Pretest-posttest research designs are frequently employed in various research fields to eliminate individual variability so as to precisely assess treatment effects . In pretestposttest designs, screening is often performed on the baseline values to determine whether subjects are to be enrolled to the study. To assess the effectiveness of the treatment considered, the t test or the analysis of variance is often employed. Such procedures require normality of the underlying distribution. Even if the pretest and posttest scores jointly follow a bivariate normal distribution, screening of the pretest score will unquestionably depart from the normality assumption. Little research, however, has been done to assess the extent of non-normality under such a situation. The present paper examines the extent of non-normality caused by screening of the pretest scores. Under a bivariate normal distribution for pretest and posttest scores, the degree of departure from normality is assessed in terms of Kullback-Leibler divergence, skewness, and kurtosis of distributions for several types of screening schemes. Situations of maximum departure from normality will be identified. It is shown that, even at such a maximum departure from normality, the extent of departure is not so large, and hence our use of the t test and the analysis of variance can be validated from the viewpoint of robustness.
{"title":"ASSESSMENT OF NON-NORMALITY IN PRETEST-POSTTEST RESEARCH UNDER SCREENING OF THE PRETEST SCORE","authors":"Y. Kawata, Manabu Iwasaki","doi":"10.5183/JJSCS1988.21.31","DOIUrl":"https://doi.org/10.5183/JJSCS1988.21.31","url":null,"abstract":"Pretest-posttest research designs are frequently employed in various research fields to eliminate individual variability so as to precisely assess treatment effects . In pretestposttest designs, screening is often performed on the baseline values to determine whether subjects are to be enrolled to the study. To assess the effectiveness of the treatment considered, the t test or the analysis of variance is often employed. Such procedures require normality of the underlying distribution. Even if the pretest and posttest scores jointly follow a bivariate normal distribution, screening of the pretest score will unquestionably depart from the normality assumption. Little research, however, has been done to assess the extent of non-normality under such a situation. The present paper examines the extent of non-normality caused by screening of the pretest scores. Under a bivariate normal distribution for pretest and posttest scores, the degree of departure from normality is assessed in terms of Kullback-Leibler divergence, skewness, and kurtosis of distributions for several types of screening schemes. Situations of maximum departure from normality will be identified. It is shown that, even at such a maximum departure from normality, the extent of departure is not so large, and hence our use of the t test and the analysis of variance can be validated from the viewpoint of robustness.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114673164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EXTRACTING NON-LINEAR ADDITIVE REGRESSION STRUCTURE WITH POWER-ADDITIVE SMOOTHING SPLINES","authors":"Wataru Sakamoto","doi":"10.5183/JJSCS1988.20.83","DOIUrl":"https://doi.org/10.5183/JJSCS1988.20.83","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115464213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For square contingency tables with ordered categories, Tomizawa, Miyamoto and Hatanaka (2001) considered a measure that represents the degree of departure from symmetry. This paper extends the measure to multi-way tables with ordered categories. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure could be useful for comparing the degrees of departure from symmetry in several multi-way tables with ordered categories. Examples are given.
{"title":"A MEASURE OF ASYMMETRY FOR MULTI-WAY CONTINGENCY TABLES WITH ORDERED CATEGORIES","authors":"K. Yamamoto, S. Tomizawa","doi":"10.5183/JJSCS1988.20.39","DOIUrl":"https://doi.org/10.5183/JJSCS1988.20.39","url":null,"abstract":"For square contingency tables with ordered categories, Tomizawa, Miyamoto and Hatanaka (2001) considered a measure that represents the degree of departure from symmetry. This paper extends the measure to multi-way tables with ordered categories. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure could be useful for comparing the degrees of departure from symmetry in several multi-way tables with ordered categories. Examples are given.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116704678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Individuals' choices of categories observed on two occasions are described by transition frequency matrices. In this paper, a penalized optimal scaling method is presented to analyze a set of the matrices obtained from multiple sources and graphically represent a transition trend for each source as a vector. This method finds scores of individuals, those of categories, and vectors of trends, in such a way that individuals' scores become homogeneous to the scores of chosen categories and trend vectors become homogeneous to the inter-occasion changes in individuals' scores. The resulting lowdimensional configuration of trend vectors allows us easily to grasp transition trends. Further, the projection of category scores onto trend vectors gives the unidimensional scales of categories useful for scrutinizing transition trends.
