been successful. The apparent simplicity of selection experiments belies the fact that unless the effective breeding size of each parental generation is very large, genetic drift can add complications to genetic interpretations. Without replicate lines to estimate genetic variance due to random drift, the effects of drift on heritability estimates and as a possible source of spurious associations between the selected trait and other traits cannot be readily assessed.
Residuals in Structural Equation, Factor Analysis, and Path Analysis Models
Authors: Raykov Tenko
Published: September 2005

Residuals are defined for structural equation, factor analysis, and path analysis models. Their defining equations are given and it is pointed out how they can be obtained in empirical contexts. The different types of residuals are particularly useful when examining local goodness of fit for those models.
Structural Equation Modeling: Checking Substantive Plausibility
Authors: Jaffe Adi , Hershberger Scott L.
Published: September 2005

The process of construct validation involves a series of three steps, namely, concept definition, concept operationalization, and empirical confirmation. These steps lead to specifying and confirming a nomological network for the construct to be validated. Structural equation modeling efficiently confirms the substantive plausibility of the nomological network.
Linear Statistical Models for Causation: A Critical Review
Authors: Freedman D. A.
Published: September 2005

We review the basis for inferring causation by means of linear statistical models. Parameters should be stable under interventions, and so should error distributions. There are also statistical conditions that must be satisfied. Stability is difficult to establisha priori, and the statistical conditions are equally problematic. Therefore, causal relationships are seldom to be inferred from a data set by running regressions, unless there is substantial prior knowledge about the mechanisms that generated the data.
Structural Equation Modeling: Latent Growth Curve Analysis
Authors: Willett John B. , Bub Kristen L.
Published: September 2005

In this chapter, we use an example of panel data on the longitudinal development of reading in children to introduce the latent growth curve analysis. Latent growth modeling originates in a simple mapping of the standard multilevel model for change onto the general model available for covariance structure analysis (CSA). Here, we illustrate how the latent growth modeling approach can be enacted by using the CSA Y‐measurement model to contain the level‐1 individual growth model and the CSA structural model to contain the level‐2 model for interindividual differences in change. Because this mapping is possible, all fixed and random parameters in the multilevel model for change can be estimated by fitting the corresponding CSA model to data using standard structural equation modeling software (such as LISREL). Latent growth curve analysis is important because it capitalizes on the intrinsic flexibility of the general CSA model to test interesting and complex hypotheses about change, many of which are either more difficult or impossible to test using standard multilevel modeling approaches.
Structural Equation Modeling: Mixture Models
Authors: Vermunt Jeroen K. , Magidson Jay
Published: September 2005

This article discusses a modeling framework that links two well‐known statistical methods: structural equation modeling (SEM) and latent class or finite mixture modeling. Mixture SEM can either be viewed as a refinement of multivariate normal (MVN) mixtures, where the within‐class covariance matrices are smoothed according to a postulated SEM structure, or as a form of multiple group SEM, in which the group variable is unobserved. After introducing standard MVN mixtures, it is shown how the SEM framework can be used to restrict the class‐specific means and covariances. Furthermore, parameter estimation, model testing, and software is discussed, and an empirical example is provided.
Structural Equation Modeling: Multilevel
Authors: Steele Fiona
Published: September 2005

Factor analysis and structural equation modelling of clustered data are discussed. The application of these methods, with emphasis on the interpretation of results, is illustrated in analyses of students' scores on a set of science tests. These data have a two‐level hierarchical structure with students nested within schools.
Structural Equation Modeling: Nontraditional Alternatives
Authors: Rigdon Edward E.
Published: September 2005

A variety of techniques exist for modeling structural relations in situations where researchers' goals or data do not fit the demands of conventional Structural Equation Modeling. Researchers whose theory or data do not meet the rigorous standards of conventional Structural Equation Modeling (SEM) may employ Partial Least Squares (PLS), a technique based on principal components rather than common factors. Researchers seeking to find models, rather than testing a prespecified model, might employ Tetrad. Confirmatory Tetrad Analysis (CTA) allows researchers to test structural equation models without estimating model parameters. HyBlock conducts structured exploratory factor analysis, allowing researchers to model structural relations based on observed variables that are factorially complex.
Structural Equation Modeling: Software
Authors: Rigdon Edward E.
Published: September 2005

The first widely distributed special‐purpose software for estimating structural equation models appeared more than twenty years ago. Today, researchers can choose from a variety of packages that differ markedly in terms of their intellectual heritage, interface, statistical sophistication, flexibility, integration with other statistical packages, and price. Despite numerous advances, there is still substantial room for improvement.
Sensitivity Analysis in Observational Studies
Authors: Rosenbaum Paul R.
Published: September 2005

