The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower...The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower and upper quartiles. For efficient monitoring of process dispersion, we have proposed auxiliary information based Shewhart-type IQR control charts (namely IQRr and IQRp charts) based on ratio and product estimators of lower and upper quartiles under bivariate normally distributed process. We have developed the control structures of proposed charts and compared their performances with the usual IQR chart in terms of detection ability of shift in process dispersion. For the said purpose power curves are constructed to demonstrate the performance of the three IQR charts under discussion in this article. We have also provided an illustrative example to justify theory and finally closed with concluding remarks.展开更多
AIM： To compare four methods to approximate mean and standard deviation （SD） when only medians and interquartile ranges are provided.METHODS： We performed simulated meta-analyses on six datasets of 15, 30, 50, 100...AIM： To compare four methods to approximate mean and standard deviation （SD） when only medians and interquartile ranges are provided.METHODS： We performed simulated meta-analyses on six datasets of 15, 30, 50, 100, 500, and 1000 trials, respectively. Subjects were iteratively generated from one of the following seven scenarios： five theoreti-cal continuous distributions [Normal, Normal （0, 1）, Gamma, Exponential, and Bimodal] and two real-life distributions of intensive care unit stay and hospital stay. For each simulation, we calculated the pooled estimates assembling the study-specific medians and SD approximations： Conservative SD, less conservativeSD, mean SD, or interquartile range. We provided a graphical evaluation of the standardized differences.To show which imputation method produced the best estimate, we ranked those differences and calculated the rate at which each estimate appeared as the best, second-best, third-best, or fourth-best.RESULTS： Our results demonstrated that the best pooled estimate for the overall mean and SD was provided by the median and interquartile range （mean standardized estimates： 4.5 ± 2.2, P = 0.14） or by the median and the SD conservative estimate （mean standardized estimates： 4.5 ± 3.5, P = 0.13）. The less conservative approximation of SD appeared to be the worst method, exhibiting a significant difference from the reference method at the 90% confidence level. The method that ranked first most frequently is the interquartile range method （23/42 = 55%）, particularly when data were generated according to the Standard Normal, Gamma, and Exponential distributions. The second-best is the conservative SD method （15/42 = 36%）, particularly for data from a bimodal distributionand for the intensive care unit stay variable. CONCLUSION： Meta-analytic estimates are not signi-fcantly affected by approximating the missing values ofmean and SD with the correspondent values for medianand interquartile range.展开更多
文摘The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower and upper quartiles. For efficient monitoring of process dispersion, we have proposed auxiliary information based Shewhart-type IQR control charts (namely IQRr and IQRp charts) based on ratio and product estimators of lower and upper quartiles under bivariate normally distributed process. We have developed the control structures of proposed charts and compared their performances with the usual IQR chart in terms of detection ability of shift in process dispersion. For the said purpose power curves are constructed to demonstrate the performance of the three IQR charts under discussion in this article. We have also provided an illustrative example to justify theory and finally closed with concluding remarks.
文摘AIM： To compare four methods to approximate mean and standard deviation （SD） when only medians and interquartile ranges are provided.METHODS： We performed simulated meta-analyses on six datasets of 15, 30, 50, 100, 500, and 1000 trials, respectively. Subjects were iteratively generated from one of the following seven scenarios： five theoreti-cal continuous distributions [Normal, Normal （0, 1）, Gamma, Exponential, and Bimodal] and two real-life distributions of intensive care unit stay and hospital stay. For each simulation, we calculated the pooled estimates assembling the study-specific medians and SD approximations： Conservative SD, less conservativeSD, mean SD, or interquartile range. We provided a graphical evaluation of the standardized differences.To show which imputation method produced the best estimate, we ranked those differences and calculated the rate at which each estimate appeared as the best, second-best, third-best, or fourth-best.RESULTS： Our results demonstrated that the best pooled estimate for the overall mean and SD was provided by the median and interquartile range （mean standardized estimates： 4.5 ± 2.2, P = 0.14） or by the median and the SD conservative estimate （mean standardized estimates： 4.5 ± 3.5, P = 0.13）. The less conservative approximation of SD appeared to be the worst method, exhibiting a significant difference from the reference method at the 90% confidence level. The method that ranked first most frequently is the interquartile range method （23/42 = 55%）, particularly when data were generated according to the Standard Normal, Gamma, and Exponential distributions. The second-best is the conservative SD method （15/42 = 36%）, particularly for data from a bimodal distributionand for the intensive care unit stay variable. CONCLUSION： Meta-analytic estimates are not signi-fcantly affected by approximating the missing values ofmean and SD with the correspondent values for medianand interquartile range.