{"title":"TREND VECTOR REPRESENTATION OF MULTIPLE TRANSITION MATRICES BY PENALIZED OPTIMAL SCALING","authors":"K. Adachi","doi":"10.5183/JJSCS1988.20.19","DOIUrl":"https://doi.org/10.5183/JJSCS1988.20.19","url":null,"abstract":"Individuals' choices of categories observed on two occasions are described by transition frequency matrices. In this paper, a penalized optimal scaling method is presented to analyze a set of the matrices obtained from multiple sources and graphically represent a transition trend for each source as a vector. This method finds scores of individuals, those of categories, and vectors of trends, in such a way that individuals' scores become homogeneous to the scores of chosen categories and trend vectors become homogeneous to the inter-occasion changes in individuals' scores. The resulting lowdimensional configuration of trend vectors allows us easily to grasp transition trends. Further, the projection of category scores onto trend vectors gives the unidimensional scales of categories useful for scrutinizing transition trends.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116731836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In longitudinal clinical trials that compare treatments of chronic diseases missing data occur mainly because of dropouts, where patients stop participating in the trial before the completion due to various reasons. Such incomplete data are often analyzed by using so-called completer analysis and/or LOCF (Last Observation Carried Forward). However, such procedures require strong assumptions for their validity. Multiple imputation (MI) (Rubin, 1987) is a valid method under MAR (Missing At Random). This method consists of three steps ("imputation", "analysis" and "combination") and various methods for MI also have been proposed. In this paper, we evaluate the performance of four methods for MI contrasted with completer analysis and LOCF via Monte-Carlo simulations in the context of small-sample longitudinal clinical trials for comparison of two treatments. The performance of these methods with non-normal data (i.e. mixture of responders and non-responders) is also examined.
在比较慢性病治疗方法的纵向临床试验中，数据缺失的主要原因是患者中途退出，即患者因各种原因在试验结束前停止参与试验。这种不完整的数据通常通过所谓的完全分析和/或lof(最后观察结转)来分析。然而，这些程序的有效性需要强有力的假设。多重插值(Multiple imputation, Rubin, 1987)是在随机缺失(Missing At Random)情况下有效的方法。该方法包括“归算”、“分析”和“组合”三个步骤，并提出了各种MI方法。在本文中，我们通过蒙特卡罗模拟，在小样本纵向临床试验的背景下，评估了四种MI方法与完全分析和LOCF方法的性能，以比较两种治疗方法。这些方法的性能与非正常数据(即反应者和非反应者的混合物)也进行了检查。
{"title":"EVALUATION OF STATISTICAL METHODS FOR ANALYSIS OF SMALL-SAMPLE LONGITUDINAL CLINICAL TRIALS WITH DROPOUTS","authors":"Takayuki Abe, Manabu Iwasaki","doi":"10.5183/JJSCS1988.20.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.20.1","url":null,"abstract":"In longitudinal clinical trials that compare treatments of chronic diseases missing data occur mainly because of dropouts, where patients stop participating in the trial before the completion due to various reasons. Such incomplete data are often analyzed by using so-called completer analysis and/or LOCF (Last Observation Carried Forward). However, such procedures require strong assumptions for their validity. Multiple imputation (MI) (Rubin, 1987) is a valid method under MAR (Missing At Random). This method consists of three steps (\"imputation\", \"analysis\" and \"combination\") and various methods for MI also have been proposed. In this paper, we evaluate the performance of four methods for MI contrasted with completer analysis and LOCF via Monte-Carlo simulations in the context of small-sample longitudinal clinical trials for comparison of two treatments. The performance of these methods with non-normal data (i.e. mixture of responders and non-responders) is also examined.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132416041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider methods for parameter estimation of the shifted power transformation. The ordinary likelihood function is unbounded and then fails to have a local maximum. This is a non-regular problem in likelihood because the range of observations depends on the unknown shift parameter. To avoid such a difficulty , we discuss the group likelihood method and the maximum product of spacings method, in a univariate case, assuming the power-normal distribution as an underlying distribution for observations. We describe the computational procedures for parameter estimation. To evaluate the performance of the estimates from the two methods, we perform a simulation study. In addition, two examples are given to illustrate some aspects of the two methods.