In an observational study, subjects are not randomly assigned to treatment or control, as they would be in a controlled clinical trial. As a consequence, differing outcomes in treated and control groups may not reflect effects of the treatment, but rather some way the groups were not comparable prior to treatment, that is, some hidden bias. A sensitivity analysis appraises how the conclusions of a study might be altered by hidden biases of various magnitudes.
Sequential Testing
Authors: Coad D. S.
Published: September 2005

The use of sequential methods in clinical trials dates back to the 1940s. With these methods, the accruing data are inspected periodically in order to assess whether the trial should be continued. Trials can be stopped when there is convincing evidence of a treatment effect or they can be stopped for futility. The use of sequential methods can reduce the numbers of patients in the trial compared with a design with a fixed sample size.
Setting Performance Standards: Issues, Methods
Authors: Plake Barbara S.
Published: September 2005

Setting performance standards has been a controversial topic over the years. In this entry, several examinee‐based and test‐based methods for setting performance standards on educational tests are introduced.
Sex‐Limitation Models
Authors: Eley Thalia C.
Published: September 2005

Sex differences are common in the behavioral sciences. In addition to modelling mean, prevalence and variance differences, behavioral genetic sex‐limitation models can identify the presence of both quantitative and qualitative sex differences. Quantitative sex differences refer to the fact that the proportion of variance due to genes, shared, and nonshared environment may differ between the sexes. Qualitative sex differences indicate whether the same or different genes or shared environment influence the two sexes. Models are described that test for both quantitative and qualitative sex differences in variation in the normal range, underlying liability of risk to disorder, and presence of an extreme group at one end of a distribution.
Shared Environment
Authors: Dick Danielle M.
Published: September 2005

The shared environment (also called common environment) refers to environmental influences that have the effect of making siblings more similar to one another. Shared environmental influences can include shared family experiences, shared peer groups, and sharing the same school and community. In general, there has not been strong evidence for shared environmental effects on many behaviors, particularly those measured in adults. Possible reasons for this are discussed. Shared environmental effects are evident in children and adolescents, but these effects generally decrease across the life span. New developments in behavior genetic methods have made it possible to specify shared environments of importance and to tease apart familial and nonfamilial sources of shared environmental influence.
S
hepard Diagram
Authors: de Leeuw Jan
Published: September 2005

The Shepard diagram is a version of the residual plot familiar from regression analysis that is useful in nonmetric scaling. We discuss its properties and illustrate it with an example.
Sibling Interaction Effects
Authors: Boomsma Dorret I.
Published: September 2005

Human beings often grow up with siblings and the behavior of one sibling may influence the behavior of the other sibling. In such cases, part of the ‘environment’ of individuals is predictable from the genotypes of their siblings. To detect sibling interactions, which are based on
genotype
, the variances and covariances of siblings reared at different densities (e.g., twins and singletons) or siblings of different degrees of genetic relatedness (e.g., mono‐ and dizygotic twins) may be compared. In the classical
twin design
, sibling interaction effects are suggested by a difference in phenotypic variance between mono‐ and dizygotic twins, and a pattern of twin correlations that is inconsistent with additive genetic influences.
Signal Detection Theory
Authors: Wixted John T.
Published: September 2005

Signal‐detection theory is a framework for understanding the process of decision making under conditions of uncertainty. Its essential claim is that subjective evidence for the presence or absence of a stimulus is a continuous variable. That is, evidence comes in degrees and is never entirely present or entirely absent even though the stimulus itself is. Although the average amount of subjective evidence is higher on trials in which the stimulus actually is present, trial‐to‐trial variability is such that no evidence value perfectly distinguishes stimulus‐present trials from stimulus‐absent trials. As such, the observer is assumed to select a criterion evidence value above which the stimulus is declared to be present and below which it is declared to be absent. This way of thinking sheds light on an extremely wide range of decision problems ranging from auditory detection to the detection of a psychiatric condition, and it offers a measure of discrimination (
d
′) that, unlike percent correct, is theoretically uncontaminated by response bias.
Signed Ranks Test
Authors: Sawilowsky Shlomo , Fahoome Gail
Published: September 2005

The Signed Rank test is a nonparametric alternative to the one‐sample or paired samples parametric
t
Test.
Simple Random Assignment
Authors: Thach Chau , Berger Vance W.
Published: September 2005

