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This study investigated the sustainability effects of the schema-based instruction (SBI) program and corresponding PD on the instructional practices of two cohorts of teachers (i.e., SBI experienced-teacher implementers and SBI novice-teacher implementers) and on students' ability to reason with proportions and overall mathematics performance. SBI is a multicomponent program that focuses on recognizing the underlying mathematical problem structure (e.g., ratios, rates, percent) needed to reason with proportions. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was an SBI experience effect on the immediate test of proportional problem-solving (PPS), but not on a 11-week retention test of PPS, a general measure of problem solving, or the end-of-year state mathematics achievement tests. [ABSTRACT FROM AUTHOR]

This formative study of a multiplicative reasoning (MR) intervention explored the intervention's potential for improving the ability of third‐grade struggling students' ability to reason with multiplicative concepts and procedures. The feasibility of the study was examined in a school setting before a randomized control trial was conducted. Students who scored between the 10th and 35th percentile on a district‐administered math screening test received the MR intervention from their teachers. We developed intervention units to build a conceptual foundation in a student‐centered approach to Tier 2 instruction that included opportunities for students to engage in critical thinking as they generalized big ideas, participated in classroom discourse, and modeled multiplicative relationships with multiple representations. Preliminary data demonstrate the potential of the intervention to promote students' MR skills. Instructional implications are discussed in terms of opportunities for these students to engage in grade‐level mathematics content. [ABSTRACT FROM AUTHOR]

Proportional reasoning is the cornerstone of many higher-level mathematics topics. We evaluated the sustainability effects of schema-based instruction (SBI) on proportional reasoning and the impact of professional development (PD) on the instructional practices of two cohorts of seventh-grade teachers (i.e., SBI-experienced-teacher implementers, who taught SBI in a previous study; SBI-novice-teacher implementers, who taught SBI for the first time with PD) and mathematics outcomes of students with mathematics learning difficulties. SBI was implemented for 6 weeks by 49 teachers in two distal states. Despite the cessation of PD provided to SBI experienced-teacher implementers, teachers in both cohorts demonstrated similar levels of fidelity. Results indicated no SBI experience effect on the immediate and 11-week retention tests of proportional problem solving, on a general measure of problem solving, and on an end-of-year mathematics achievement test, suggesting that the effectiveness of SBI generalizes over time to different cohorts of teachers and students. [ABSTRACT FROM AUTHOR]

This study used integrative data analysis (Curran & Hussong, 2009), which allows combining data from different studies, to examine the generalizability of a research-based mathematics program, schema-based instruction (SBI), with a focus on proportional reasoning. Data were pooled from existing SBI studies spanning three U.S. states in which teachers and their classrooms were randomly assigned to either a SBI or control condition. Results of a series of multilevel (i.e., two-level, students within teachers) models indicated the effectiveness of SBI in improving students' mathematical problem-solving performance. The pooled data findings clarify that SBI improves students' mathematical problem solving more so for proximal than distal measures. These findings also show Black and Hispanic students continue to lag behind White students, that teachers with more experience tend to be associated with higher performing classrooms, and that increasing concentrations of students eligible for free or reduced price lunch and students receiving special education services are generally associated with weaker performances. Implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

The difference in two coefficients of variation is proposed as an effect size to capture variance heterogeneity for two groups across a sample of studies, and five tests of homogeneity of this effect size were studied. Capturing within-study differences in variability across a sample of studies should enhance understanding of treatment effects estimated by traditional mean-based effect sizes by providing information about the extent to which subjects in a treatment group responded similarly across studies relative to a control group. Monte Carlo results suggested the Miller-Feltz test can be used to test homogeneity of within-study variability. [ABSTRACT FROM AUTHOR]

