bluuebunny/crossref_metadata_2025 huggingface dataset:
Finance Equalization and Within-School Equity: The Relationship Between Education Spending and the Social Distribution of Achievement
Authors: Wenglinsky Harold
Published: March 2008

This study relates various types of educational spending to mean mathematics achievement and its social distribution among students. A nationally representative database of 7,217 12th graders was developed by linking the 1992 National Assessment of Educational Progress in mathematics to the U.S. Common Core of Data and the School District Data Book. Through applying hierarchical linear modeling to the database, the study found that spending on instruction and capital expenditures, while not related to mean achievement levels, were related to differences in achievement between SES groups; lower spending levels are associated with greater achievement gaps within schools.
Notes: What Does the Third International Mathematics and Science Study Tell Us About Where to Draw the Line in the Top-Down Versus Bottom-Up Debate?
Authors: Schmidt William H. , Prawat Richard S.
Published: March 2008

Many educational policymakers in this country favor a hybrid top-down, bottom-up approach to reform, arguing that it provides for the best of both worlds—that is, guidance and accountability at the state level combined with ample room to move at the local level. There is considerable uncertainty about how best to implement such an approach, however. Should states, districts, schools, or teachers be responsible for decisions about grade-level content? If so, in what form? This study uses data gathered as part of the Third International Mathematics and Science Study to shed light on these issues. Examining how a range of decisions is made worldwide, from those relating to overall systems goals to specific pedagogical practices in the classroom, should help ground the debate about educational governance in this country.
Notes: Do Faculty Connect School to Work? Evidence From Community Colleges
Authors: Brewer Dominic J. , Gray Maryann Jacobi
Published: March 2008

Despite an emphasis in recent policy on connecting school to work, relatively little is known about how these connections are made and what they look like. In this article, we explore the relationship between community college faculty and their local labor markets. We use a unique national survey that provides the first systematic data from a large number of faculty on this issue, supplemented by case studies. We show that faculty engage in a range of relatively low-level connecting activities; stronger connections are rare. Faculty receive minimal institutional support for such efforts. There are several important barriers to improving linkages related to faculty time and institutional structures.
Notes: Privatized Delivery of Instructional Services for Urban Public School Students Placed at Risk
Authors: Mac Iver Martha Abele , Stringfield Sam
Published: March 2008

The privatization “revolution” of the last decade of the 20th century has not left public education unchallenged. While much of the recent debate has focused on “school choice” and voucher plans, there has been growing discussion of privatization within public schools. Most studies have noted the lack of evidence of student achievement gains under privatization models. In this research note we evaluate the effectiveness of private delivery of instructional services to public school students by analyzing the impact on student achievement of reading and math instruction delivered by a private company in a large urban public school system on the East Coast. Analyses of score data from the Comprehensive Test of Basic Skills (Fourth Edition) indicate differential effects of instructional service delivery by this private company, depending on subject matter (reading vs. math), grade level, and student characteristics (especially gender). The impact on student achievement is particularly notable in mathematics, but we found no evidence that reading comprehension achievement is significantly improved by this private remedial reading program in high poverty urban schools. This study underscores the importance of formal evaluation of privatization efforts to ascertain impacts on student achievement, since there has been considerable expansion of privatized delivery of instructional services to urban school districts, using Title I (Chapter I) funds, with little solid evidence of the effectiveness of these programs.
Robust Statistics: A Survey and Some Prescriptions
Authors: Wainer Howard
Published: March 2008

It is noted that the usual estimators that are optimal under a Gaussian assumption are very vulnerable to the effects of outliers. A survey of robust alternatives to the mean, standard deviation, product moment correlation, t-test, and analysis of variance is offered. Robust methods of factor analysis, principal components analysis and multivariate analysis of variance are also surveyed, as are schemes for outlier detection.
The Use of Probabilistic Models in the Assessment of Mastery
Authors: Macready George B. , Dayton C. Mitchell
Published: March 2008

Descriptions are presented of two related probabilistic models that can be used for making classification decisions with respect to mastery of specific concepts or skills. Included are the development of procedures for: (a) assessing the adequacy of “fit” provided by the models; (b) identifying optimal decision rules for mastery classification; and (c) identifying minimally sufficient numbers of items necessary to obtain acceptable levels of misclassification.
Covariance Analysis in the Evaluation of an Enrichment Program
Authors: Samaniego Francisco J. , Rickard Scott T.
Published: March 2008

The Summer Enrichment Program at the Davis campus of the University of California is an academic and orientation program which is directed toward aiding low-income and minority students in making the transition to the college curriculum. Participants in the program are high-potential students who are admitted to the University via waivers of standard requirements. An evaluation of the program is described in which analysis of covariance is used to focus on the impact of the program on college academic work. The integration of this statistical study into the decision making process of an evaluation task force is also described.
Testing Complex a Priori Contrasts on Means from Independent Samples
Authors: Kohr Richard L. , Games Paul A.
Published: March 2008