There are two types of simple random assignment – unrestricted random assignment and the random allocation rule. Unrestricted random assignment occurs when each subject in a study is assigned to a treatment with a fixed probability, completely independent of all previous assignments in the study. The total sample size does not need to be known in advance for this procedure. In contrast, the total sample size does need to be known in advance when using the random allocation rule, which occurs when a randomly chosen subset of subjects in a study is assigned to one treatment group and the other subset is assigned to the other treatment group. Unrestricted random assignment is the easiest and best way to minimize various biases, such as selection and accidental bias. However, it can also result in substantial imbalance if the sample size is small or in the early stages of the study. The random allocation rule also has little selection (if the assignment for all subjects is done simultaneously) and accidental bias.
Simple Random Sampling
Authors: Berger Vance W. , Zhang Jialu
Published: September 2005

When a census of the entire population of interest is difficult to obtain, a sample is often used. There are many sampling designs that can be used to obtain a sample that would hopefully be representative of the population, and among these sampling designs, several allocate the same inclusion probability to each unit in the population. If each unit in the population has the same inclusion probability and all the units are independent, then we have a simple random sample. Another way to formulate this is to state that each sample consisting of a given number of units has the same probability of becoming the selected sample.
Simple V Composite Tests
Authors: Macdonald Ranald R.
Published: September 2005

If a null hypothesis takes the form θ = 
c
, where c is a constant and θ is the only unknown parameter in the supposed chance probability distribution, then this hypothesis is called a simple hypothesis. Where the chance distribution has more than one unknown parameter, the null hypothesis is said to be composite. Often, but not always, composite hypotheses are phrased in terms of several parameters. Examples include θ
1
 = 
c
1
, θ
2
 = 
c
2
, …θ

k

 = 
c

k

or θ
1
 = θ
2
 = θ
3
 = ⋯ = θ

k

. Where this is the case, the overall null hypothesis can be split into separate testable component hypotheses and this raises multiple testing issues.
Simulation Methods for Categorical Variables
Authors: von Weber Stefan , von Eye Alexander
Published: September 2005

The results of a simulation study on the performance of measures for the analysis of 2 × 2 tables are reported. The simulations included 11 measures for 2 × 2 tables: Pearson's?, the standard normal z, the log‐odds ratio, the log‐linear interaction, Goodman's (1991) weighted log‐linear interaction, Vogel's z, the binomial test, Lehmacher's (1981) asymptotic hypergeometric test, Perli, Hommel, and Lehmacher's (1985) asymptotic test, Lindner's (1984) exact hypergeometric test, and Lausch and von Weber's (2002) adaptation of Dunkl and von Eye's (1990) test. The factors varied in the simulations were (1) type of sampling distribution, (2) sample size, (3) strength of association in the 2 × 2 table, (4) the symmetry of the distribution in the 2 × 2 table, and (5) the nominal a. Results suggest that the distribution of these 11 tests is very near the normal under all conditions. Of the five factors, only the type of the sampling distribution has no strong effects on the ß‐curves of the 11 measures. Finally, it was found that the 11 measures respond differently to the five factors such that the rank order of performance varies with the simulated conditions.
Simultaneous Confidence Interval
Authors: Dracup Chris
Published: September 2005

When a number of parameters are to be estimated at the same time, simultaneous confidence intervals are employed to control the probability that all the intervals to be constructed will contain their true parameter values. If Tukey's method is used to calculate simultaneous 95% confidence intervals for the differences between all pairs of population means in a multigroup experiment, then, in the long run, all the intervals so constructed will contain the true population mean differences for 95% of experiments. Scheffé's method allows the construction of simultaneous confidence intervals for more complex contrasts between means.
Single and Double‐Blind Procedures
Authors: Well Arnold D.
Published: September 2005

When an experiment is conducted, there are many factors other than the independent variable that may influence the behavior of both participants and researchers, possibly leading to biased results. Sources of bias that depend on knowledge about the purpose of the experiment or the details of the research design may be removed by keeping participants and researchers ‘blind’ to such information.
Slicing Inverse Regression
Authors: Chen Chun‐Houh
Published: September 2005

Sliced inverse regression (SIR) is a computationally simple and fast method for reducing the dimension of the explanatory variablesxin regression problems. SIR does the following: (a) it determines the dimension of a subspace spanned by the linear combinations ofxthat contains all information needed for describing the relationship betweenxand the output variableY; (b) it assesses the significance of the contribution from each input variable to dimension reduction; (c) it provides a foundation for further exploratory graphical analysis and nonparametric regression. (Color versions of the figures presented in this article can be obtained fromhttp://gap.stat.sinica.edu.tw)
Skewness
Authors: Wuensch Karl L.
Published: September 2005

