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Peer reviewedNie, Jianyun – Information Processing and Management, 1989
Argues that most currently used information retrieval models are unsuitable to describe recent techniques such as semantic based retrieval. A more general model is presented in which the basis for information retrieval is viewed as logical implication and the estimation of the correspondence between queries and documents is described in terms of…
Descriptors: Evaluation Criteria, Information Retrieval, Logic, Mathematical Models
Peer reviewedAdams, Arthur J.; Shiffler, Ronald E. – Educational and Psychological Measurement, 1989
New methods of analysis--equations and graphs for iso-r(sup 2) contours--were introduced and used to illustrate location effects for pooled data sets. The "r(sup 2)" is the coefficient of determination. Results are used to highlight imprecise statements in the literature about the behavior of the correlation coefficient for pooled data…
Descriptors: Correlation, Equations (Mathematics), Graphs, Mathematical Models
Peer reviewedLaird, Nan M.; Louis, Thomas A. – Journal of Educational Statistics, 1989
Based on the Gaussian model, methods for using measurements that depend on the true attribute to compute rankings are proposed and compared. Measurements based on an empirical Bayes model produce estimates that differ from ranking observed data. Ranking methods are illustrated with school achievement data. (TJH)
Descriptors: Bayesian Statistics, Class Rank, Mathematical Formulas, Mathematical Models
Peer reviewedTanaka, Yutaka; Odaka, Yoshimasa – Psychometrika, 1989
A method is proposed for detecting influential observations in iterative principal factor analysis. Theoretical influence functions are derived for two components of the common variance decomposition. The major mathematical tool is the influence function derived by Tanaka (1988). (SLD)
Descriptors: Equations (Mathematics), Factor Analysis, Mathematical Models, Research Methodology
Peer reviewedWoodruff, David J. – Applied Psychological Measurement, 1989
Linear equating methods for the common-item non-equivalent populations design were compared when true-score correlation between the test and anchor was less than unity. Scores from two groups of approximately 300 examinees illustrated three methods: (1) the Tucker equating method; (2) the Angoff-Levine method; and (3) the Congeneric-Levine method.…
Descriptors: Comparative Analysis, Equated Scores, Mathematical Models, Research Design
Peer reviewedUmesh, U. N.; And Others – Educational and Psychological Measurement, 1989
An approach is provided for calculating maximum values of the Kappa statistic of J. Cohen (1960) as a function of observed agreement proportions between evaluators. Separate calculations are required for different matrix sizes and observed agreement levels. (SLD)
Descriptors: Equations (Mathematics), Evaluators, Heuristics, Interrater Reliability
Peer reviewedBeaton, Albert E.; Johnson, Eugene G. – Journal of Educational Statistics, 1990
The average response method (ARM) of scaling nonbinary data was developed to scale data from the assessments of writing conducted by the National Assessment of Educational Progress (NAEP). The method is described and illustrated with data from the 1983-84 NAEP. (SLD)
Descriptors: Elementary Secondary Education, Equations (Mathematics), Mathematical Models, Scaling
Peer reviewedThissen, David; Wainer, Howard – Journal of Educational Statistics, 1990
Confidence envelopes for one-parameter, two-parameter, and three-parameter logistic item response models are illustrated. M-line plots showing the genesis of the envelope and the density of lines in the confidence region are described and illustrated. (Author/SLD)
Descriptors: Equations (Mathematics), Graphs, Item Response Theory, Mathematical Models
Peer reviewedHumphreys, Lloyd G.; Drasgow, Fritz – Applied Psychological Measurement, 1989
Issues arising from difference scores with zero reliability that nevertheless allow a powerful test of change are discussed. Issues include the appropriateness of underlying statistical models for psychological data and the relationship between difference scores and power. Increases in reliability always increase power for a fixed effect size.…
Descriptors: Goodness of Fit, Mathematical Models, Power (Statistics), Psychometrics
Peer reviewedCavin, Edward S.; Ohls, James C. – Evaluation Review, 1990
A technique to estimate variances of weighted estimates in program evaluation is discussed. BRR estimates of variance are constructed from orthogonally weighted subsamples and can provide better estimates from complex samples than can other methods. Use of BRR is illustrated in a government evaluation of a food service program. (SLD)
Descriptors: Estimation (Mathematics), Evaluation Methods, Mathematical Models, Program Evaluation
Peer reviewedHarwell, Michael R.; Serlin, Ronald C. – Journal of Educational Statistics, 1989
Two forms, pure-rank and mixed-rank, of a nonparametric, general, linear model-based statistic that can be used to test several hypotheses are presented. A Monte Carlo study was used to investigate the distributional properties of these forms, and their use is discussed. (SLD)
Descriptors: Hypothesis Testing, Mathematical Models, Monte Carlo Methods, Simulation
Peer reviewedMensink, Ger-Jan; Raaijmakers, Jeroen G. W. – Psychological Review, 1988
A model of interference and forgetting based on the search of associative memory (SAM) theory is presented. The SAM theory describes retrieval processes in long-term memory. A model of contextual fluctuation processes is incorporated to provide a time-dependent variable to handle time-based interference phenomena. (SLD)
Descriptors: Cognitive Processes, Long Term Memory, Mathematical Models, Memory
Peer reviewedGrayson, D. A. – Psychometrika, 1988
Two-group classification is discussed when a unidimensional latent trait "theta" is appropriate for explaining data. If data have a monotone likelihood ratio, then optimal allocation rules can be based on its magnitude when allocation must be made to one of the two groups related to the unidimensional latent trait. (SLD)
Descriptors: Equations (Mathematics), Latent Trait Theory, Mathematical Models, Scoring
Peer reviewedSilvia, E. Suyapa M.; MacCallum, Robert C. – Multivariate Behavioral Research, 1988
The effects of several specification search strategies used with Covariance Structure Modeling to obtain more parsimonious models are examined. The initial models vary in their degree of "correctness." Restricting modifications to those justified by prior theoretical knowledge improves the success of a specification search. (TJH)
Descriptors: Analysis of Covariance, Mathematical Models, Research Methodology, Search Strategies
Peer reviewedLee, Sik-Yum; And Others – Psychometrika, 1989
The frequencies of "m" independent "p-way" contingency tables are analyzed by a model that assumes that the ordinal category data in each of "m" groups are generated from a latent continuous multivariate normal distribution. The model permits analysis of several groups of individuals simultaneously. (TJH)
Descriptors: Algorithms, Equations (Mathematics), Mathematical Models, Multivariate Analysis