The robustness of the t statistic on complex contrasts, ψ, using MSW in the estimate of sψ is compared with that of t”, a statistic derived by Welch (1947) . The t statistic is robust to violations of the homogeneity of variance assumption only if n's are equal and all weights have the same absolute value. The Welch t” is robust for all combinations explored with any set of weights and either equal or unequal n's. Since heterogeneous variances are often encountered in behavioral experiments, the Welch t” is recommended as the benchmark test for complex contrasts.
Quantal Response Techniques for Random Predictor Variables
Authors: McSweeney Maryellen , Schmidt William H.
Published: March 2008

The relationship between quantitative predictors and the probability of occurrence of one or more levels of a qualitative criterion can be analyzed by quantal response techniques. This paper presents two quantal response models. The first model treats the predictors as mathematical variables used as a stratification dimension; the second model uses random variables as predictors. Model II estimation techniques are presented for dichotomous and polychotomous criteria and for single and multiple predictors. The estimation techniques are illustrated with examples of the use of MMPI scale scores to predict the diagnostic classification of psychiatric patients and to model the actual diagnostic classifications of judges. These uses of quantal response methodology are contrasted with those of multiple linear regression and discriminant analysis. Many of the dependent variables collected in school settings are qualitative, e.g., the passing or failing of an item, the mastery or non-mastery of a task, the presence or absence of a behavioral trait or skill. When the interest of the researcher is to relate these variables to quantitative variables, quantal response procedures are potentially applicable for such educational data analyses.
National Evaluation of the Emergency School Aid Act (ESAA): a Review of Methodological Issues
Authors: Coulson John E.
Published: March 2008

Large-scale field evaluations of education programs typically present complex and competing design requirements that can rarely be satisfied by ideal, textbook solutions. This paper uses a recently completed national evaluation of the federally-funded Emergency School Aid Act (ESAA) Program to illustrate in concrete fashion some of the problems often encountered in major program evaluations, and traces the evolution of efforts in that three-year longitudinal study—both in the original design conceptualization and in the actual implementation and data analysis phases—to resolve competing demands and to provide as much methodological rigor as possible under field conditions. Issues discussed here include the selection of experimental versus quasi-experimental designs; the development of sampling procedures to provide maximum precision in treatment-control comparisons; the selection of achievement tests and difficulties in developing and administering other, non-cognitive outcome measures; and the importance of ascertaining whether the underlying assumptions of a true experimental design have been met before conclusions about program impact are drawn on the basis of treatment-control comparisons.
Bayesian Comparison of Two Regression Lines
Authors: Tsutakawa Robert K.
Published: March 2008

The comparison of two regression lines is often meaningful or of interest over a finite interval I of the independent variable. When the prior distribution of the parameters is a natural conjugate, the posterior distribution of the distances between two regression lines at the end points of I is bivariate t. The posterior probability that one regression line lies above the other uniformly over I is numerically evaluated using this distribution.
A Note on Bayesian, Likelihood, and Sampling Distribution Inferences
Authors: Rubin Donald B.
Published: March 2008

A simple example is presented that illustrates advantages of Bayesian and likelihood methods of inference relative to sampling distribution methods of inference. It is argued that Bayesian and likelihood methods of inference should be utilized more generally to analyze real data. Sampling distributions should be used to evaluate the long term performance of procedures.
A Simple Exposition of Jensen’s Error
Authors: Milkman Roger
Published: March 2008

Jensen (1969 , 1973) has used within-population heritability data to support his contention that IQ differences between races have a considerable genetic basis. Criticism of this reasoning has been frequent, but perhaps never categorical. A method is now described for illustrating the error simply and quantitatively. An example shows that high heritability of a property within each of two populations is consistent with a vanishingly small heritability in the combined population.
An Empirical Comparison of the Large Sample Approximations for the Coefficient of Concordance and Weighted Average Tau
Authors: Stamm Carol Lee
Published: March 2008

Two rather similar statistics, the coefficient of concordance (W) and weighted average tau (Wa), have been suggested for estimating the communality between rankings. Two large sample tests have been suggested for each statistic when the values of m (the number of judges) and n (the number of objects) are larger than tabled values. The purpose of this study was to determine empirically which of the large sample approximations for the statistic, W or Wa, was more appropriate for selected values of m and n. The procedures for the investigation involved manipulating m × n rankings using generated data sets. The results of the comparisons of the distributions of the large sample approximations for W and Wa with their empirical distributions indicated that neither approximation was better for all sets of value m and n that were examined. However, the results suggest that the computationally simple approximation, χ2r for W and χ2n for Wa, are appropriate for values of m and n chat are smaller than those recommended previously.
Post Hoc Procedures for Some K-Sample Nonparametric Tests for Scale
Authors: Penfield Douglas A. , Koffler Stephen L.
Published: March 2008