{"title":"A COMPARISON OF METHODS FOR PARAMETER ESTIMATION OF THE SHIFTED POWER TRANSFORMATION","authors":"T. Hamasaki, Tomoyuki Sugimoto","doi":"10.5183/JJSCS1988.20.65","DOIUrl":"https://doi.org/10.5183/JJSCS1988.20.65","url":null,"abstract":"We consider methods for parameter estimation of the shifted power transformation. The ordinary likelihood function is unbounded and then fails to have a local maximum. This is a non-regular problem in likelihood because the range of observations depends on the unknown shift parameter. To avoid such a difficulty , we discuss the group likelihood method and the maximum product of spacings method, in a univariate case, assuming the power-normal distribution as an underlying distribution for observations. We describe the computational procedures for parameter estimation. To evaluate the performance of the estimates from the two methods, we perform a simulation study. In addition, two examples are given to illustrate some aspects of the two methods.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131655639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"SEMIPARAMETRIC TRANSFORMATION FOR THEORETICAL MODEL","authors":"Masanori Ito, M. Goto","doi":"10.5183/JJSCS1988.19.57","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.57","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128712003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to develop a nonparametric k-sample test based on a modified Baumgartner statistic. We define a new modified Baumgartner statistic B* and give some critical values. Then we compare the power of the B* statistic with the t-test, the Wilcoxon test, the Kolmogorov-Smirnov test, the Cramer-von Mises test, the Anderson-Darling test and the original Baumgartner statistic. The B* statistic is more suitable than the Baumgartner statistic for the location parameter when the sample sizes are not equal. Also, the B* statistic has almost the same power as the Wilcoxon test for location parameter. For scale parameter, the power of the B* statistic is more efficient than the Cramer-von Mises test and the Anderson-Darling test when the sizes are equal. The power of the B* statistic is higher than the Kolmogorov-Smirnov test for location and scale parameters. Then the B* statistic is generalized from two-sample to k-sample problems. The Bk* statistic denotes a k-sample statistic based on the B* statistic. We compare the power of the Bk* statistic with the Kruskal-Wallis test, the k-sample Kolmogorov-Smirnov test, the k-sample Cramer-von Mises test, the k-sample Anderson-Darling test and the k-sample Baumgartner statistic. Finally, we investigate the behavior of power about the Bk* statistics by simulation studies. As a result, we obtain that the Bk* statistic is more suitable than the other statistics.
