For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its...For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.展开更多
一般说来,科技英语中的括号部分无论长短,汉译时,仍保留其括号。如: Sen.Patrick Leahy(D)of Vermont last month securedthe promise of Senate Agricultute Appropriations Com-mittee Chairman Thad Cochran(R)of Mississippi for a8...一般说来,科技英语中的括号部分无论长短,汉译时,仍保留其括号。如: Sen.Patrick Leahy(D)of Vermont last month securedthe promise of Senate Agricultute Appropriations Com-mittee Chairman Thad Cochran(R)of Mississippi for a8250,000 grant for sugar maple research at the Universityof Vermont. 美国佛蒙特州参议员Patrick Leahy(民主党人)展开更多
It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (...It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).展开更多
Counterfeit medicines are a growing problem in both developing and industrialised countries. In general the evaluation of these medicines is limited to the identification and the dosage of the active ingredients. In t...Counterfeit medicines are a growing problem in both developing and industrialised countries. In general the evaluation of these medicines is limited to the identification and the dosage of the active ingredients. In this study in vitro dissolution tests were conducted on two sets of counterfeit medicines containing PDE-5 inhibitors （sildenafil citrate and tadalafil）. The dissolution profiles were statistically compared to the ones of the genuine products using the f2-method and a comparison at each time point using the Cochran test. The results showed low equivalences between counterfeit and genuine products as well as higher variations around the mean dissolution value at the different time points for the counterfeit products.展开更多
In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the ...In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.展开更多
Data visualization blends art and science to convey stories from data via graphical representations.Considering different problems,applications,requirements,and design goals,it is challenging to combine these two comp...Data visualization blends art and science to convey stories from data via graphical representations.Considering different problems,applications,requirements,and design goals,it is challenging to combine these two components at their full force.While the art component involves creating visually appealing and easily interpreted graphics for users,the science component requires accurate representations of a large amount of input data.With a lack of the science component,visualization cannot serve its role of creating correct representations of the actual data,thus leading to wrong perception,interpretation,and decision.It might be even worse if incorrect visual representations were intentionally produced to deceive the viewers.To address common pitfalls in graphical representations,this paper focuses on identifying and understanding the root causes of misinformation in graphical representations.We reviewed the misleading data visualization examples in the scientific publications collected from indexing databases and then projected them onto the fundamental units of visual communication such as color,shape,size,and spatial orientation.Moreover,a text mining technique was applied to extract practical insights from common visualization pitfalls.Cochran’s Q test and McNemar’s test were conducted to examine if there is any difference in the proportions of common errors among color,shape,size,and spatial orientation.The findings showed that the pie chart is the most misused graphical representation,and size is the most critical issue.It was also observed that there were statistically significant differences in the proportion of errors among color,shape,size,and spatial orientation.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11401148)Ministry of Education of China,Humanities and Social Science Projects(Grant Nos.14YJC910005,10YJC790184)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LY14A010030)Zhejiang Provincial Philosophy and Social Science Planning Project of China(Grant No.13NDJC089YB)Houji Scholar Fund of Northwest A and F University,China
文摘For the linear mixed model with skew-normal random effects, this paper gives the density function, moment generating function and independence conditions. The noncentral skew chi-square distribution is defined and its density function is shown. The necessary and sufficient conditions under which a quadratic form is distributed as noncentral skew chi-square distribution are obtained. Also, a version of Cochran＇s theorem is given~ which modifies the result of Wang et al. （2009） and is used to set up exact tests for fixed effects and variance components of the proposed model. For illustration, our main results are applied to a real data problem.
文摘一般说来,科技英语中的括号部分无论长短,汉译时,仍保留其括号。如: Sen.Patrick Leahy(D)of Vermont last month securedthe promise of Senate Agricultute Appropriations Com-mittee Chairman Thad Cochran(R)of Mississippi for a8250,000 grant for sugar maple research at the Universityof Vermont. 美国佛蒙特州参议员Patrick Leahy(民主党人)
文摘It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).
文摘Counterfeit medicines are a growing problem in both developing and industrialised countries. In general the evaluation of these medicines is limited to the identification and the dosage of the active ingredients. In this study in vitro dissolution tests were conducted on two sets of counterfeit medicines containing PDE-5 inhibitors （sildenafil citrate and tadalafil）. The dissolution profiles were statistically compared to the ones of the genuine products using the f2-method and a comparison at each time point using the Cochran test. The results showed low equivalences between counterfeit and genuine products as well as higher variations around the mean dissolution value at the different time points for the counterfeit products.
文摘In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.
文摘Data visualization blends art and science to convey stories from data via graphical representations.Considering different problems,applications,requirements,and design goals,it is challenging to combine these two components at their full force.While the art component involves creating visually appealing and easily interpreted graphics for users,the science component requires accurate representations of a large amount of input data.With a lack of the science component,visualization cannot serve its role of creating correct representations of the actual data,thus leading to wrong perception,interpretation,and decision.It might be even worse if incorrect visual representations were intentionally produced to deceive the viewers.To address common pitfalls in graphical representations,this paper focuses on identifying and understanding the root causes of misinformation in graphical representations.We reviewed the misleading data visualization examples in the scientific publications collected from indexing databases and then projected them onto the fundamental units of visual communication such as color,shape,size,and spatial orientation.Moreover,a text mining technique was applied to extract practical insights from common visualization pitfalls.Cochran’s Q test and McNemar’s test were conducted to examine if there is any difference in the proportions of common errors among color,shape,size,and spatial orientation.The findings showed that the pie chart is the most misused graphical representation,and size is the most critical issue.It was also observed that there were statistically significant differences in the proportion of errors among color,shape,size,and spatial orientation.