Post hoc multiple comparison procedures useful in assessing differences in population variability are formulated for three nonparametric alternatives to the parametric Bartlett test. The three nonparametric tests are the generalized Puri K-sample extensions of the Siegel-Tukey, Mood, and Klotz tests. Theory surrounding the development of these post hoc procedures is outlined and is based upon the chi-square analog to Scheffé’s theorem. An example illustrating an application of the methodology is presented.
An Index for a Domain of Completion or Short Answer Items
Authors: Harris Chester W. , Pearlman Andrea Pastorok
Published: March 2008

Characteristics of the Lazarsfeld-Kendall “turnover” model adapted for completion or short answer achievement items are examined, and an index describing a domain of items based on this model is proposed. Estimation is discussed, and data that indicate the model is useful for the analysis of addition, subtraction, multiplication, and division items are presented.
Forgetting, Guessing, and Mastery: The Macready and Dayton Models Revisited and Compared with a Latent Trait Approach
Authors: van der Linden Wim J.
Published: March 2008

Macready and Dayton (1977) introduced two probabilistic models for mastery assessment based on an idealistic all-or-none conception of mastery. Although these models are in statistical respects complete, the question is whether they are a plausible rendering of what happens when an examinee responds to an item. First, a correction is proposed that takes account of the fact that a master who is not able to produce the right answer to an item may guess. The meaning of this correction and its consequences for estimating the model parameters are discussed. Second, Macready and Dayton’s latent class models are confronted with the three-parameter logistic model extended with the conception of mastery as a region on a latent variable. It appears that from a latent trait theoretic point of view, the Macready and Dayton models assume item characteristic curves that have the unrealistic form of a step function with a single step. The implications of the all-or-none conception of mastery for the learning process will be pointed out shortly. Finally, the interpretation of the forgetting parameter of the Macready and Dayton models is discussed and approached form a latent trait theoretic point of view.
Analyzing Multilevel Data in the Presence of Heterogeneous Within-Class Regressions
Authors: Burstein Leigh , Linn Robert L. , Capell Frank J.
Published: March 2008

The concerns of this investigation are multiple sources of complications in the analysis of multilevel educational data. The focus is on problems that arise when within-group regressions of outcome on input are related to teacher/ school characteristics. Single-level and multilevel analytical approaches are applied to hypothetical data for which the relationship between teacher/class quality and the heterogeneity of within-class slopes is varied systematically. It is shown that single-level analyses and the proposed multilevel approaches can all yield mislèading estimates of teacher/class effects on mean class outcomes. However, selected multilevel methods provide some indication of misspecification and can identify the direction of the bias in estimating teacher/class effects on mean class outcomes.
An Empirical Investigation of Sampling Errors In Educational Survey Research
Authors: Ross Kenneth N.
Published: March 2008

This investigation examines the influence of sample design on the sampling errors of several multivariate statistics which are frequently used in educational survey research. Student’s empirical sampling technique is used to generate sampling distributions for several complex sample designs which are often used to sample schools, classrooms and students. Some results are presented for two error estimation techniques: “Jackknifing” and “Balanced Repeated Replication”.
A Critique of“A Simple Exposition of Jensen’s Error”
Authors: Wolff Joseph L.
Published: March 2008

Milkman (1978) accuses Arthur Jensen of misapplying heritability data in speculating on the causes of racial differences in intelligence test scores. He then offers a method for illuminating Jensen’s alleged “error”. It is contended in this article that Milkman (1978) has misconstrued Jensen’s (1973) argument and that, as a consequence, his method is without point.
The Two Kinds of Linear Discriminant Functions and their Relationship
Authors: Green Bert F.
Published: March 2008

Fisher’s two-group discriminant function has been generalized in two different ways for the case of three or more groups. Both generalizations have been called discriminant functions, leading to confusion in the literature. A reasonable nomenclature is canonical discriminant functions and classification functions. The precise functional relation between the two functions is derived, and the interpretation of the two functions is discussed. An illustrative example is provided.
Medical School Admission and Residence of Applicants: Empirical Bayes Estimates of Logit Coffficients
Authors: Rolph John E. , Williams Albert P. , Lee Carolyn L.
Published: March 2008