Measures of socioeconomic status (SES) are widely used in educational research and policy applications in no small part because of a deeply rooted belief of the importance of SES. This paper argues that the usefulness of common SES measures can be undermined by (a) an atheoretical approach to conceptualizing SES and selecting measures, which creates uncertainty about what SES represents; (b) modest correlations between SES measures and outcome variables that limit the effectiveness of SES as a control variable in statistical analyses; and (c) the continued use of the profoundly flawed eligibility for a free/reduced-price lunch variable. These factors can produce biased inferences and speak to an important gap between the perceived impact of SES in educational settings and the usefulness of common SES measures and also can provide a prescription for change that promotes a deeper understanding and more effective use of SES in educational research and policy. [ABSTRACT FROM AUTHOR]

The emphasis of reform-oriented science education today focuses on engineering integration in K-12 science classrooms. However, there is little research, particularly longitudinal research, on how different approaches to engineering integration influence student learning and interest. To address this gap in the literature, this study analyzed a middle school life science teacher's enactment of three design-focused life science units and student performances over a 3-year period. Findings indicate that the design and enactment of each unit reflects a unique engineering integration approach: add on, implicit, and explicit. Moreover, the ways the teacher talked about engineering varied among each curriculum unit. Through the analyses of 330 students' pre- and post-content tests and interest surveys as well as videotaped classroom instruction, we found that explicit engineering integration and engineering language use in classroom instruction resulted in higher student learning gains in science and engineering, but they did not have significant effects on students' interest in science and engineering. We explore the implications for curricular materials and discuss a need for long-term professional development and support for teachers. [ABSTRACT FROM AUTHOR]

Computer simulation studies represent an important tool for investigating processes difficult or impossible to study using mathematical theory or real data. Hoaglin and Andrews recommended these studies be treated as statistical sampling experiments subject to established principles of design and data analysis, but the survey of Hauck and Anderson suggested these recommendations had, at that point in time, generally been ignored. We update the survey results of Hauck and Anderson using a sample of studies applying simulation methods in statistical research to assess the extent to which the recommendations of Hoaglin and Andrews and others for conducting simulation studies have been adopted. The important role of statistical applications of computer simulation studies in enhancing the reproducibility of scientific findings is also discussed. The results speak to the state of the art and the extent to which these studies are realizing their potential to inform statistical practice and a program of statistical research. [ABSTRACT FROM AUTHOR]

The present study used a regression discontinuity approach to test whether schema-based instruction (SBI) was effective for students identified with varying levels of mathematics difficulties (MD) who received Tier-1 instruction. The performance of these students was compared to similar students who received business-as-usual Tier-1 instruction. Results indicated SBI on average raised scores regardless of whether a student was categorized as having MD on outcome measures of mathematics problem solving, suggesting that SBI is effective for a wide range of proportional reasoning skills and general mathematical proficiency, which broadens the population of students who could benefit from SBI. Standardized slopes for the treatment effect also provide evidence of the effectiveness of SBI. Implications for practice and research are discussed. [ABSTRACT FROM AUTHOR]

This randomized controlled study investigated the efficacy of a Tier 1 intervention—schema-based instruction—designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment condition (schema-based instruction) or control condition (business as usual). Participants included 373 students, of whom 253 demonstrated MD. A measure of proportional problem solving (PPS) was administered at pre- and posttesting and at 11 weeks following treatment, along with a general mathematical problem-solving measure at pre- and posttesting. For the full sample, posttest differences favoring the treatment group were statistically significant for all measures. For students with MD, posttest differences favored the treatment group for the PPS posttest and PPS delayed posttest but not for general problem-solving posttest. [ABSTRACT FROM AUTHOR]

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance. [ABSTRACT FROM AUTHOR]

The new science education reform documents call for integration of engineering into K-12 science classes. Engineering design and practices are new to most science teachers, meaning that implementing effective engineering instruction is likely to be challenging. This quasi-experimental study explored the influence of teacher-developed, engineering design-based science curriculum units on learning and achievement among grade 4-8 students of different races, gender, special education status, and limited English proficiency (LEP) status. Treatment and control students ( n = 4450) completed pretest and posttest assessments in science, engineering, and mathematics as well as a state-mandated mathematics test. Single-level regression results for science outcomes favored the treatment for one science assessment (physical science, heat transfer), but multilevel analyses showed no significant treatment effect. We also found that engineering integration had different effects across race and gender and that teacher gender can reduce or exacerbate the gap in engineering achievement for student subgroups depending on the outcome. Other teacher factors such as the quality of engineering-focused science units and engineering instruction were predictive of student achievement in engineering. Implications for practice are discussed. [ABSTRACT FROM AUTHOR]