A skewed distribution is one that has an asymmetric tail on the left (negative) or the right (positive) side. Skewness is most commonly defined in terms of the third moment about the mean. Measures of skewness may alert the behavioral researcher to the need to investigate outliers, consider using the median rather than the mean, transform the data, and/or choose analytic techniques that do not assume normality.
Social Validity
Authors: Kazdin Alan E.
Published: September 2005

Social validity is a concept that is used in intervention research in which the focus is on treatment, prevention, rehabilitation, education, and, indeed, any area in which the goal is to produce change in human behavior and adaptive functioning. Social validity draws attention to whether the goals of treatment, the intervention techniques that are used, and the outcomes that are achieved are acceptable, relevant, and useful to individuals who are stakeholders, consumers, or recipients of the intervention. In clinical trials of treatment, judgments are made about the effects of the intervention based on statistical significance and magnitude of effect. Social validity alerts us to the issues about the applied value of the intervention, and whether the intervention has had a palpable impact and actually helped people in ways that are evident in everyday life.
Teaching Statistics: Sources
Authors: Beins Bernard C.
Published: September 2005

Seven books, six journals, and a web page devoted to material on teaching statistics are reviewed. Sources are ordered from general to technical, and examples illustrative of the content are provided.
S
pearman's Rho
Authors: Kornbrot Diana
Published: September 2005

Spearman's rho,
r

s

, is a correlation measure of association based on ranks of scores rather than raw scores. 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.
Sphericity Test
Authors: Keselman H. J.
Published: September 2005

Classical test statistics, such as the usual
F
test, for the analysis of repeated measures or longitudinal treatment effects, will provide accurate assessments (i.e., correct Type I error probabilities) of null hypotheses when their assumptions of independence, normality, and homogeneity hold. Homogeneity in this context is referred to as sphericity or circularity. This paper enumerates the validity assumptions for simple‐order and higher‐order repeated measures designs, as well as discussing why for many behavioral science applications sphericity will not be satisfied, and concludes by noting procedures that researchers can adopt to circumvent the biasing effects of nonsphericity.
Standard Deviation
Authors: Clark‐Carter David
Published: September 2005

The standard deviation is a measure of spread (or dispersion). It is defined as the square root of the variance. It is used to put a mean in context. It allows the comparison of different distributions of numbers by showing their relative spread.
Standard Error
Authors: Clark‐Carter David
Published: September 2005

The standard error is the standard deviation of the distribution of a sample statistic. The standard error of the mean (SEM) plays an important role in inferential statistics such as
z
tests and
t
Tests and in confidence intervals.
Standardized Regression Coefficients
Authors: Landis Ronald S.
Published: September 2005

Standardized regression coefficients reflect the standard deviation change in a criterion variable associated with a standard deviation change in a predictor variable. Standardized regression coefficients permit comparisons of predictor–criterion relationships across studies in which the variables have been measured using different units of measure.
Stanine Scores
Authors: Clark‐Carter David
Published: September 2005

A stanine score is a form of standardized score on a nine‐point scale. It is used to compare scores of different people on the same measure or the same person on different measures.
Star and Profile Plots
Authors: Everitt Brian S.
Published: September 2005

Star and profile plots are graphical displays for multivariate data. They consist of an array of small individual plots, each corresponding to a single multivariate observation. In any individual plot, every variable is represented by a line whose length is proportional to the value of the variable. In a star plot, the lines form spokes radiating from a central point, while in a profile plot, they are vertical spikes. In each case, the ends of the lines are connected across variables.

These displays can provide useful insight into the structure of the data, especially when groups of plots with similar shapes, or particular individuals that seem different from the rest, can be identified.
Test Translation
Authors: Hershberger Scott L. , Fisher Dennis G.
Published: September 2005

Semantic and conceptual equivalence should characterize tests translated from one language to another. Semantic equivalence concerns the degree to which the ideas implied by the words and phrases of the original test have been captured by those in the test's translation. Various methods of confirming semantic equivalence include direct translation, translation/back‐translation, the ultimate test, the parallel blind technique, and the random probe technique. Semantic equivalence is most likely when the two test versions have been developed in tandem. Conceptual equivalence concerns the similarity of the construct measured by the two test versions. Methods for confirming conceptual equivalence tend to be more statistical than those methods used to confirm semantic equivalence, and include exploratory and confirmatory factor analyses, and item response theory (IRT)
Statistical Models
Authors: Kenny David A.
Published: September 2005

