Suhaida Abdullah

Performance of the modified Wilcoxon signed rank test

Nonparametric methods require only few assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid. The Wilcoxon signed rank test applies to matched pairs studies. For two tail test, it tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference. The test is based on the Wilcoxon signed rank statistic W, which is the smaller of the two ranks sums. The steps to compute W consider the positive and negative differences and omit all the zero differences. In this study, we modify the Wilcoxon signed rank test using the indicator function of positive, zero and negative differences to compute the Wilcoxon statistic, W. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under different distributional shapes, sample sizes, and number of replications. The modified Wilcoxon signed rank test was found to be robust under symmetric distributions even though the values are quite conservative. The finding also demonstrated that different number of replication does not influence the result because there is not much difference in the value of the Type I error rates obtained.Nonparametric methods require only few assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid. The Wilcoxon signed rank test applies to matched pairs studies. For two tail test, it tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference. The test is based on the Wilcoxon signed rank statistic W, which is the smaller of the two ranks sums. The steps to compute W consider the positive and negative differences and omit all the zero differences. In this study, we modify the Wilcoxon signed rank test using the indicator function of positive, zero and negative differences to compute the Wilcoxon statistic, W. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under different distributional shapes, sample sizes, and number of replications. The modified W...

Robust correlation coefficient based on Qn estimator

This paper presents a new robust correlation coefficient called Qn correlation coefficient. This coefficient is developed as an alternative for classical correlation coefficient as the performance of classical correlation coefficient is nasty under contamination data. This study applied robust scale estimator called Qn because this estimator have high breakdown point. Simulation studies are carried out in determining the performances of the new robust correlation coefficient. Clean and contamination data are generated in assessing the performance of these coefficient. The performances of the Qn correlation coefficient is compared with classical correlation coefficient based on the value of coefficient, average bias and standard error. The outcome of the simulation studies shows that the performance of Qn correlation coefficient is superior compared to the classical and existing robust correlation coefficient.

Median based robust correlation coefficient

Real datasets usually include a fraction of outliers and other contaminations. The classical correlation coefficient is much affected by these outliers and often gives misleading results. The problem of computing the correlation estimate from bivariate data containing a portion of outliers has been deliberated in this study. The classical correlation uses non-robust mean and standard deviation as the location and scale estimator respectively. In this study, two robust correlation coefficients based on high breakdown point median estimator were examined. The performance of the classical correlation together with the robust correlation coefficient was measured and compared in terms of the correlation value, average bias and standard error for the clean and contaminated data. Simulation studies reveal that all correlation coefficients perform well for clean data. However, under contaminated data, the findings show that median based robust correlation coefficient gives better results as compared to the classical correlation coefficient.Real datasets usually include a fraction of outliers and other contaminations. The classical correlation coefficient is much affected by these outliers and often gives misleading results. The problem of computing the correlation estimate from bivariate data containing a portion of outliers has been deliberated in this study. The classical correlation uses non-robust mean and standard deviation as the location and scale estimator respectively. In this study, two robust correlation coefficients based on high breakdown point median estimator were examined. The performance of the classical correlation together with the robust correlation coefficient was measured and compared in terms of the correlation value, average bias and standard error for the clean and contaminated data. Simulation studies reveal that all correlation coefficients perform well for clean data. However, under contaminated data, the findings show that median based robust correlation coefficient gives better results as compared to the classi...

The performance of robust correlation coefficient under contaminated bivariate data

Classical correlation coefficient is a powerful statistical analysis when measuring a relationship between the bivariate normal distribution when the assumptions are fulfill. However, this classical correlation coefficient performs poor in the presence of outlier. Thus, this study aims to propose new version of robust correlation coefficient based on MADn and Sn. The performance of this proposed robust correlation coefficient will be evaluated based on three indicators which were the value of the correlation coefficient, average bias and standard error. The proposed procedure is expected to produce MADn correlation coefficient and Sn correlation coefficient. Both coefficients are expected to perform better than classical correlation coefficient and resistance to the outlier.

Modified H-statistic with adaptive Winsorized mean in two groups test

t-test is a commonly used test statistics when comparing two independent groups. The computation of this test is simple yet it is powerful under normal distribution and equal variance dataset. However, in real life data, sometimes it is hard to get dataset which has this package. The violation of assumptions (normality and equal variances) will give the devastating effect on the Type I error rate control to the t-test. On the same time, the statistical power also will be reduced. Therefore in this study, the adaptive Winsorised mean with hinge estimator in H-statistic (AWM-H) is proposed. The H-statistic is one of the robust statistics that able to handle the problem of nonnormality in comparing independent group. This procedure originally used Modified One-step M (MOM) estimator which employed trimming process. In the AWM-H procedure, the MOM estimator is replaced with the adaptive Winsorized mean (AWM) as the central tendency measure of the test. The Winsorization process is based on hinge estimator HQ ...