Using data on all applicants to U.S. medical schools in 1975, we analyzed how an applicant’s characteristics affect the probability of his admission to medical school. Specifically, separate logit regressions for minority and majority applicants are performed to estimate this probability as a function of the applicant’s academic attributes (admission test scores, grade point averages, etc.) and of his non-academic attributes (state of residence, age, etc.). The coefficients of the state of residence dummy variables in the logit equation are estimated by discriminant analysis and then modified by empirical Bayes methods to give more accurate estimates of the state of residence effects. These modified estimates show that state of residence has a much larger effect for majority applicants than for minority applicants. An exploratory regression analysis indicates that legal residents of states with high ratios of medical school places to population are more likely to be admitted to a medical school.
Biserial Estimators in the Presence of Guessing
Authors: Ashler Daniel
Published: March 2008

As estimators of correlation of a criterion variable with the continuous latent variable that underlies a dichotomous test item score, both the biserial correlation coefficient, rb, and Brogden’s coefficient of selective efficiency, S*, are severely depressed (negatively biased) by guessing, regardless of sample size or true latent correlation. Formulas and charts are given for computing better estimates, r̂ and Ŝ*, free of guessing bias, based on observed proportions of right, wrong, and omitted answers. In Monte Carlo studies both r̂ and Ŝ* had smaller mean square errors in the presence of guessing than rb and S*, and Ŝ* stayed on target even when the latent and criterion variable were given (the same) rectangular, bimodal, or chi square distribution.
A Review of Estimation Procedures for the Rasch Model with an Eye toward Longish Tests
Authors: Wainer Howard , Morgan Anne , Gustafsson Jan-Eric
Published: March 2008

Two estimation procedures for the Rasch Model are reviewed in detail, particularly with respect to new developments that make the more statistically rigorous Conditional Maximum Likelihood estimation practical for use with longish tests. Emphasis of the review is on European developments which are not well known in the English writing world.
Robustness of the Distribution Theory of the Propuct Moment Correlation Coefficient
Authors: Kraemer Helena Chmura
Published: March 2008

Robustness of normal test theory for correlation coefficients is at least asymptotically ensured for bivariate distributions satisfying a linearity and a homoscedasticity condition for the null theory and a further kurtosis condition for the nonnull theory. If any one of these conditions fall, it may be demonstrated that robustness may fail as well. This result is applied to study of the point biserial, multiserial correlation coefficients, and the ψ-coefficient.
The Use of Cutting Scores in Selection Procedures
Authors: Owen D. B. , Li Loretta
Published: March 2008

A procedure for Screening is given for the case where an underlying joint bivariate normal distribution is assumed for the screening variate and the performance variate. This is extended to the situation with unknown parameters. The procedure for attaining a preset goal for the performance variable is given. An analysis is also made to determine the effect of a preset selection procedure on the performance when the parameters of the bivariate normal distribution are unknown.
Validity of Randomization Tests for one-Subject Experiments
Authors: Edgington Eugene S.
Published: March 2008

Valid Statistical tests for one-subject experiments are necessary to justify Statistical inferences and to ensure the acceptability of research reports to a wide range of journals and readers. The validity of randomization tests for one-subject experiments is examined in this paper.

A randomization test is a procedure for determining significance in the following manner. A test statistic (e.g., t or F) is computed for a set of research data. The value of the test statistic is called the “obtained test statistic value.” The data are then divided repeatedly, and the test statistic is computed for each data division. If the proportion of the data divisions giving a test statistic value as large as the obtained test statistic value is no greater than α, the test statistic is significant at the α level.

Any Statistical test is said to be a randomization test when the significance of its test statistic is determined by the randomization test procedure. Determination of significance by the randomization test procedure permits the valid application of any Statistical test, whether it be as simple as a t test or as complex as factorial multivariate analysis of variance, for one-subject as well as multiple-subject experiments. For the randomization test procedure to be valid for a one-subject experiment, there must be random assignment of treatment times to treatments (i.e., random determination of when each treatment is to be given); specification, before observing the data, of the test statistic and the criterion to be employed for discarding data; and, in the determination of significance, division of the data in a manner consistent with the random assignment procedure.
A Comparison of the Power of Wilcoxon's Rank-Sum Statistic to that of Student'st Statistic Under Various Nonnormal Distributions
Authors: Blair R. Clifford , Higgins James J.
Published: March 2008

Computer generated Monte Carlo techniques were used to compare the power of Wilcoxon's rank-sum test to the power of the two independent means t test for situations in which samples were drawn from (1) uniform, (2) Laplace, (3) half-normal, (4) exponential, (5) mixed-normal, and (6) mixed-uniform distributions. Sample sizes studied were ( n1, n2) = (3,9), (6,6), (9,27), (18,18), (27,81), and (54,54).

