This paper compares ridit analysis with modified ridit analysis. The comparison was then illustrated with an example. It was observed from the example at least, that when the sample sizes of the two samples being compared are too disparate, a more reliable conclusion using the Bross ridit analysis is likely to be reached only when the group with the larger sample size is used as the reference group. Otherwise Bross ridit analysis would lead to conflicting conclusions, depending on which group is used as the reference group. Modified ridit analysis treats the groups being studied as samples drawn from some larger populations in which the variances or standard deviations as well as the results obtained are the same no matter which sample is used as the reference group. The modified procedure is therefore preferable to ridit analysis especially in cases where the groups being compared are samples from some populations.
This paper proposes and develops a statistic here termed the 'relative performance index' or the index of relative performance' by subjects both within and between several sampled populations for preferentially rank-ordering subjects by their relative performance in comparison with other subjects from these populations involved in a test or contest. The proposed index would enable decisions on the preferential selection of subjects both within and between various classifications for management purposes. The proposed method enables the estimation of the median and other tiles of not only each of the sampled populations but also the common median of the several populations as functions of the relative performance indices. The method unlike some other methods used for the analysis of many samples is based mostly on individual subjects rather than on only summary indices or averages. Test statistics also based on subject specific relative performance indices are developed to test desired hypothesis concerning population. The proposed indices being subject specific rather than merely summary averages easily enables one to more clearly and succinctly examine individual subjects relative performance or level of seriousness in a condition in comparison with other subjects from the sampled populations thereby providing subject targeted information to better guide any interventionist actions on a condition of research interest. The method is illustrated with some data and shown to compare favorably with some existing methods.
This paper proposes a statistical method called 'the G method' to highlight its generalized nature for the determination and assignment of ranks to sample observations drawn from several populations for possible use in further analyses. The sampled populations may be measurements on as low as the ordinal scale and need not be continuous or even numeric. The proposed rank determination statistical model intrinsically and structurally provides for the breaking of possible ties between sample observations and automatically assigning such observations their mean ranks. This approach and hence the proposed model therefore obviate the need for the sampled populations to be continuous. They may be discrete or even non-numeric measurements on as low as the ordinal scale. The proposed method is of more generalized and wider applicability than an existing formulation which can be used with only continuous populations and is easier to use in practice than the usual traditional method which is often tedious and cumbersome, especially with large samples. The proposed method is illustrated with some data and shown to yield the same results as other existing methods where these methods are equally applicable.
This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.
Abstract:This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with 'c' treatments or conditions considered as fixed, while the row as second factor with say 'k' subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the 'c' treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman's two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.