Statistical models summarize by a set of equations the covariation between a set of variables. Models can either be causal or predictive. Models usually contain a deterministic component or fit and a random component or error. Assumptions are made about the distribution of the error component. Models can be either exploratory or confirmatory.
Stem and Leaf Plot
Authors: Lovie Sandy
Published: September 2005

The stem and leaf plot is a more information‐rich version of the basic histogram that allows one to make judgments about the sample shape besides permitting reconstruction of the original data.
Decision Making Strategies
Authors: Ranyard Rob
Published: September 2005

Individual decision making is a form of problem solving with a focus on the need to choose among alternative courses of action. The goal‐state of a decision problem is usually ill‐defined and a matter of personal preference. A decision strategy is a sequence of mental operations and actions that resolve conflicts among the available options in either value, degree of risk, or both. In this entry, alternative strategies to resolve value conflicts are described, varying on two basic characteristics: compensatory versus noncompensatory, and attribute‐based versus alternative‐based. Two‐stage and multistage strategies, strategies for decisions involving risk, and some current issues in decision‐process research are discussed.
Stratification
Authors: Berger Vance W. , Zhang Jialu
Published: September 2005

When a population is composed of several subpopulations and the subpopulations vary considerably on the factors in which we are interested, stratification can reduce the variability of the estimates by dividing the population into relatively homogeneous subgroups, and treating each subgroup separately. This concept can be applied for stratified sampling (sampling from within each stratum) and stratified random allocation of subjects that need not constitute a random sample, stratified or not.
Structural Equation Modeling and Test Validation
Authors: Zumbo Bruno D.
Published: September 2005

The use of structural equation modeling in validity research is described and demonstrated in the context of an example wherein a researcher is providing construct and predictive validity evidence for inferences made from scores on the Center for Epidemiologic Studies Depression (CES‐D) scale. In this light, current concepts of validity are briefly overviewed and contrasted with those found in many research methods texts. In addition, two special cases of the generalized linear structural equation model, confirmatory factor analysis and multiple indicators multiple causes models for ordinal items, that are particularly well suited for measurement validity research, are introduced.
Structural Equation Modeling: Overview
Authors: Schumacker Randall E.
Published: September 2005

Structural equation modeling (SEM) software programs analyze theoretical models using a sample variance–covariance matrix, although a correlation matrix with means and standard deviations for the observed variables can be input because these values can be used to create a variance–covariance matrix. A LISREL‐SIMPLIS program is given below to illustrate how the theoretical model and sample data are included in a SEM program.
Structural Zeros
Authors: Berger Vance W. , Zhang Jialu
Published: September 2005

Empty or zero cells in a contingency table can be classified as structural zeros or random (sampling) zeros. A cell with a structural zero has an expected value of zero, which means that not only did no observations in the data set at hand fall into that cell, but in fact that no observation
could
fall into that cell. Structural zeros are not part of the data. Therefore, they do not contribute to the likelihood function or model fitting. A contingency table containing structural zeros is, in some sense, an incomplete table. The usual χ
2
test cannot be applied directly.
Subjective Probability and Human Judgement
Authors: Ayton Peter
Published: September 2005

Psychological research on Subjective Probability has used a variety of strategies to investigate how reliable people are at judging probabilities. The issue is of considerable practical importance as all sorts of critical decisions depend on assessment of the likelihood of events for which there is neither a method for mathematically computing its probability nor actuarial data for measuring it empirically. Since the development of Decision theory, a plethora of management technologies have emerged that can take advantage of likelihood information for decision support. While the concept of subjective probability remains a theoretically contentious notion for some, people can and do express and request judgments of the likelihood of uncertain events. Here, research investigating the validity of subjective probabilities – judged likelihood – is reviewed.
Summary Measure Analysis of Longitudinal Data
Authors: Everitt Brian S.
Published: September 2005

There are a variety of methods of analysis for longitudinal data, but one of the most straightforward is the use of summary measures that essentially reduce the problem from multivariate to univariate. Once a suitable summary measure has been chosen, analysis usually involves simple techniques such as
t
Tests, analysis of variance, or their nonparametric analogues.
Survey Questionnaire Design
Authors: Tourangeau Roger
Published: September 2005