Measures of socioeconomic status (SES) are routinely used in analyses of achievement data to increase statistical power, statistically control for the effects of SES, and enhance causality arguments under the premise that the SES-achievement relationship is moderate to strong. Empirical evidence characterizing the strength of the SES-achievement relationship and its moderators suggests that this relationship is surprisingly modest, with an average SES-achievement correlation of .22, although it appears to have strengthened in the past 3 decades. The modest SES-achievement relationship has important implications for using SES measures in educational data analyses. We provide evidence of this relationship and of the need to use theoretical models to guide the construction and selection of SES measures in analyses of achievement data. [ABSTRACT FROM AUTHOR]

Hierarchical linear models have become a familiar method for accounting for a hierarchical data structure in studies of science and mathematics achievement. This paper illustrates the use of cross-classified random effects models (CCREMs), which are likely less familiar. The defining characteristic of CCREMs is a hierarchical data structure defined by multiple random factors at higher levels. We illustrate CCREMs using data for approximately 10,000 students from more than 250 high schools who attended one of 27 four-year postsecondary institutions. The appropriate use of CCREMs helps to ensure unbiased estimates of effects and credible inferences. [ABSTRACT FROM AUTHOR]

In many countries around the world, there has been an increasing emphasis on improving science education. Recent reform efforts in the USA call for teachers to integrate scientific and engineering practices into science teaching; for example, science teachers are asked to provide learning experiences for students that apply crosscutting concepts (e.g., patterns, scale) and increase understanding of disciplinary core ideas (e.g., physical science, earth science). Engineering practices and engineering design are essential elements of this new vision of science teaching and learning. This paper presents a research study that evaluates the effects of an engineering design-based science curriculum on student learning and attitudes. Three middle school life science teachers and 275 seventh grade students participated in the study. Content assessments and attitude surveys were administered before and after the implementation of the curriculum unit. Statewide mathematics test proficiency scores were included in the data analysis as well. Results provide evidence of the positive effects of implementing the engineering design-based science unit on student attitudes and learning. [ABSTRACT FROM AUTHOR]

This study examined the relationship between the American College Testing (ACT) college mathematics readiness standard and college mathematics achievement using a sample of students who met or exceeded the minimum 3 years high school mathematics coursework recommended by ACT. According to ACT, a student who scores 22 or higher on the ACT mathematics test has a relatively high probability of earning a passing grade in his or her first college mathematics course. Data from 11,324 students who attended 1 of 27 four-year postsecondary institutions in the upper Midwest were used to study this relationship. Overall, there was evidence that meeting the mathematics readiness standard was related to college mathematics achievement for students who completed at least 3 years of high school mathematics. The results have important implications for school district staff advising college-intending students on mathematics course-taking, college admissions staff evaluating student readiness for college-level mathematics, and researchers studying college readiness. [ABSTRACT FROM AUTHOR]

Improving K-12 Science, Technology, Engineering, and Mathematics (STEM) education has a priority on numerous education reforms in the United States. To that end, developing and sustaining quality programs that focus on integrated STEM education is critical for educators. Successful implementation of any STEM program is related to the curriculum materials used. Educators increasingly recognize the challenge of finding quality curriculum materials for integrated STEM education. In this study, 48 teachers participated in a year-long professional development program on STEM integration, and they designed 20 new engineering design-based STEM curriculum units. Each STEM curriculum unit includes an engineering challenge in which students develop technologies to solve the challenge; each unit also integrates grade level appropriate mathematics (data analysis and measurement) and one of the three science content areas: life science, physical science, or earth science. A total of 20 STEM integration units were assessed using the STEM Integration Curriculum Assessment (STEM-ICA) tool. Comparisons among the STEM units showed that the context or the engineering activities in physical science focused STEM units were more engaging and motivating comparing to the authentic contexts used in life science and earth science focused STEM units. Moreover, mathematics integration and communicating mathematics, science, and engineering thinking were not found to strongly contribute to the overall quality of the STEM units. Implications for designing effective professional development on integrated STEM education will be discussed. [ABSTRACT FROM AUTHOR]

