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1.
The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.  相似文献   

2.
This study examined the effect of model size on the chi-square test statistics obtained from ordinal factor analysis models. The performance of six robust chi-square test statistics were compared across various conditions, including number of observed variables (p), number of factors, sample size, model (mis)specification, number of categories, and threshold distribution. Results showed that the unweighted least squares (ULS) robust chi-square statistics generally outperform the diagonally weighted least squares (DWLS) robust chi-square statistics. The ULSM estimator performed the best overall. However, when fitting ordinal factor analysis models with a large number of observed variables and small sample size, the ULSM-based chi-square tests may yield empirical variances that are noticeably larger than the theoretical values and inflated Type I error rates. On the other hand, when the number of observed variables is very large, the mean- and variance-corrected chi-square test statistics (e.g., based on ULSMV and WLSMV) could produce empirical variances conspicuously smaller than the theoretical values and Type I error rates lower than the nominal level, and demonstrate lower power rates to reject misspecified models. Recommendations for applied researchers and future empirical studies involving large models are provided.  相似文献   

3.
We argue for decreasing the use of the word spread when describing the statistical idea of dispersion or variability in introductory statistics courses. In addition, we argue for increasing the use of the word variability as a replacement for spread.  相似文献   

4.
This article describes the most compact 100c% interval for a probability density for 0 < c < 1. An unbiased, distribution‐free estimator when c = 0.5 is presented.  相似文献   

5.
In this paper, the dice game Unders and Overs is described and presented as an active learning exercise to introduce basic probability concepts. The implementation of the exercise is outlined and the resulting presentation of various probability concepts are described.  相似文献   

6.
The authors used Johnson's transformation with approximate test statistics to test the homogeneity of simple linear regression slopes when both xij and xij may have nonnormal distributions and there is Type I heteroscedasticity, Type II heteroscedasticity, or complete heteroscedasticity. The test statistic t was first transformed by Johnson's method for each group to correct the nonnormality and to correct the heteroscedasticity; also an approximate test, such as the Welch test or the DeShon-Alexander test, was applied to test the homogeneity of the regression slopes. Computer simulations showed that the proposed technique can control Type I error rate under various circumstances. Finally, the authors provide an example to demonstrate the calculation.  相似文献   

7.
Although our students correctly define the terms p‐value, Type I and Type II errors, they sometimes misinterpret results from real data. In this work we present an assignment intended to clear up these misconceptions.  相似文献   

8.
Fitting a large structural equation modeling (SEM) model with moderate to small sample sizes results in an inflated Type I error rate for the likelihood ratio test statistic under the chi-square reference distribution, known as the model size effect. In this article, we show that the number of observed variables (p) and the number of free parameters (q) have unique effects on the Type I error rate of the likelihood ratio test statistic. In addition, the effects of p and q cannot be fully explained using degrees of freedom (df). We also evaluated the performance of 4 correctional methods for the model size effect, including Bartlett’s (1950), Swain’s (1975), and Yuan’s (2005) corrected statistics, and Yuan, Tian, and Yanagihara’s (2015) empirically corrected statistic. We found that Yuan et al.’s (2015) empirically corrected statistic generally yields the best performance in controlling the Type I error rate when fitting large SEM models.  相似文献   

9.
This paper presents the results of a simulation study to compare the performance of the Mann-Whitney U test, Student?s t test, and the alternate (separate variance) t test for two mutually independent random samples from normal distributions, with both one-tailed and two-tailed alternatives. The estimated probability of a Type I error was controlled (in the sense of being reasonably close to the attainable level) by all three tests when the variances were equal, regardless of the sample sizes. However, it was controlled only by the alternate t test for unequal variances with unequal sample sizes. With equal sample sizes, the probability was controlled by all three tests regardless of the variances. When it was controlled, we also compared the power of these tests and found very little difference. This means that very little power will be lost if the Mann-Whitney U test is used instead of tests that require the assumption of normal distributions.  相似文献   

10.
When the assumption of multivariate normality is violated and the sample sizes are relatively small, existing test statistics such as the likelihood ratio statistic and Satorra–Bentler’s rescaled and adjusted statistics often fail to provide reliable assessment of overall model fit. This article proposes four new corrected statistics, aiming for better model evaluation with nonnormally distributed data at small sample sizes. A Monte Carlo study is conducted to compare the performances of the four corrected statistics against those of existing statistics regarding Type I error rate. Results show that the performances of the four new statistics are relatively stable compared with those of existing statistics. In particular, Type I error rates of a new statistic are close to the nominal level across all sample sizes under a condition of asymptotic robustness. Other new statistics also exhibit improved Type I error control, especially with nonnormally distributed data at small sample sizes.  相似文献   

11.
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12.
《学校用计算机》2013,30(1-2):147-156
Abstract

Maddux, Johnson, and Willis mentioned in 1992 some “yet-to-be-developed types” that “have the potential to be Type II software if they are used in such a way that the user is given the ability to learn in new and better ways.” The authors of this paper will frame the discussion of learning management systems (LMS) around the concept of Type I and Type II applications of computers in education. We suggest that with the new trends of interoperability within WebCT, more researchers will accept WebCT as a potential Type II application. As more interactive learning objects are developed and shared on the WebCT format, it should be easier for instructors to create and teach courses that reflect the value systems expressed in the concept of Type II learning.  相似文献   