Survey questionnaire design encompasses a variety of activities ranging from library research to formal experiments that estimate the reliability or validity of different versions of a questionnaire. Although handbooks with advice for survey questionnaire designers first appeared more than 50 years ago, it has only been during the last 20 years that researchers have attempted to provide a firm theoretical and empirical foundation for such guidelines, based on a cognitive analysis of the survey response process. The last 20 years or so have also seen an expansion in the methodological and statistical tools used in developing survey questionnaires; these tools include focus groups, cognitive interviews, field tests, behavior coding of respondent‐interviewer exchanges, reinterviews, and experiments.
T
au‐Equivalent and Congeneric Measurements
Authors: Berge Jos M. F. Ten
Published: September 2005

To evaluate the reliability of a test, one needs a parallel test. When parallel tests are absent, one option is to rely on hypotheses such as that the test parts are essentially tau‐equivalent or congeneric, having only one factor in factor analysis. Such hypotheses are unrealistic, except that a test may be congeneric when there are only three test parts; in that case, however, it is impossible to decide what the number of factors really is. A preferable option is to use lower bounds to reliability, such as coefficient alpha. The Jackson & Agunwamba greatest lower bound (glb) is better than alpha but has a sampling bias problem. Bias correction methods are still under study. Nevertheless, when compared to reliability estimates derived from the hypothesis of congeneric tests, the glb is already to be preferred, because these estimates behave very similarly to glb, and display the same sampling bias but do not rely on the hypothesis of a congeneric test
Teaching Statistics to Psychologists
Authors: Spilich George
Published: September 2005

The introduction of computerized statistical packages over the past three decades has dramatically altered graduate education in psychology for better and for worse. Students now are more broadly trained in technique but this improvement has occurred at the expense of training in design. The availability of statistical packages in the hands of those without professional training has implications for psychology as a profession.
Telephone Surveys
Authors: Driskell Robyn Bateman
Published: September 2005

Telephone survey methodology is often the preferred approach to surveying as it is a valid and reliable means of collecting data. The advantages of telephone surveys include cost efficiency, reduced survey time, and the ability to reach a large, representative sample. With the recent technologies of random‐digit dialing and computer‐assisted telephone‐interviewing, telephone survey methodologies have enhanced and improved. While some limitations exist in telephone surveys, the advantages outweigh the disadvantages, resulting in an efficient and effective method for collecting data.
Test Bias Detection
Authors: Beller Michal
Published: September 2005

Much of the criticism of psychological tests is derived from the observation that certain groups differ extensively in test performance. However, much of the polemic concerning the issues of test bias rests on two main areas of confusion: (a) differences in test performance among groups are often regarded, in and of themselves, as an indication of test bias, ignoring performance on the external criterion that the test is designed to predict. Often, groups that perform poorly on tests also tend to perform poorly on measures of the criterion. Furthermore, analysis of the relationship between tests and criteria often reveals similar regression lines for the various groups; and (b) the issue of test bias is often confused with the possibility of bias in the content of some individual items included in a test. Group differences in test performance are attributed to the content of specific items, and rather than eliminating problematic items in a systematic way (i.e., checking all items for differential performance), this confusion has, in some cases, led to suggestions of a wholesale rejection of reliable and valid test batteries.
Test Construction
Authors: Gierl Mark J.
Published: September 2005

Item response theory (IRT) provides a method to determine the amount of psychometric information each item (i.e., item information function) and combination of items (i.e., test information function) provides in the estimation of an examinee's ability. In a 1977 paper, Lord described a basic four‐step procedure for using these functions to construct a test using calibrate items from a bank. Lord's procedure requires specifying a target function, selecting items from the bank to fill this target, adding the item information functions together during the selection process, and continuing until the test information function approximates the target function. Some key issues related to specifying the target function and selecting items are presented and discussed. More recent developments in test construction using item and test information functions are also described.
Independence: Chi‐square and Likelihood Ratio Tests
Authors: Brown Bruce L. , Hendrix Kent A.
Published: September 2005

Chi‐square is the most common and simplest test of independence. It is a nonparametric test intended for use with categorical data. The conceptual basis for testing independence with a chi‐square analysis is closely related to the rationale for using F tests in the analysis of variance to test interactions among two or more independent variables. Indeed, the
general linear model
that applies to analysis of variance can also be applied as a logarithmic linear analysis of categorical data. These
log‐linear models
are a more general, elegant, and sophisticated way of testing independence based upon the
general linear model
.
Tetrachoric Correlation
Authors: Hershberger Scott L.
Published: September 2005

The tetrachoric correlation is used to estimate the Pearson product‐moment correlation between two continuous, bivariate‐normally distributed variables from dichotomized versions of those variables. Two common areas of application of the tetrachoric correlation are to the behavior genetic analysis of twin data and to the factor analysis of item data from cognitive ability tests.
Theil Slope Estimate
Authors: Lunneborg Clifford E.
Published: September 2005