The purpose of this study was to develop, scale, and validate assessments in engineering, science, and mathematics with grade appropriate items that were sensitive to the curriculum developed by teachers. The use of item response theory to assess item functioning was a focus of the study. The work is part of a larger project focused on increasing student learning in science, technology, engineering, and mathematics ( STEM)-related areas in grades 4-8 through an engineering design-based, integrated approach to STEM instruction and assessment. The fact that the assessments are available to school districts at no cost, and represent psychometrically sound instruments that are sensitive to STEM-oriented curriculum, offers schools an important tool for gauging students' understanding of engineering, science, and mathematics concepts. [ABSTRACT FROM AUTHOR]

There is a need for more students to be interested in science, technology, engineering, and mathematics ( STEM) careers to advance U. S. competitiveness and economic growth. A consensus exists that improving STEM education is necessary for motivating more students to pursue STEM careers. In this study, a survey to measure student (grades 4-6) attitudes toward STEM and STEM careers was developed and administered to 662 students from two STEM-focused and three comprehensive (non- STEM-focused) schools. Cronbach's alphas for the whole survey and subscales indicated a high internal consistency. Statistically significant difference in means between students attending the STEM-focused and comprehensive schools on the two subscales of the survey and the overall survey were found. However, the explained variance for these results was approximately 1%. The survey is a useful tool to assess efficacy of STEM education programs on student attitudes toward STEM and STEM careers. [ABSTRACT FROM AUTHOR]

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student’s high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student’s high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed. [ABSTRACT FROM AUTHOR]

The first college mathematics course a student enrolls in is often affected by performance on a college mathematics placement test. Yet validity evidence of mathematics placement tests remains limited, even for nationally standardized placement tests, and when it is available usually consists of examining a student’s subsequent performance in mathematics courses. This study expands on existing literature by considering whether a nationally standardized college mathematics placement test (ACCUPLACER) contributes to the prediction of enrollment and success in developmental and nondevelopmental mathematics courses above and beyond prediction associated with the ACT mathematics test. Results for a sample of more than 1,300 students from 20 postsecondary institutions suggest that ACCUPLACER does not contribute to either the prediction of enrollment or subsequent success in such courses, and that comparable information is provided by using the ACT mathematics score alone. Implications of these findings are discussed. [ABSTRACT FROM PUBLISHER]

Recent 'math wars' have drawn attention to how well various high school mathematics curricula prepare students for college-level mathematics. The purpose of this study was to investigate the relationship between the high school mathematics curricula and students' post-secondary mathematics placement recommendation, specifically how students responded to the mathematics placement recommendations and the students' performance in the first college mathematics class. The results showed no relationship between students' participation in a particular high school mathematics curriculum and mathematics placement recommendation, or between student high school mathematics curriculum and students' responses to a university mathematics placement recommendation. However, students who took a more/less difficult class than what was recommended achieved significantly lower/higher grades than those who followed the recommendation. The findings have implications for high school mathematics curricula selection, post-secondary student placement, and future research in this area. [ABSTRACT FROM AUTHOR]

The use of eligibility for a free lunch as a measure of a student's socioeconomic status continues to be a fixture of quantitative education research. Despite its popularity, it is unclear that education researchers are familiar with what student eligibility for a free lunch does (and does not) represent. The authors examine the National School Lunch Program, which is responsible for certifying students as eligible for a free lunch, and conclude that free lunch eligibility is a poor measure of socioeconomic status, which suffers from important deficiencies that can bias inferences. A table characterizing key strengths and weaknesses of variables used as measures of socioeconomic status is provided to facilitate comparisons. [ABSTRACT FROM AUTHOR]