It was concluded that (1) generally speaking, the Wilcoxon statistic held very large power advantages over the t statistic, (2) asymptotic relative efficiencies were reasonably good indicators of the relative power of the two statistics, (3) results obtained from smaller samples were often markedly different from the results obtained from larger samples, and (4) because of the narrow ranges of population shapes and sample sizes investigated in some widely cited previous studies of this type, the conclusions reached in those studies must now be deemed questionable.
A Review of the Beta-Binomial Model and its Extensions
Authors: Wilcox Rand R.
Published: March 2008

Both the binomial and beta-binomial models are applied to various problems occurring in mental test theory. The paper reviews and critiques these models. The emphasis is on the extensions of the models that have been proposed in recent years, and that might not be familiar to many educators.
Bias and Mean Square Errors of Estimators as Criteria for Evaluating Competing Analysis Strategies in Quasi-Experiments
Authors: Olejnik Stephen F. , Porter Andrew C.
Published: March 2008

The evaluation of competing analysis strategies based on estimator bias and the mean square errors of estimators is demonstrated using gains in standard scores and analysis of covariance adjusted for errors of measurement procedures for quasi-experiments conforming to the fan spread hypothesis. Some confusion in the appropriateness of these analysis procedures is resolved by considering the fan spread model defined in latent and manifest variables, large and small sample properties of the estimators, and explicitly stating the nature of individual academic growth patterns. For a linear model of individual academic growth both procedures provide an unbiased estimator with equal mean square errors when the samples are large. With small samples, analysis of covariance adjusted for errors of measurement provides an unbiased estimator, while the gain in standard scores estimator is biased and has a spuriously low mean square error. Under a nonlinear model and large samples only gains in standard scores provide an unbiased estimator. Neither procedure is appropriate for a nonlinear model with small samples. A data example is provided to demonstrate the study's findings. It is recommended that both criteria of bias and mean square errors of estimators be considered when evaluating recently developed analytic strategies for quasi-experiments.
The Cross-Validational Accuracy of Sample Regressions
Authors: Rozeboom William W.
Published: March 2008

Browne's definitive but complex formulas for the cross-validational accuracy of an OSL-estimated regression equation in the random-effects sampling model are here reworked to achieve greater perspicuity and extended to include the fixed-effects sampling model.
Adequacy of Asymptotic Normal Theory in Estimating Reliability for Mastery Tests Based on the Beta-Binomial Model
Authors: Huynh Huynh
Published: March 2008

Simulated data based on five test score distributions indicate that a slight modification of the asymptotic normal theory for the estimation of the p and kappa indices in mastery testing will provide results which are in close agreement with those based on small samples from the beta-binomial distribution. The modification is achieved through the multiplication of the asymptotic standard errors of estimate by the constant 1 + 1/m¾ where m is the sample size.
Statistical Power with Group Mean as the Unit of Analysis
Authors: Barcikowski Robert S.
Published: March 2008

In 1940 Lindquist presented a discussion of an analysis of variance using the group mean as the unit of analysis. Unfortunately, most modern writers on statistical methodology have ignored this important topic and some of the best text-book book writers make the error of using the individual as the unit of analysis when the group mean would be more appropriate. The reluctance to use group mean as the unit of analysis is due in part to the belief that the resultant drop in the number of observations per treatment greatly reduces the probability of detecting a treatment effect. This concern is put in perspective in this paper and equations are presented to facilitate power estimates when the group mean is the unit of analysis.
Sample Size and the Accuracy of Predictions Made from Multiple Regression Equations
Authors: Sawyer Richard
Published: March 2008

Some rules of thumb are given for estimating the accuracy of predictions based on a multiple regression equation developed from a random sample of a multivariate normal population. The distribution of the prediction error in this case can be approximated usefully by a normal distribution. Formulas are given for the moments of the distribution and for other parameters such as the mean absolute error (MAE). The approximate inflation in MAE (over its asymptotic value) due to estimating the regression coefficients is a simple function of the base sample size and the number of predictors.
Empirical Power of Procedures for Comparing two Groups onp Variables
Authors: Ramsey Philip H.
Published: March 2008

Monte Carlo results are used to evaluate several procedures for discriminating between two groups on two or more variables. Depending on the conditions examined, either a multiple testing version of Hotelling’s T 2 or a Bonferroni procedure is shown to be the most powerful for detecting at least one true difference between the groups. A multiple Bonferroni procedure is shown to be generally superior in power for detecting all true differences.
A Note on a Geometric Interpretation of the Correlation Coefficient
Authors: Marks Edmond
Published: March 2008

An alternate geometric interpretation of the correlation coefficient to that given in most statistics texts for psychology and education is presented. This interpretation is considered to be more consistent with the statistical model for the data, and richer in geometric meaning.
Fitting Continuous Models to Effect Size Data
Authors: Hedges Larry V.
Published: March 2008