A nonparametric hypothesis test for the slope in simple linear regression proposed by Theil (1950) also provides the basis for a distribution‐free estimate of that parameter.
Three Dimensional (3
D
) Scatterplots
Authors: Wright Daniel B. , Williams Siân E.
Published: September 2005

A three‐dimensional scatterplot displays the relationship between three continuous variables at once. The data are represented as a cloud of points within the three‐dimensional space formed by the three axes of the plot. Such plots can be difficult to interpret and other methods of representing the third variable are generally more effective.
Three‐Mode Component and Scaling Methods
Authors: Kroonenberg Pieter M.
Published: September 2005

In this entry, the basic principles and rationale for three‐mode analysis of three‐way data are introduced. The wealth of the three‐mode world is sketched, and the power of its methods is illustrated with a three‐mode component analysis analyzing how children cope in several school‐related situations and an individual differences scaling analysis of the perception of pain.
Time Series Analysis
Authors: Brockwell P. J.
Published: September 2005

The time‐domain approach to the modeling and forecasting of time series is outlined. Weakly stationary processes are introduced, and an introduction to ARMA processes and their properties is given. Estimation, model selection, and prediction with these models are considered, and extensions to multivariate time series, state‐space models and nonlinear models are indicated.
Tree Models
Authors: Daniels Richard , Shi Dailun
Published: September 2005

Tree models are statistical tools which allow for the estimation of hypothetical parameters that represent probabilities of unobservable events. They are appropriate for analyzing categorical data, where each observation belongs to one of a finite set of categories. We describe the structure and characteristics of multinomial tree models, and provide an illustrative example.
Trellis Graphics
Authors: Everitt Brian S.
Published: September 2005

In trellis graphics two or more variables are plotted for (conditioned on) different values or categories of a given variable (or variables). Component graphs for each level of the selected variable are arranged in a single display in order to make comparisons. Many different types of plot lend themselves to this treatment, including
scatterplots
and
three‐dimensional scatterplots
. Trellis graphics are helpful help in understanding both the structure of the data and how well proposed models for the data actually fit.
Trend Tests for Counts and Proportions
Authors: Liu Li , Berger Vance W. , Hershberger Scott L.
Published: September 2005

In a contingency table, one may be interested in whether there is a trend along the row variable or the column variable. In an R by 2 or 2 by C contingency table, where one variable is binary and the other is ordinal, the Cochran–Armitage test for trend can be used to test whether the binomial proportions have a linear trend across the ordinal variable. In an R by C contingency table, where one variable is ordinal and the other variable is nominal, the Jonckheere–Terpstra trend test can used to determine whether, within each level of the nominal variable, the proportions are distributed identically.
Trimmed Means
Authors: Wilcox Rand R.
Published: September 2005

A trimmed mean discards a fixed proportion of the largest and smallest observations and averages the rest. With a proper choice for the amount of trimming, good efficiency can be obtained under normality as well as under nonnormal distributions where the mean performs poorly.
T‐Scores
Authors: Clark‐Carter David
Published: September 2005

T
‐scores are standardized scores whose distribution has a mean of 50 and a standard deviation (SD) of 10. They are useful to compare, for example, different people on the same measure or the same person on different measures.
T
ukey Quick Test
Authors: Sawilowsky Shlomo
Published: September 2005

A distribution‐free test of the equivalence of two population medians. Because of its ease of computation, it is sometimes known as Tukey's Quick Test.
Twin Designs
Authors: Spinath Frank M.
Published: September 2005

The classical twin study compares the phenotypic resemblances of identical or
monozygotic
(MZ) and fraternal or
dizygotic
(DZ) twins. MZ twins derive from the splitting of one fertilized zygote and, therefore, inherit identical genetic material. DZ twins are first‐degree relatives because they develop from separately fertilized eggs and are 50% genetically identical on average. It follows that a greater within‐pair similarity in MZ, compared to DZ twins suggests that genetic variance influences the trait under study.
Twins Reared Apart Design
Authors: Segal Nancy L.
Published: September 2005

Twins reared apart provide direct estimates of genetic influence. Past and ongoing studies show that genetic effects on behavioral development are pervasive. Twins reared apart can be used to test hypotheses generated by a variety of theoretical perspectives.
Two by Two Contingency Tables
Authors: Liu Li , Berger Vance W.
Published: September 2005

