Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

MAXIMUM TEST FOR A SEQUENCE OF QUADRATIC FORM STATISTICS ABOUT SCORE TEST IN LOGISTIC REGRESSION MODEL

This article proposes the maximum test for a sequence of quadratic form statistics about score test in logistic regression model which can be applied to genetic and medicine fields.Theoretical properties about the maximum test are derived.Extensive simulation studies are conducted to testify powers robustness of the maximum test compared to other two existed test.We also apply the maximum test to a real dataset about multiple gene variables association analysis.

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

Testing for Homogeneity of Linkage Disequilibrium Across Strata

In this article, using the likelihood score theory extended to nuisance parameters we derive a new homogeneity score test for comparing linkage disequilibrium across several strata. Power and sample size formulae are also obtained.

Relationship between English Leaming Motivation and SCET-3 Scores of Non-English Major Students in CDSI

Motivation is considered an important factor for non-English major students in their language learning. In the study, questionnaires and interviews were used to explore the relationship between learning motivations of CDSI （Chengdu Sport Institute）＇s non-English major students and their test scores in SCET-3 （Sichuan English Test-level 3）. The results found that in general non-English major students＇ motivation is not high with no significant gender differences; their learning motivation shows some correlation with their vocabulary level; their external motivation has more impact on the non-English major students. Therefore, language learning motivation has a positive relation with students＇ English learning achievement. Considering the characteristics of the non-English major students, suggestions on English teaching methods are made to stimulate students＇ learning motivation and cultivate their learning strategies, so as to improve the quality of English teaching and students＇ English level.

MAXIMIN EFFICIENCY ROBUST TEST FOR MULTIPLE NUISANCE PARAMETERS AND ITS STATISTICAL PROPERTIES

We propose the maximin efficiency robust test（MERT） for multiple nuisance parameters based on theories about the maximin efficiency robust test for only one nuisance parameter and investigate some theoretical properties about this robust test.We explore some theoretical properties about the power of the MERT for multiple nuisance parameters in a specified scenario intuitively further more.We also propose a meaningful example from statistical genetic field to which the MERT for multiple nuisance parameters can be well applied.Extensive simulation studies are conducted to testify the robustness of the MERT for multiple nuisance parameters.

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

Excisional hemorrhoidal surgery and its effect on anal continence

AIM:To investigate the role of anal cushions in hemorrhoidectomy and its effect on anal continence of the patients.METHODS:Seventy-six consecutive patients(33 men and 43 women) with a mean age of 44 years were included.They underwent Milligan-Morgan hemorrhoidectomy because of symptomatic third-and fourth-degree hemorrhoids and failure in conservative treatment for years.Wexner score was recorded and liquid continence test was performed for each patient before and two months after operation using the techniques described in our previous work.The speed-constant rectal lavage apparatus was prepared in our laboratory.The device could output a pulsed and speed-constant saline stream with a high pressure,which is capable of overcoming any rectal resistance change.The patients were divided into three groups,group A(< 900 mL),group B(900-1200 mL) and group C(> 1200 mL) according to the results of the preoperative liquid continence test.RESULTS:All the patients completed the study.The average number of hemorrhoidal masses excised was 2.4.Most patients presented with hemorrhoidal symptoms for more than one year,including a mean duration of incontinence of 5.2 years.The most common symptoms before surgery were anal bleeding(n = 55),prolapsed lesion(n = 34),anal pain(n = 12) and constipation(n = 17).There were grade Ⅲ hemorrhoids in 39(51.3%) patients,and grade Ⅳ in 37(48.7%) patients according to Goligher classification.Five patients had experienced hemorrhoid surgery at least once.Compared with postoperative results,the retained volume in the preoperative liquid continence test was higher in 40 patients,lower in 27 patients,and similar in the other 9 patients.The overall preoperative retained volume in the liquid continence test was 1130.61 ± 78.35 mL,and postoperative volume was slightly decreased(991.27 ± 42.77 mL),but there was no significant difference(P = 0.057).Difference was significant in the test value before and after hemorrhoidectomy in group A(858.24 ± 32.01 mL vs 574.18 ± 60.28 mL,P = 0.011),but no obvious difference was noted in group B or group C.There was no significant difference in Wexner score before and after operation(1.68 ± 0.13 vs 2.10 ± 0.17,P = 0.064).By further stratified analysis,there was significant difference before and 2 months after operation in group A(2.71 ± 0.30 vs 3.58 ± 0.40,P = 0.003).In contrast,there were no significant differences in group B or group C(1.89 ± 0.15 vs 2.11 ± 0.19,P = 0.179;0.98 ± 0.11 vs 1.34 ± 0.19,P = 0.123).CONCLUSION:There is no difference in the continence status of patients before and after Milligan-Morgan hemorrhoidectomy.However,patients with preoperative compromised continence may have further deterioration of their continence,hence Milligan-Morgan hemorrhoidectomy should be avoided in such patients.