The selection of K-12 mathematics curricula has become a polarizing issue for schools, teachers, parents, and other educators and has raised important questions about the long-term influence of these curricula. This study examined the impact of participation in either a National Science Foundation-funded or commercially developed mathematics curriculum on the difficulty level of the first university mathematics course a student enrolled in and the grade earned in that course. The results provide evidence that National Science Foundation-funded curricula do not prepare students to initially enroll in more difficult university mathematics courses as well as commercially developed curricula, but once enrolled students earn similar grades. These findings have important implications for high school mathematics curriculum selection and for future research in this area. [ABSTRACT FROM AUTHOR]

There is general agreement that meta-analysis is an important tool for synthesizing study results in quantitative educational research. Yet, a shared feature of many meta-analyses is a failure to report sufficient information for readers to fully judge the reported findings, such as the populations to which generalizations are to be made, inclusion and exclusion criteria for studies, the rationale underlying coded variables, including their scaling, relationship to study goals, and the sensitivity of conclusions to the chosen methodology. The authors provide (a) evidence of the prevalence of deficiencies of reporting and (b) suggestions about the kind of information that meta-analysts should typically provide. Providing readers with that information should significantly improve readers' ability to evaluate the credibility of a meta-analysis. [ABSTRACT FROM AUTHOR]

Results from exact statistical theory and Monte Carlo studies have provided evidence that the test size and power of the F test in analysis of covariance are sensitive to violations of certain assumptions. However, a comprehensive summary of the effect of assumption violations has not been available. In this article, meta-analytic methods are used to summarize the results of Monte Carlo studies of the test size and power of the F test in the single-factor, fixed-effects analysis of covariance model, updating and extending narrative reviews of this literature. Monte Carlo results for the nonparametric rank-transform test in the analysis of covariance model are also analyzed. Guidelines for using these tests when assumptions are violated are presented to promote more judicious use of these procedures. [ABSTRACT FROM PUBLISHER]

Mu'tah University is one of the premier undergraduate institutions in Jordan, with an educational mission that focuses on providing the country with highly trained specialists in the fields of science, technology, and the arts including education. The current study attempted to answer two questions: (1) To what extent does the achievement level of education students at Mu'tah University vary as a function of student background variables such as family characteristics (family size), parental education, prior academic background of students as measured by an exit test for secondary school (TAWJIHI), and sex? (2) What factors do education students believe are responsible for the level of achievement by education students at Mu'tah University? The results showed that there is an interaction effect between mother's education and father's education, and father's education and the sex of the student on the student's grade point average (GPA). A revised student questionnaire following factor analysis showed that the lack of family support for a student is the main factor behind a low level of student achievement (GPA). [ABSTRACT FROM AUTHOR]

Demonstrates how the item response theory (IRT) can be used to rescale ordinal data to an interval scale. Scales of measurement for variables; Problems associated with the use of ordinal data; Options for analyzing ordinal data; Software for analyzing data for IRT models.

Suggests two complementary frameworks for providing validity evidence for educational rating data. Discussion on the use of trained raters; Validity of ratings from a traditional measurement perspective; Experimental designs employed in rating studies; Variables threatening internal validity; Summary.

Examines the meta-analytic method proposed for studying variance heterogeneity. Investigation of relationship between study characteristics and effect sizes; Indication that this test cannot be recommended to meta-analysts.