Two by two contingency tables are generated by cross classifying subjects by two binary variables. In such tables, one may be interested in testing for an association between the two variables, and, if it is found, then also in estimating the strength of the association. The χ
2
test of independence and Fisher's exact test are illustrated to test independence. The difference in proportions, relative risk, and odds ratio are shown to measure the association. Sensitivity, specificity, the false positive rate, and the false negative rate are used to evaluate a test method. Simpson's paradox is introduced to illustrate the difference between marginal tables and partial tables.
Two‐Way Factorial: Distribution‐Free Methods
Authors: Toothaker Larry E.
Published: September 2005

Nonparametric and resampling approaches for the two‐way factorial design include permutation tests, bootstrap tests, the rank transform, aligned ranks tests, tests on trimmed means, and a rank‐based ANOVA method that allows heteroscedastic variances, one known as the BDM method, or combinations of these such as bootstrap tests on trimmed means. Research shows the BDM method, parametric tests on trimmed means, and bootstrap tests on trimmed means to be the most promising methods in terms of α‐control and power.
Ultrametric Inequality
Authors: Murtagh Fionn
Published: September 2005

The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Ultrametric distance is defined from p‐adic valuation.
Ultrametric Trees
Authors: Murtagh Fionn
Published: September 2005

The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Any hierarchical agglomerative clustering can be considered as the mapping of points in a metric or indeed nonmetric space into an ultrametric space.
Unidimensional Scaling
Authors: de Leeuw Jan
Published: September 2005

We discuss the one‐dimensional special case of multidimensional scaling and the various algorithms that have been proposed to solve the corresponding computational problem. We concentrate on least squares unidimensional scaling and on the combinatorial nature of finding the best scaling. Examples from paired comparison analysis and genetic location analysis are discussed.
Urban,
F M
Authors: Ross Helen
Published: September 2005

Urban was born in Austro‐Hungary, worked in the USA, suffered under the First and Second World Wars, and lived in various countries. He contributed probability weightings to the calculation of the psychometric function.
Utility Theory
Authors: Read Daniel , Airoldi Mara
Published: September 2005

The term utility is used to denote either the quantity of pleasure or pain arising from an outcome, or the preferences over outcomes reflected in choice behavior. The first use of the term is associated with utilitarian philosophers of the last century, and the second with twentieth‐century economists. Recent developments in psychology and behavioral economics have attempted to reconcile both uses of the term.
Validity Theory and Applications
Authors: Sireci Stephen G.
Published: September 2005

Theories regarding ways in which test scores should be validated are about as old as the practice of testing itself. In this entry, I describe contemporary validity theory using an historical perspective. I also discuss current approaches for validating tests and other measures used in the behavioral sciences. Validity is a complex topic involving both philosophy of science and statistical methods. Thankfully, there is a long history to guide those who need to evaluate particular measures for specific purposes.
Variable Selection
Authors: Mulaik Stanley A.
Published: September 2005

Choosing from among variables those that are to be deemed important can be difficult. Such choices should begin with an understanding of what a variable is and what the specific variables in question are. Attributions of importance should be influenced by both theoretical and empirical information.
Variance
Authors: Clark‐Carter David
Published: September 2005

The variance is a measure of spread or dispersion. It is defined as the mean of the squared deviations of a set of numbers about their mean. Many inferential procedures draw on the variance or its close relative, the standard deviation.
Variance Components
Authors: Longford Nicholas T.
Published: September 2005

Variance components provide a compact description of the contexts present in the studied problem. In the simplest models, the influence of each context is identified with a contribution to the overall variance. Observations within contexts are correlated, and their correlation depends on the relative sizes of the variance components.
W
alsh Averages
Authors: Lunneborg Clifford E.
Published: September 2005

Walsh averages date back to 1949 and are used in the nonparametric estimation of the median, providing both a point estimator and confidence bounds.
W
ilcoxon–
M
ann–
W
hitney Test
Authors: DePuy Venita , Berger Vance W. , Zhou YanYan
Published: September 2005

The Wilcoxon‐Mann‐Whitney test evaluates the difference in medians between two similarly shaped populations, which have the same variance. This nonparametric test is similar to the two‐sample Student's
t
Test. The primary differences are that the
t
Test requires the assumption of normality, while the Wilcoxon‐Mann‐Whitney test can be performed where only rankings, that is, ordinal data, are recorded. While exact computations of the test statistic are possible, a large sample approximation is often used for ease of calculation. Both methods are available in various commercial statistical packages.
W
insorized Robust Measures
Authors: Wilcox Rand R.
Published: September 2005

Winsorizing observations leads to robust measures of location, variation, and correlation, and it plays a fundamental role when making inferences about trimmed means.