Nor Aishah Ahad

Sensitivity analysis of Welch’s t-test

Welch t-test is the parametric test for comparing means between two independent groups without assuming equal population variances. This statistic is robust for testing the mean equality when homogeneity assumption is not satisfied, but Welch test is not always robust. When multiple problems such as the distribution is non-normal, variance is heterogeneous and unequal size of groups occur simultaneously, the Type I error will inflate. In this study, various conditions such as sample sizes, type of distributions and unequal group variances were manipulated to investigate on the non robust conditions of Welch test. The Type I error rates and power of the test for different design specifications were obtained and compared. The results indicated that this test did not perform well under non-normal distributions especially when group sizes and unequal group variances are inversely associated or negatively paired. The estimated Type I error inflated as the power of the test improved.

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.

Robustness of S1 statistic with Hodges-Lehmann for skewed distributions

Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of non- normal and heteroscedastic settings. When the assumptions are violated, researchers are looking for alternative such as Kruskal-Wallis under nonparametric or robust method. This study focused on flexible method, S1 statistic for comparing groups using median as the location estimator. S1 statistic was modified by substituting the median with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MADn to produce two different test statistics for comparing groups. Bootstrap method was used for testing the hypotheses since the sampling distributions of these modified S1 statistics are unknown. The performance of the proposed statistic in terms of Type I error was measured and compared against the original S1 statistic, ANOVA and Kruskal-Wallis. The propose ...

S1 statistic with Hodges-Lehmann in two groups case for skewed distribution

This study is focused on the modification of S1 statistic, a procedure for testing the equality of groups, by replacing median with Hodges-Lehmann estimator as the location measure in two groups case under skewed distribution. The modification is also extended to the default scale estimator of Hodges-Lehmann, S1(HL) and robust scale estimator, MADn, S1(MADn). The purpose of the modifications is to improve the robustness of the statistic. To test the strengths and weaknesses of S1(HL) and S1(MADn), a simulation study was conducted. Several variables such as the shape of distributions, balanced and unbalanced group sizes, equal and unequal variances and nature of pairings were manipulated to create various conditions for the data. Since the distribution of S1 statistic is unknown, bootstrap method was used for data generation. According to Guo and Luh, a test statistic is considered robust if its empirical error rate does not exceed 0.075 when α = 0.05. Refer to the results obtained, S1(HL) and S1(MADn) can...

Robustness of S1 with Hodges-Lehmann

The classical methods for comparing groups can be highly inefficient under the influence of non-normal and heteroscedastic settings. Investigators are looking for alternatives which are more flexible in terms of assumptions. Robust methods are known to be one such alternative. This study looks into S1 statistic, flexible method for comparing groups using median as the location estimator. Works on S1 mostly focussed on the searching of a more favorable alternative of the standard error of sample medians to achieve better control of Type I error. In this study, instead of targetting on the standard error, the investigation on the S1 statistic focusses on the sample median itself. The modified S1 statistic replaced the medians with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MADn to produce two different test statistics for comparing groups. Since the sampling distributions of these modified S1 statistics are unknown, bootstrap method was used for testing the hypoth...

An application of importance satisfaction analysis (ISA) method in improving the internship programme for Malaysia Higher Learning Institution

Nowadays most of the university students are required to undergo internship as a requirement before graduation. Internship is very important for students to practice what they have learned in the classroom. During internship students are exposed to the actual situation of how to deal with customers and suppliers which can provide added value to the students. In the choice of company for internship, students also consider a number of things such as internship allowances, work environment, interesting work, stable work shift and other fridge benefits. Study on the importance and satisfaction of students is important to improve the internship program. Importance means how students feel important to the attributes and satisfaction means how students feel after undergoing internship. The aim of this study is to investigate the gaps between students’ important and satisfaction on the internship programme and to identify the internship experience factors that need to be improved. Gap analysis has been used to sh...

The selection criteria in determining the robustness of t-test

Robustness in the context of hypothesis testing is the ability of a procedure to control Type I error rate of a test close to the nominal value and stable over a range of distributions even with some deviations from its assumptions. Procedures that were deemed robust for some researchers could be considered not robust for others. Some researchers would consider that the procedures with conservative Type I error rates fail to perform. However, other researchers may assume otherwise, such that any value less than or equal to the nominal level can still be considered as robust. Many quantitative measures or criteria can be used to evaluate the robustness of a statistical test such as the t-test. In this study, the robustness of t-test was evaluated using five different robustness criteria. For each criteria, Type I error of the t-test was measured under different conditions namely sample sizes, group variances, type of distributions, and nature of pairings. The results showed that different robust criterion ...