Quantitative methods for research synthesis usually involve calculation of an estimate of effect size for each of a series of studies. Statistical analyses in research synthesis attempt to relate explanatory variables to the effect sizes obtained from the series of studies. Some problems with ad hoc methods, such as ordinary least squares regression analysis using estimates of effect size, are described. Maximum likelihood estimation of the parameters in linear models for effect sizes is discussed and the asymptotic distribution of the estimators is obtained. An alternative estimator is derived which is computationally simpler, but has the same asymptotic distribution as the maximum likelihood estimator. A natural test for model specification is also given. The small sample accuracy of the asymptotic distribution theory derived in this paper is investigated via a simulation study.
A Simulation Study of Reliability and Validity of Multiple-Choice Test Scores Under Six Response-Scoring Modes
Authors: Frary Robert B.
Published: March 2008

Responses to a 40-item, four-choice test were simulated for 120 examinees under six response-scoring modes including number-right, corrected-for-guessing and answer-until-correct. Separate score sets were generated to reflect five levels of prevalence of misinformation (belief that an answer is a distractor) and five levels of propensity-to-guess contrary to instructions for modes designed to inhibit guessing. Criteria were simulated using the number-right mode with five levels of misinformation prevalence and four levels of true-score relationship with the predictor. The entire process was repeated with the introduction of normally distributed, random error at the item level. This process yielded 260 sets of five scores (predictor and four criteria), which were examined to determine differential effects on reliability and validity attributable to the response-scoring modes. Modes permitting multiple responses to an item were found to yield genuine increases in internal consistency reliability, which tended to carry over into validity coefficients. However, the validity differences among all the response-scoring modes simulated were small, probably too small to justify the additional cost and complexity of modes other than number-right.
F-Test Alternatives to Fisher’s Exact Test and to the Chi-Square Test of Homogeneity in 2 × 2 Tables
Authors: Overall John E. , Starbuck Robert R.
Published: March 2008

A binomial model is proposed for testing the significance of differences in binary response probabilities in two independent treatment groups. Without correction for continuity, the binomial statistic is essentially equivalent to Fisher’s exact probability. With correction for continuity, the binomial statistic approaches Pearson’s chi-square. Due to mutual dependence of the binomial and F distributions on the beta distribution, a simple F statistic can be used for computation instead of the binomial.
Theory of Estimation and Testing of Effect Sizes: Use in Meta-Analysis
Authors: Kraemer Helena Chmura
Published: March 2008

Approximations to the distribution of a common form of effect size are presented. Single sample tests, confidence interval formulation, tests of homogeneity and pooling procedures are based on these approximations. Caveats are presented concerning statistical procedures as applied to sample effect sizes commonly used in meta-analysis.
The Role of Permutation Groups in Randomization Tests
Authors: Edgington Eugene S.
Published: March 2008

Randomization tests are usually represented as strategies for determining significance through the comparison of the value of an obtained test statistic with a distribution of such values associated with every possible random assignment of subjects to treatments. Randomization tests can, however, also be conducted on the basis of a subset of all possible assignments and justified through the concept of a permutation group as defined by Chung and Fraser (1958). This idea is useful in acquiring a deeper understanding of randomization tests and in facilitating the development of new classes of tests.
A Fail-SafeN for Effect Size in Meta-Analysis
Authors: Orwin Robert G.
Published: March 2008

Rosenthan’s (1979) concept of fail-safe N has thus far been applied to probability levels exclusively. This note introduces a fail-safe N for effect size.
Instrumental Variable Methods for the Estimation of Test Score Reliability
Authors: Ecob Russell , Goldstein Harvey
Published: March 2008

The method of Instrumental Variables is suggested as an alternative to traditional methods for estimating the reliability of mental test scores which avoids certain drawbacks of these methods. The consistency and efficiency of the instrumental variable method are examined empirically using data from the British National Child Development Study in an analysis of 16 year, 11 year and 7 year old scores on tests of mathematics and reading.
Item Response Models for Grouped Data
Authors: Mislevy Robert J.
Published: March 2008

The most familiar models of item response theory (IRT) are defined at the level of individual subjects; the form and the parameters of a model specify the probability of a correct response to a particular item from a particular subject. It is possible, however, to define an item response model at the level of salient groups of subjects; the form and the parameters of such a model would specify the probability of a correct response to a particular item from a subject selected at random from a particular group of subjects. So-called “group level” models extend the machinery of IRT to data gathered in the maximally efficient multiple-matrix sampling design, under which each sampled subject is administered only one item from a scale. This paper discusses group-level item response models, their uses, their relationships to subject-level item response models, and the estimation of model parameters.
N = 1 Designs: The Failure of ANOVA-Based Tests
Authors: Toothaker Larry E. , Banz Martha , Noble Cindy , Camp Jill , Davis Diana
Published: March 2008