Evaluating texts is an important activity associated with teaching statistics. Surprisingly, the statistical education literature offers little guidance on how these evaluations should be conducted. This lack of guidance may be at least partly responsible for the fact that published evaluations of statistics texts almost invariably employ evaluation criteria that lack any theory-based rationale. This failing is typically compounded by a lack of empirical evidence supporting the usefulness of the criteria. This article describes the construction and piloting of instruments for evaluating statistics texts that are grounded in the statistical education and text evaluation literatures. The study is an initial step in a line of research which we hope will result in the establishment and maintenance of a database of evaluations of statistical texts. Evaluative information of this kind should assist instructors wrestling with text selection decisions and individuals charged with performing evaluations, such as journal reviewers, and should ultimately benefit the direct consumers of these texts-the students. [ABSTRACT FROM PUBLISHER]

Monte Carlo studies provide information that can assist researchers in selecting a statistical test when underlying assumptions of the test are violated. Effective use of this literature is hampered by the lack of an overarching theory to guide the interpretation of Monte Carlo studies. The problem is exacerbated by the impressionistic nature of the studies, which can lead different readers to different conclusions. These shortcomings can be addressed using meta-analytic methods to integrate the results of Monte Carlo studies. Quantitative summaries of the effects of assumption violations on the Type I error rate and power of a test can assist researchers in selecting the best test for their data. Such summaries can also be used to evaluate the validity of previously published statistical results. This article provides a methodological framework for quantitatively integrating Type I error rates and power values for Monte Carlo studies. An example is provided using Monte Carlo studies of Bartlett's (1937) test of equality of variances. The importance of relating meta-analytic results to exact statistical theory is emphasized. [ABSTRACT FROM PUBLISHER]

Meta-analytic methods were used to integrate the findings of a sample of Monte Carlo studies of the robustness of the F test in the one- and two-factor fixed effects ANOVA models. Monte Carlo results for theWelch (1947) and Kruskal-Wallis (Kruskal & Wallis, 1952) tests were also analyzed. The meta-analytic results provided strong support for the robustness of the Type I error rate of the F test when certain assumptions were violated. The F test also showed excellent power properties. However, the Type I error rate of the F test was sensitive to unequal variances, even when sample sizes were equal. The error rate of the Welch test was insensitive to unequal variances when the population distribution was normal, but nonnormal distributions tended to inflate its error rate and to depress its power. Meta-analytic and exact statistical theory results were used to summarize the effects of assumption violations for the tests. [ABSTRACT FROM PUBLISHER]

Puri and Sen (1969Puri and Sen (1985) presented a nonparametric test statistic based on a general linear model approach that is appropriate for testing a wide class of hypotheses. The two forms of this statistic, pure- and mixed-rank, differ according to whether the original predictor values or their ranks are used. Both forms permit the use of standard statistical packages to perform the analyses. The applicability of these statistics in testing a number of hypotheses is highlighted, and an example of their use is given. A simulation study for the multivariate-multiple-regression case is used to examine the distributional behavior of the pure- and mixed-rank statistics and an important competitor, the rank transformation of Conover and Iman (1981). The results suggest that the pure- and mixed-rank statistics are superior with respect to minimizing liberal Type I error rates, whereas the Conover and Iman statistic produces larger power values. [ABSTRACT FROM PUBLISHER]

The Bock and Aitkin (1981) Marginal Maximum Likelihood/EM approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. Unfortunately, the complexity of the underlying mathematics and the terse nature of the existing literature has made understanding of the approach difficult. To make the approach accessible to a wider audience, the present didactic paper provides the essential mathematical details of a marginal maximum likelihood/EM solution and shows how it can be used to obtain consistent item parameter estimates. For pedagogical purposes, a short BASIC computer program is used to illustrate the underlying simplicity of the method. [ABSTRACT FROM PUBLISHER]

The computation of elementary symmetric functions and their derivatives is an integral part of conditional maximum likelihood estimation of item parameters un der the Rasch model. The conditional approach has the advantages of parameter estimates that are consistent (assuming the model is correct) and statistically rigorous goodness-of-fit tests. Despite these characteristics, the conditional approach has been limited by problems in computing the elementary symmetric functions. The in troduction of recursive formulas for computing these functions and the availability of modem computers has largely mediated these problems; however, detailed documentation of how these formulas work is lacking. This paper describes how various recursion formulas work and how they are used to compute elementary symmetric functions and their derivatives. The availabil ity of this information should promote a more thorough understanding of item parameter estimation in the Rasch model among both measurement specialists and practitioners. [ABSTRACT FROM PUBLISHER]