A new interpretation and quantitative method for diplopia test： 304 cases of ocular motor nerve palsy for clinical test and verify

We introduce a new interpretation and quantitative method for computerized diplopia test. By comparing this new method to the Hess screen test, we validate its applicability among 304 patients with ocular motor nerve palsy. This new method shows great assistant value as the Hess screen test in making accurate diagnosis and quantitative evaluation the severity of diplopia. Furthermore, it is more convenient and suitable for daily clinical use.

Quasi-Binomial Regression Model for the Analysis of Data with Extra-Binomial Variation

Objectives: Developing inference procedures on the quasi-binomial distribution and the regression model. Methods: Score testing and the method of maximum likelihood for regression parameters estimation. Data: Several examples are included, based on published data. Results: A quasi-binomial model is used to model binary response data which exhibit extra-binomial variation. A partial score test on the binomial hypothesis versus the quasi-binomial alternative is developed and illustrated on three data sets. The extended logit transformation on the binomial parameter is introduced and the large sample dispersion matrix of the estimated parameters is derived. The Nonlinear Mixed Procedure (NLMIXED) in SAS is shown to be very appropriate for the estimation of nonlinear regression.

A Study of Writing Test in CET-4

The paper discusses the ＂Writing Test＂ in College English Test - Band Four in two aspects. One is the design of the ＂Writing＂ form; the other is the scoring process. From the discussion the paper comes to a conclusion that the ＂Writing Test＂ in CET-4 should be reformed in two ways： the single style of the ＂Writing＂ structure should be changed to various styles in design, and the ＂global scoring＂ principle used in marking the writing should be changed to ＂local scoring＂. At last, the author suggests some ways of how to put the reforming into reality,

Spatial Structure of Peer Networks and Academic Achievement Based on a Random Control Trial Experiment

This paper investigates whether changing the seating arrangement in a classroom can facilitate positive spillovers from top-performing students to others,using a field experiment conducted in a Chinese high school.Among study groups with balanced abilities,the treatment altered the spatial distribution by assigning the two top students to seats in the spatial center of each group.In the reference groups where students were allowed to choose their own seating arrangements,the lowest performing were significantly less likely to sit next to a top student than they would be under a random assignment.The results suggest that,in the treated groups,there could be enhanced academic spillovers from the top students.The treatment especially benefited the two lowest performing students in science subjects.In contrast,the treatment exerted negative effects on the test scores of the two middle-performing students,due to a disruption mechanism.The results suggest that the spatial layout of a peer network can have a significant impact on learning outcomes.

A Score Type Test for General Autoregressive Models in Time Series

This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.

Test Score or Student Progress?A Value-Added Evaluation of School Effectiveness in Urban China

Outcome-oriented evaluation of school effectiveness is often based on student test scores in certain critical examinations.This study provides another method of evaluation-value-added-which is based on student achievement progress.This paper introduces the method of estimating the value-added score of schools in multi-level models.Based on longitudinal student achievement data,two measures of school effectiveness in one local education authority in China are compared.It is found that the between-school difference in both test-score and value-added is large comparable with that of Western countries.The results of the two measures of school effectiveness are highly different.The value-added measures lack consistency across different subject areas within schools while the test score measures are highly correlated between subjects.Teachers show their preference for value-added measures over test-score measures of education quality.It is suggested that value-added measures of school effectiveness should be used as a complement to rather than a substitute for test-score measures.The shortcomings of value-added approach are also discussed.

Score Tests for Zero-inflated Double Poisson Regression Models

Count data with excess zeros encountered in many applications often exhibit extra variation. There- fore, zero-inflated Poisson （ZIP） model may fail to fit such data. In this paper, a zero-inflated double Poisson model （ZIDP）, which is generalization of the ZIP model, is studied and the score tests for the significance of dis- persion and zero-inflation in ZIDP model are developed. Meanwhile, this work also develops homogeneous tests for dispersion and/or zero-inflation parameter, and corresponding score test statistics are obtained. One numer- ical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.