Several methods have been proposed for the analysis of data from single-subject research settings. This research focuses on the modifications of ANOVA-based tests proposed by Shine and Bower, a procedure that precedes the ANOVA F test by preliminary testing of within-phase lag one serial correlation and the one-way ANOVA as presented by Gentile, Roden and Klein. Monte Carlo simulation is used to investigate these tests with respect to robustness and power. Each test was analyzed under various patterns of serial correlation, various patterns of phase and trial means, normal and exponential distributions, and equal and unequal phase variances. The findings indicate that the probability of a Type I error for these ANOVA-based tests is seriously inflated by nonzero serial correlation. These tests, therefore, cannot be recommended for use with data that have nonzero serial correlation.
A Postscript to “A Note on a Geometric Interpretation of the Correlation Coefficient”
Authors: Sorensen Philip H.
Published: March 2008

Essential dimensions for drawing an ellipse that bounds a constant probability area of a bivariate normal distribution may be computed from only knowledge of the correlation coefficient ( ρ) or the standardized regression coefficient ( ßzx). The length of the latus rectum of the ellipse is [Formula: see text] (1 – ρ) and the distance between focal points is [Formula: see text] (1 + ρ). Other values may be expressed in terms of ρ or derived from the foregoing. The geometry is illustrated and a set of curves for reading values directly from knowledge of ρ> 0 is provided.
Was there One Distractor too Many?
Authors: Wainer Howard , Wadkins J. R. Jefferson , Rogers Alfred
Published: March 2008

A mathematics item on the SAT—the Rolling Circle Problem—was found to be faulty. This paper reports a detailed investigation into its mathematical and psychometric properties. In addition to examining performance of the item with more than 100,000 examinees, two small studies were performed with the aid of a physical model of the problem. It was found that the problem could be considered ambiguous due to the nonspecification of the frame of reference, but that almost no one noticed this lack.
On an Application of Statistical Ranking and Selection Tables to the Identification of the Learning Disabled
Authors: Sobel Milton , Kelemen Eve
Published: March 2008

The statistical consequences of giving a student more than one achievement test to determine whether he or she is learning disabled (LD) is discussed. The standard rule is based on one achievement (and one intelligence) test so that if several of the former (say, b) are taken and the lowest score is used, there will be a discrepancy between the proportion of students that are actually labeled LD and the proportion we would originally expect. Ranking and selection tables are used in this paper in a dual manner: (a) to find the expected proportion of LD students as a function of the cut-off point for different values of b and different correlation structures, and (b) to find the appropriate cut-off point as a function of the given expected proportion of LD students. The appropriate table for problem (a) is included.
On Two-Stage Multiple Comparison Procedures When there are Unequal Sample Sizes in the First Stage
Authors: Wilcox Rand R.
Published: March 2008

A problem of considerable practical importance when applying multiple comparison procedures is that unequal variances can seriously affect power and the probability of a Type I error. A related problem is getting a precise indication of how many observations are required so that the length of the confidence intervals will be reasonably short. Two-stage procedures have been proposed that give an exact solution to these problems, the first stage being a pilot study for the purpose of obtaining sample estimates of the variances. However, the critical values of these procedures are available only when there are equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes.
Robust Analysis of a Nonlinear Model for Multilevel Educational Survey Data
Authors: Rachman-Moore Dalia , Wolfe Richard G.
Published: March 2008

A statistical model is proposed that describes the determination of an educational outcome variable as a nonlinear function of explanatory variables defined at different levels of a survey data hierarchy, say students and classes. The model hypothesizes that the student-level explanatory variables form a composite such that the intercept and slope in the regression of the outcome on the composite vary across classes systematically as functions of class-level variables and aggregates. A method is described for estimating the parameters of the model using robust techniques. The theoretical and practical derivation of the model is discussed, and an example is given.
The Scale-Linkage Algorithm: Construction of a Universal Criterion Scale for Families of Institutions
Authors: Braun Henry I. , Szatrowski Ted H.
Published: March 2008

A new approach to the construction of a universal criterion scale for a family of comparable institutions is presented. Proceeding through the development of a sequence of paired calibrations determined by a hierarchical clustering algorithm, the method does not rely on covariate information such as scores on common examinations. As such it is perfectly suited to be employed in aggregated validity studies that combine data from many institutions. Such applications are explored in our companion paper, “Validity Studies Based on a Universal Criterion Scale” (in this issue). The procedure is illustrated with data from American Law Schools.
On Comparing Treatment Effects to a Standard when the Variances are Unknown and Unequal
Authors: Wilcox Rand R.
Published: March 2008

