110,959 research outputs found

    Optimal design of the Wilcoxon-Mann-Whitney-test

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    In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes mm and nn for fixed N=m+nN = m + n) that maximizes the power of the applied statistical test. It is known that the two-sample t-tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the non-parametric Wilcoxon-Mann-Whitney-test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design m=nm = n in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions. Please cite this paper as published in the Biometrical Journal (https://doi.org/10.1002/bimj.201600022)

    Mann-whitney criterion

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    In the work, a practical problem is solved by Mann-Whitney test. Mann-Whitney test is a statistical criterion used to evaluate differences between two independent samples in terms of any sign of measured quantitatively; it allows to detect differences in the value of the parameter between small samples. This criterion is widely used in psychology for data analysis

    Pelatihan Berfikir Positif untuk Meningkatkan Self-Esteem pada Remaja Yatim Piatu di Yogyakarta

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    The aim of this research is to test the effectivennes the effects of positif thinking training in self-esteem of teen orphanage woman ‘X’ Yogyakarta. Subjects were 12 adolescents divided into 6 subjects of the experimental group and 6 subjects of the control group with low and medium self-esteem categories. Self-esteem category obtained from score scale Coopersmith Self Esteem Inventory (CSEI) from Coopersmith (1967) adapted and modified by the researchers. The research design used pre-post control group design with data analysis technique used Mann-Whitney test and Wilcoxon test. The Mann-Whitney test was used to see the difference in scores in the experimental and control groups. The result of data analysis with Mann-Whitney test showed that there was no significant difference of self-esteem in the experimental group after being treated with self-esteem control group without being treated (p = 0,746> 0,05). The result of data analysis with Wilcoxon test showed that there was a significant difference of self-esteem in experimental group before and after treatment (p = 0,027 <0,05).The aim of this research is to test the effectivennes the effects of positif thinking training inself-esteem of teen orphanage woman ‘X’ Yogyakarta. Subjects were 12 adolescentsdivided into 6subjects of the experimental group and 6 subjects of the control group with lowand medium self-esteem categories. Self-esteem category obtained from score scaleCoopersmithSelf Esteem Inventory (CSEI) from Coopersmith (1967) adapted and modifiedby theresearchers. The research design used pre-post control group design with dataanalysis technique used Mann-Whitney test and Wilcoxon test. The Mann-Whitney test wasused to see the difference in scores in the experimental and control groups. The result ofdata analysis with Mann-Whitney test showed that there was no significant difference of selfesteemintheexperimentalgroupafterbeingtreatedwithself-esteemcontrolgroupwithoutbeingtreated(p=0,746>0,05).TheresultofdataanalysiswithWilcoxontestshowedthattherewasasignificantdifferenceofself-esteeminexperimentalgroupbeforeandaftertreatment(p=0,027<0,05)

    Sensitivity analysis of the refinement to the mann-whitney test

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    The aim of researchers when comparing two independent groups is to collect large normally distributed samples unless they lack the resources to access them. In these situations, there are a myriad of non-parametric tests to select, of which the Mann Whitney U test is the most commonly used. In spite of its great advantages of usage, the U test is capable of producing inflated Type I error when applied in situation of heterogeneity or distinct variances. This current study will present a viable alternative called the refined Mann-Whitney test (RMW). A Monte Carlo evaluation test is conducted on RMW using artificial data of various combinations of extreme test conditions. This study reviews that the RMW test justified its development by enhancing the performance of the U test. The RMW test is able to control well its Type I error rates even though it has a lower power

    Hypothesis testing for two population means: parametric or non-parametric test?

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    The parametric Welch tt-test and the non-parametric Wilcoxon-Mann-Whitney test are the most commonly used two independent sample means tests. More recent testing approaches include the non-parametric, empirical likelihood and exponential empirical likelihood. However, the applicability of these non-parametric likelihood testing procedures is limited partially because of their tendency to inflate the type I error in small sized samples. In order to circumvent the type I error problem, we propose simple calibrations using the tt distribution and bootstrapping. The two non-parametric likelihood testing procedures, with and without those calibrations, are then compared against the Wilcoxon-Mann-Whitney test and the Welch tt-test. The comparisons are implemented via extensive Monte Carlo simulations on the grounds of type I error and power in small/medium sized samples generated from various non-normal populations. The simulation studies clearly demonstrate that a) the tt calibration improves the type I error of the empirical likelihood, b) bootstrap calibration improves the type I error of both non-parametric likelihoods, c) the Welch tt-test with or without bootstrap calibration attains the type I error and produces similar levels of power with the former testing procedures, and d) the Wilcoxon-Mann-Whitney test produces inflated type I error while the computation of an exact p-value is not feasible in the presence of ties with discrete data. Further, an application to real gene expression data illustrates the computational high cost and thus the impracticality of the non parametric likelihoods. Overall, the Welch t-test, which is highly computationally efficient and readily interpretable, is shown to be the best method when testing equality of two population means.Comment: Accepted for publication in the Journal of Statistical Computation and Simulatio

    Analisis Perbandingan Kinerja Portofolio Optimal Markowitz Model dan Treynor Black Model pada Saham LQ45 di Bursa Efek Indonesia

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    Penelitian ini bertujuan untuk menganalisis kinerja portofolio optimal Model Markowitz dan Model Treynor Black selama periode 2011-2018. Penelitian menggunakan populasi berupa saham di Bursa Efek Indonesia (BEI) yang tergolong saham LQ45 dengan sampel sebanyak 20 perusahaan. Teknik pengambilan sampel menggunakan purposive sampling. Analisis data dalam penelitian ini adalah portofolio optimal dan uji Mann Whitney Test. Hasil penelitian menunjukkan Teori Portofolio Markowitz menekankan pada upaya memaksimalkan ketidakpastian risiko dalam pemilihan dan penyusunan portofolio yang optimal. Sedangkan Model Treynor diperoleh dengan cara menurunkan rata-rata return saham dengan return investasi bebas risiko yang akan menghasilkan premi risiko, kemudian membaginya dengan beta saham. Semakin tinggi nilai yang dihasilkan maka semakin baik kinerja saham. Hasil Mann Whitney Test menunjukkan bahwa rata-rata return portofolio saham selama tahun 2011-2018 yaitu model Markowitz lebih tinggi dari rata-rata portofolio return saham model Treynor selama tahun 2011- 2018. Hal ini menunjukkan bahwa return portofolio saham model Markowitz lebih baik dibandingkan model Treynor. Dari hasil Mann-Whitney Test juga terdapat perbedaan Kinerja Model Markowitz dan Model Treynor Black.     &nbsp
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