Adaptive and automatic trimming in testing the equality of two group case

In testing the equality of two independent groups, t-test plays a very important role for the purpose. This test is reliable when the data is normally distributed. Based on central limit theorem, the normality assumption is fulfilled with large data set, but getting large data set is not always feasible. Most of the time, the researchers have to make do with small sample sizes which are hardly normally distributed. There are many causes of non normality, and one of it is the presence of outliers. One way to handle outliers is by using robust estimator with trimming approach. In this study, robust estimators using different trimming approaches namely adaptive and automatic trimming were proposed as the center measures in Alexander-Govern (AG) test. The results of the Type I error rate was then compared with the original AG test and the classical t-test. The AG test with the adaptive and automatic trimming showed robustness across distributions. The two trimming approaches are comparable to each other in most conditions. As expected the original AG test and classical t-test cannot maintain their robustness especially under skewed distribution.

Testing the equality of students’ performance using Alexander-Govern test with adaptive trimmed means

Analyzing the equality of independent group has to be done with caution. The classical approaches such as ttest for two groups and analysis of variance (ANOVA) for more than two groups always are favorable selection by researchers. However, sometime these methods were abused by the presence of nonnormality or variance heterogeneity or both. It is known that ANOVA is restricted to the assumptions of normality and homogeneity of variance. In real life data, sometimes these requirements are hard to attain. The Alexander-Govern test with adaptive trimmed mean (AG_atm) is one approach that can be chosen as alternative to the classical tests when their assumptions are violated. In this paper, the performances of AG_atm were compared to the original AG test and ANOVA using simulated and real life data. The simulation study proved that the AG_atm performs better than the original AG test and the classical test. For real life data, student’s performance in decision analysis course, measured by final examination sc...

H-statistic with winsorized modified one-step M-estimator for two independent groups design

Two-sample independent t-test is a classical method which is widely used to test the equality of two groups. However, this test is easily affected by any deviation in normality, more obvious when heterogeneity of variances and group sizes exist. It is well known that the violation in the assumption of these tests will lead to inflation in Type I error rate and depression in statistical test power. In mitigating the problem, robust methods can be used as alternatives. One such method is H-statistic. When used with modified one-step M-estimator (MOM), this test statistic (MOM-H) produce good control of Type I error even under small sample size but inconsistent across certain conditions investigated. Furthermore, power of the test is low which might be due to the trimming process. In this study, MOM is winsorized (WMOM) to sustain the original sample size. The H-statistic with WMOM as the central tendency measures (denoted as WMOM-H) showed better control of Type I error as compared to MOM-H especially under...

Winsorization approach in testing the equality of independent groups

In testing the equality of independent groups, the ordinary approaches use classical tests such as t-test and analysis of variance (ANOVA) F test. However, these tests are known to have two common weaknesses namely nonnormality and heteroscedasticity. The Alexander-Govern test is acknowledged as a good alternative to these tests in the presence of heteroscedasticity, but not in the case of considerable deviation from normality. Modifications were done to improve the performance of this test across various conditions, but the progress was still below satisfaction especially under heavy tailed distribution. For that reason, this study proposed a new approach of the Alexander-Govern test which employed the process of Winsorization. This process aims to eliminate the influence of nonnormality and unequal variances simultaneously. The results show that the proposed method performs better than the original method especially when the distribution is heavy tailed.

P-method post hoc test for adaptive trimmed mean, HQ

Adaptive trimmed mean, HQ, which is one of the latest additions in robust estimators, had been proven to be good in controlling Type I error in omnibus test. However, post hoc (pairwise multiple comparison) procedure for HQ was yet to be developed then. Thus, we have taken the initiative to develop post hoc procedure for HQ. Percentile bootstrap method or P-Method was proposed as it was proven to be effective in controlling Type I error rate even when the sample size was small. This paper deliberates on the effectiveness of P-Method on HQ, denoted as P-HQ. The strength and weakness of the proposed method were put to test on various conditions created by manipulating several variables such as shape of distributions, number of groups, sample sizes, degree of variance heterogeneity and pairing of sample sizes and group variances. For such, a simulation study on 2000 datasets was conducted using SAS/IML Version 9.2. The performance of the method on various conditions was based on its ability in controlling Ty...