Let δ = μ e– μ c be the difference between the means of an experimental and control group, and suppose it is desired to determine whether δ ≥ δ0, where δ0 is a known constant specified by the experimenter. In this paper, I describe how to determine whether enough observations have been sampled to be reasonably certain that a correct decision will be made about how δ compares to δ0. The solution is exact regardless of what the variances might be. In particular, equal variances are not assumed.
Satisfying a Simplex Structure is Simpler than it should be
Authors: Rogosa David , Willett John B.
Published: March 2008

Markedly different types of growth (learning) curves may generate indistinguishable covariance structures. We illustrate with an example of a 5 × 5 covariance matrix representing longitudinal measurements at five occasions. This example appears to conform closely to a simplex correlation pattern, and a simplex covariance structure provides an excellent fit (using LISREL V) to this covariance matrix. However, the (known) structure of this example differs greatly from the simplex model. In addition to indicating that an excellent fit of a simplex structure can be misleading, this example provides an opportunity to question common uses of covariance structure models for the study of growth.
Section Pre-Equating in the Presence of Practice Effects
Authors: Holland Paul W. , Thayer Dorothy T.
Published: March 2008

Section pre-equating (SPE) is a new method for equating tests that was developed in response to test disclosure legislation. It is designed to equate a new test to an old test prior to the actual use of the new test, and makes extensive use of experimental sections of a testing instrument. This paper extends the theory behind SPE to allow for the effects of practice on both the old and the new tests, and gives a unified and generalized account of SPE.
Standard Errors of Equipercentile Equating for the Common Item Nonequivalent Populations Design
Authors: Jarjoura David , Kolen Michael J.
Published: March 2008

An equating design in which two groups of examinees from slightly different populations are administered different test forms that have a subset of items in common is widely used. A procedure for equipercentile equating under this design has been previously outlined, but standard errors for this rather complex procedure have not been provided. This paper provides these standard errors and a simulation that verifies the equations for large samples. A real data example is provided for considering issues involved in using these procedures.
A Longitudinal Analysis Using the Lisrel-Model with Structured Means
Authors: Hanna Gila , Lei Hau
Published: March 2008

The Lisrel-model with structured means was used to study similarities and differences between two groups of students on a longitudinal set of data. Inferences were made about the differences between the two groups in the development of mathematical ability as measured by two tests on three successive occasions, by testing the hypothesis that the slopes in the regression of true final scores on true initial scores are equal across the two groups, and by estimating the difference in the intercept alpha in the structural equation.

The results indicated that the two groups started with equivalent mathematics ability. The Immersion group had a significantly higher level (2.52 points) of growth in mathematics ability than the Regular group at Grade 5; in the subsequent year, however, the Regular group exceeded the Immersion group by 2.15 points in its average growth. In comparison with the Regular group, the Immersion group grew more rapidly from grade 4 to 5 and more slowly from grade 5 to 6.
Elementary Estimates: An Introduction to Nonparametrics
Authors: Noether Gottfried E.
Published: March 2008

The paper presents a unified approach to some of the more popular nonparametric methods in current use. The approach provides the reader with new insights by exhibiting relationships to relevant population parameters, such as location and scale parameters for the one- and two-sample problems and regression parameters for bivariate data. For each parameter, a set of so-called elementary estimates is defined. The elementary estimates are then used to determine point estimates, confidence intervals, and test statistics for testing relevant nonparametric hypotheses. Among the tests discussed are the sign test, the Wilcoxon one- and two-sample tests, and Kendall’s test of independence.
Estimating the Probability of Success for Classroom Demonstrations in Statistics
Authors: Huck Schuyler W. , Clark Sheldon B. , Ranney Gipsie B.
Published: March 2008

Classroom demonstrations, if well designed, can help students gain insights into statistical concepts and phenomena. Unfortunately, however, some instructors choose not to use this instructional device for fear that the data generated will turn out to be “uncooperative”; other instructors use demonstrations but use them unscientifically, ending up with data sets that either yield no insights or constitute “overkill.” After discussing four kinds of demonstrations for which a “proper N” can and should be computed, we present three possible approaches for determining how much data are needed for the demonstration to have a reasonable probability of success. Examples from the literature are used to illustrate the need for a more scientific approach to this form of instruction.
Behavioral Statistics Textbooks: Source of Myths and Misconceptions?
Authors: Brewer James K.
Published: March 2008

Six behavioral statistics textbooks listed by their publishers as “bestsellers” during 1982 were reviewed by the author. The intent was to detect the presence of and discuss the nature of some theoretical inferential inaccuracies, misinterpretations, and errors, that is, statistical “myths and misconceptions.” Approximately 43 quotes were found that to some degree reflected misconceptions of statistical theory and that may mislead the behavioral researcher. These quotes were classified in general categories of half-truths, definitional errors, constant-cum-variable, cart-before-the-horse, and unitary inference.