{"title":"A K-SAMPLE RANK TEST BASED ON MODIFIED BAUMGARTNER STATISTIC AND ITS POWER COMPARISON","authors":"H. Murakami","doi":"10.5183/JJSCS1988.19.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.1","url":null,"abstract":"The purpose of this paper is to develop a nonparametric k-sample test based on a modified Baumgartner statistic. We define a new modified Baumgartner statistic B* and give some critical values. Then we compare the power of the B* statistic with the t-test, the Wilcoxon test, the Kolmogorov-Smirnov test, the Cramer-von Mises test, the Anderson-Darling test and the original Baumgartner statistic. The B* statistic is more suitable than the Baumgartner statistic for the location parameter when the sample sizes are not equal. Also, the B* statistic has almost the same power as the Wilcoxon test for location parameter. For scale parameter, the power of the B* statistic is more efficient than the Cramer-von Mises test and the Anderson-Darling test when the sizes are equal. The power of the B* statistic is higher than the Kolmogorov-Smirnov test for location and scale parameters. Then the B* statistic is generalized from two-sample to k-sample problems. The Bk* statistic denotes a k-sample statistic based on the B* statistic. We compare the power of the Bk* statistic with the Kruskal-Wallis test, the k-sample Kolmogorov-Smirnov test, the k-sample Cramer-von Mises test, the k-sample Anderson-Darling test and the k-sample Baumgartner statistic. Finally, we investigate the behavior of power about the Bk* statistics by simulation studies. As a result, we obtain that the Bk* statistic is more suitable than the other statistics.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"2017 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120847176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ranked preference data arise in the situation that a large number of people (voters) rank several objects (candidates) in order of their extent of preference, for instance, multiple voting with ranking or a questionnaire of preference ranking. Such data are supposed to include the information about similarity among candidates in the sense that those who are highly preferred by the same voter would seem to be similar to the voter. Based on this idea, we have proposed a method to evaluate the geometrical configuration and distance between candidates by applying multidimensional scaling (MDS) on ranked preference data in which each voter votes multiple candidates consistently with their preference ranking. In this paper, we have an experiment in order to investigate the feasibility of this method. Using simulative data, we examine whether our method can retrieve the original configuration. We generate candidates and voters simulatively and apply this method to the data obtained. We also have an application to actual data obtained from students about allocation to advisory professor at undergraduate course (for bachelor degree).
{"title":"A METHOD TO EVALUATE GEOMETRICAL CONFIGURATION OF CANDIDATES FROM RANKED PREFERENCE DATA","authors":"T. Obata, H. Ishii","doi":"10.5183/JJSCS1988.19.27","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.27","url":null,"abstract":"Ranked preference data arise in the situation that a large number of people (voters) rank several objects (candidates) in order of their extent of preference, for instance, multiple voting with ranking or a questionnaire of preference ranking. Such data are supposed to include the information about similarity among candidates in the sense that those who are highly preferred by the same voter would seem to be similar to the voter. Based on this idea, we have proposed a method to evaluate the geometrical configuration and distance between candidates by applying multidimensional scaling (MDS) on ranked preference data in which each voter votes multiple candidates consistently with their preference ranking. In this paper, we have an experiment in order to investigate the feasibility of this method. Using simulative data, we examine whether our method can retrieve the original configuration. We generate candidates and voters simulatively and apply this method to the data obtained. We also have an application to actual data obtained from students about allocation to advisory professor at undergraduate course (for bachelor degree).","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122450732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For square contingency tables with ordered categories, the marginal homogeneity (MH) model is equivalent to the equality of row and column marginal ridits. This paper proposes a measure to represent what degree the row marginal ridit departs from the column marginal ridit. The measure is expressed by using the Cressie-Read powerdivergence or Patil-Taillie diversity index, which is applied to the marginal ridits. It is useful for comparing the degree of departure from MH in several tables. Examples are given. The proposed measure is also compared with the measure of departure from MH by Tahata, Iwashita and Tomizawa (2006), and with the goodness-of-fit test statistic of the MH model.
{"title":"A MEASURE OF ASYMMETRY OF MARGINAL RIDITS FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES","authors":"Kouji Tahata, Kousei Tajima, S. Tomizawa","doi":"10.5183/JJSCS1988.19.69","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.69","url":null,"abstract":"For square contingency tables with ordered categories, the marginal homogeneity (MH) model is equivalent to the equality of row and column marginal ridits. This paper proposes a measure to represent what degree the row marginal ridit departs from the column marginal ridit. The measure is expressed by using the Cressie-Read powerdivergence or Patil-Taillie diversity index, which is applied to the marginal ridits. It is useful for comparing the degree of departure from MH in several tables. Examples are given. The proposed measure is also compared with the measure of departure from MH by Tahata, Iwashita and Tomizawa (2006), and with the goodness-of-fit test statistic of the MH model.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121252585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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