Monte carlo studies are being used in item response theory (IRT) to provide information about how validly these methods can be applied to realistic datasets (e.g., small numbers of examinees and multidimensional data). This paper describes the conditions under which monte carlo studies are appropriate in IRT-based re search, the kinds of problems these techniques have been applied to, available computer programs for gen erating item responses and estimating item and exam inee parameters, and the importance of conceptualizing these studies as statistical sampling experiments that should be subject to the same principles of experimen tal design and data analysis that pertain to empirical studies. The number of replications that should be used in these studies is also addressed. [ABSTRACT FROM PUBLISHER]

The marginal maximum likelihood estimation (MMLE) procedure (Bock & Lieberman, 1970; Bock & Aitkin, 1981) has led to advances in the estima tion of item parameters in item response theory. Mislevy (1986) extended this approach by employ ing the hierarchical Bayesian estimation model of Lindley and Smith (1972). Mislevy's procedure posits prior probability distributions for both abili ty and item parameters, and is implemented in the PC-BILOG computer program. This paper extends the work of Harwell, Baker, and Zwarts (1988), who provided the mathematical and implemen tation details of MMLE in an earlier didactic paper, by encompassing Mislevy's marginalized Bayesian estimation of item parameters. The purpose was to communicate the essential conceptual and math ematical details of Mislevy's procedure to prac titioners and to users of PC-BILOG, thus making it more accessible. [ABSTRACT FROM PUBLISHER]

Long-standing difficulties in estimating item parameters in item response theory (IRT) have been addressed recently with the application of Bayesian estimation models. The potential of these methods is enhanced by their availability in the BILOG com puter program. This study investigated the ability of BILOG to recover known item parameters under varying conditions. Data were simulated for a two- parameter logistic IRT model under conditions of small numbers of examinees and items, and different variances for the prior distributions of discrimina tion parameters. The results suggest that for samples of at least 250 examinees and 15 items, BILOG accurately recovers known parameters using the default variance. The quality of the estimation suffers for smaller numbers of examinees under the default variance, and for larger prior variances in general. This raises questions about how practi tioners select a prior variance for small numbers of examinees and items. [ABSTRACT FROM PUBLISHER]

A fundamental analysis decision researchers in psychology and education is the choice between parametric and nonparametric test. Despite the statistical and substantive implications of this important decision, many researchers unerringly employ parametric tests and thus ignore the advantages of their nonparametric counterparts. One justification for this behavior has the absence of guidelines for choosing between these procedures. A second has been the lack of a comprehensive nonparametric test that is computational manageable. In this article, the author discusses several statistical and substantive criteria that can be used to choose between parametric and nonparametric tests. A nonparametric test capable of testing a number of statistical hypotheses using existing computer packages is also presented. Recommendations are made encouraging researchers to routinely use nonparametric tests in their data analytic work.
The purpose here is to encourage researchers to use both statistical and substantive criteria in choosing between a PAR or NPAR test and to alert them to the availability of an NPAR test whose flexibility, breadth, and ease of application should encourage its routine use. The discussion should also encourage consumers of research in psychology and education to critically evaluate published research that uses one kind of test (i.e., PAR or NPAR) rather than another. [ABSTRACT FROM AUTHOR]

Analyzes the results of Monte Carlo studies in item response theory used in educational measurement and psychometrics. Advantages of conceptualizing Monte Carlo studies as statistical sampling experiments; Using of inferential methods to analyze Monte Carlo results in item response theory.

Examines distributive justice development in children of ages seven, nine and eleven from Sweden and the U.S. Performance of logical reasoning tasks; Assessment of reasoning in different contexts; High levels of reasoning elicited by family stimuli.

Explains how to adjust observed cell means to accurately characterize the nature of an interaction for two- and three-factor designs when lower-order effects are statistically significant. Why the misinterpretation of interaction effects is so common; Details on two- and three-factor designs; Examples from the counselling literature.