13.
Investigating the fit of a parametric model plays a vital role in validating an item response theory (IRT) model. An area that has received little attention is the assessment of multiple IRT models used in a mixed-format test. The present study extends the nonparametric approach, proposed by Douglas and Cohen (2001), to assess model fit of three IRT models (three- and two-parameter logistic model, and generalized partial credit model) used in a mixed-format test. The statistical properties of the proposed fit statistic were examined and compared to S-X2 and PARSCALE’s G2. Overall, RISE (Root Integrated Square Error) outperformed the other two fit statistics under the studied conditions in that the Type I error rate was not inflated and the power was acceptable. A further advantage of the nonparametric approach is that it provides a convenient graphical inspection of the misfit.  相似文献   

14.
Abstract

A Provocative Collection The War against the Intellect: Episodes In the Decline of Discourse By Peter Shaw Iowa City: University of Iowa Press, 1989, 181 pages, $22.50 hardcover, $10.95 paperback. Reviewed by Robert L. Spaeth

Giving Freshmen What They Deserve The Freshman Year Experience M. Lee Upcraft, John N. Gardner and Associates San Francisco: Jossey-Bass, 1989, 443 pages, $32.95 Reviewed by Roy Starling  相似文献   

15.
Type I error rate and power for the t test, Wilcoxon-Mann-Whitney (U) test, van der Waerden Normal Scores (NS) test, and Welch-Aspin-Satterthwaite (W) test were compared for two independent random samples drawn from nonnormal distributions. Data with varying degrees of skewness (S) and kurtosis (K) were generated using Fleishman's (1978) power function. Five sample size combinations were used with both equal and unequal variances. For nonnormal data with equal variances, the power of the U test exceeded the power of the t test regardless of sample size. When the sample sizes were equal but the variances were unequal, the t test proved to be the most powerful test. When variances and sample sizes were unequal, the W test became the test of choice because it was the only test that maintained its nominal Type I error rate.  相似文献   

16.
Students in psychology generally have difficulties to successfully accomplish mandatory courses in statistics. Group peer-tutoring is a pedagogical strategy to support them with a peer that has already successfully mastered the content of such a course. In order to specifically tailor group peer-tutoring to the needs of students and to sustain tutees’ participation, it is important to understand how they conceptualize tutoring. The aim of this study was to provide an empirical investigation of psychology students’ conceptualization regarding cross-year group peer-tutoring in statistics. A multivariate concept mapping analysis generated a relevant three-cluster structure (Tutoring setup, Tutor knowledge, interpersonal skills, and relational dynamics and Student role and commitment to the course) that underlies students’ cognitive structure regarding group peer-tutoring. The implications of the results for selecting and training peer-tutors are discussed.  相似文献   

17.
在认知诊断模型中进行题目功能差异(DIF)的检测,目的在于保证测验的质量与效果。在以往研究的基础上,本研究重点探索在CDMs框架下,MH、LR、CSIBTEST、WObs、WSw、WXPD 6种DIF检测方法在Q矩阵是否正确设定以及有关DIF影响因素等条件下的表现。结果表明:在Q矩阵正确设定时,WObs、WSw和WXPD统计量表现要好于MH、LR和CSIBTEST方法;在Q矩阵错误设定时,6种方法都会出现Ⅰ类错误率膨胀和统计检验力较低的现象。相对而言,MH、LR和CSIBTEST方法的表现比较稳定,WObs、WSw和WXPD统计量的表现变化较大,WObs、WSw和WXPD统计量的Ⅰ类错误率和统计检验力的结果依然好于MH、LR、CSIBTEST方法。  相似文献   

18.
We describe and evaluate a random permutation test of measurement invariance with ordered-categorical data. To calculate a p-value for the observed (?)χ2, an empirical reference distribution is built by repeatedly shuffling the grouping variable, then saving the χ2 from a configural model, or the ?χ2 between configural and scalar-invariance models, fitted to each permuted dataset. The current gold standard in this context is a robust mean- and variance-adjusted ?χ2 test proposed by Satorra (2000), which yields inflated Type I errors, particularly when thresholds are asymmetric, unless samples sizes are quite large (Bandalos, 2014; Sass et al., 2014). In a Monte Carlo simulation, we compare permutation to three implementations of Satorra’s robust χ2 across a variety of conditions evaluating configural and scalar invariance. Results suggest permutation can better control Type I error rates while providing comparable power under conditions that the standard robust test yields inflated errors.  相似文献   

19.
This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object – in particular, as a square. A series of displays show how the standard deviation is the size of the average square.  相似文献   

20.
Students can struggle to understand and use terms that describe probabilities. Such struggles lead to difficulties comprehending classroom conversations. In this article, we describe some specific misunderstandings a group of students (ages 11–12) held in regard to vocabulary such as certain, likely and unlikely. We discuss our efforts to help the students use such terms appropriately. In particular, we show how engaging students in a game requiring the use of the terms helped them begin to develop their vocabulary more fully. We also explain how a probability ladder visual organizer helped students begin to organize their thinking about the meanings of terms relative to one another.  相似文献   

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