Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of ...Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.展开更多
A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, an...A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, and exponentially weighted moving average （EWMA） are applied to detect damage information according to statistical process control （SPC） theory. It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution. On the other hand, the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter. A suitable moderate confidence level is explored for more significant damage location and quantification detection, and the impact of noise is investigated to illustrate the robustness of the method.展开更多
Standard deviation(SD)and standard error of the mean(SEM)have been applied widely as error bars in scientific plots.Unfortunately,there is no universally accepted principle addressing which of these 2 measures should ...Standard deviation(SD)and standard error of the mean(SEM)have been applied widely as error bars in scientific plots.Unfortunately,there is no universally accepted principle addressing which of these 2 measures should be used.Here we seek to fill this gap by outlining the reasoning for choosing SEM over SD and hope to shed light on this unsettled disagreement among the biomedical community.The utility of SEM and SD as error bars is further discussed by examining the figures and plots published in 2 research articles on pancreatic disease.展开更多
文摘Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.
基金Natural Natural Science Foundation of China Under Grant No 50778077 & 50608036the Graduate Innovation Fund of Huazhong University of Science and Technology Under Grant No HF-06-028
文摘A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, and exponentially weighted moving average （EWMA） are applied to detect damage information according to statistical process control （SPC） theory. It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution. On the other hand, the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter. A suitable moderate confidence level is explored for more significant damage location and quantification detection, and the impact of noise is investigated to illustrate the robustness of the method.
基金BZ research was supported,in part,by the National Institutes of Health grant U24 AA026968the University of Massachusetts Center for Clinical and Translational Science grants UL1TR001453,TL1TR01454,and KL2TR01455.
文摘Standard deviation(SD)and standard error of the mean(SEM)have been applied widely as error bars in scientific plots.Unfortunately,there is no universally accepted principle addressing which of these 2 measures should be used.Here we seek to fill this gap by outlining the reasoning for choosing SEM over SD and hope to shed light on this unsettled disagreement among the biomedical community.The utility of SEM and SD as error bars is further discussed by examining the figures and plots published in 2 research articles on pancreatic disease.
