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.
Setting a question paper for test, quiz, and examination is one of the teachers’ tasks. The factors that are usually taken into consideration in carrying out this particular task are the level of difficulty of the questions and the level of the students’ ability. In addition, teachers will also have to consider the number of questions that have impact on the examination. This research describes a model-based test theory to study the confidence intervals for the projected number of items of a test, given the reliability of the test, the difficulty of the question, and the students’ ability. Using the simulated data, the confidence intervals of the projected number of items were examined. The probability coverage and the length of the confidence interval were also used to evaluate the confidence intervals. The results showed that the data with a normal distribution, the ratio variance components of 4:1:5 and reliability equal to 0.80 gave the best confidence interval for the projected number of items.
For testing the homogeneity of variances, modifications of well-known tests are known which combine rigorous theory with resampling (bootstrap). We propose versions of these tests, which are computationally simpler (although asymptotically equivalent). The earlier procedures used the smooth bootstrap with two thousand bootstrap replications per sample whereas our proposals use only the classical bootstrap (or percentile method) with just one thousand bootstrap replications per sample, and also required much less computing time. Our proposals cover the Ansari-Bradley-, Mood- and Klotz-tests. We explain their superiority over the existing methodologies available in textbooks and packages.
This article investigates the performance of two-sample pseudo-median based procedure in testing differences between groups. The procedure is a modification of the one-sample Wilcoxon procedure using the pseudo-median of differences between group values as the central measure of location. The test was conducted on two groups with moderate sample
sizes of symmetric and asymmetric distributions. The performance of the procedure was measured in terms of Type I error and power rates computed via Monte Carlo methods. The performance of the procedure was compared against the t-test and Mann-Whitney-Wilcoxon test. The findings from this study revealed that the pseudo-median procedure performed very
well in controlling Type I error rates close to the nominal value. The pseudo-median procedure outperformed the MannWhitney-Wilcoxon test and is comparable to the t-test in controlling Type I error and maintaining adequate power.
Ujian Alexander-Govern merupakan ujian kesamaan sukatan memusat yang teguh pada keadaan varians heterogen. Malangnya ujian ini tidak teguh pada keadaan data tidak normal. Adaptasi penganggar teguh seperti penganggar M satu langkah terubah suai (MOM) sebagai sukatan memusat menggantikan min didapati berupaya meningkatkan keteguhan ujian ini apabila dijalankan pada data terpencong. Penganggar ini mempunyai kelebihan berbanding min kerana tidak dipengaruhi oleh data yang tidak normal. Kajian ini mendapati bahawa ujian Alexander-Govern yang telah diubah suai ini berupaya mengawal Ralat Jenis I dengan baik pada data terpencong untuk semua keadaan. Kadar Ralat Jenis I yang dihasilkan kebanyakannya berada di dalam selang kriteria teguh ketat (0.045 hingga 0.055) pada aras keertian 0.05. Berbeza dengan kaedah pengujian asal yang mana pada kebanyakan keadaan, ujian teguh tetapi hanya dengan kriteria liberal (0.025 hingga 0.075), malahan ada kedaan yang mana ujian tidak teguh. Prestasi kaedah yang diubah suai ini juga setanding dengan keadah asal pada keadaan data normal. Kajian ini juga membandingkan kaedah Alexander Govern yang diubah suai dengan kaedah pengujian klasik seperti ujian-t dan ANO VA dan menyaksikan bahawa kaedah klasik tidak teguh pada keadaan varians heterogen.
In many statistical analyses, data need to be approximately normal or normally distributed. The Kolmogorov-Smirnov test, Anderson-Darling test, Cramer-von Mises test, and Shapiro-Wilk test are four statistical tests that are widely used for checking normality. One of the factors that influence these tests is the sample size. Given any test of normality mentioned, this study determined the sample sizes at which the tests would indicate that the data is not normal. The performance of the tests was evaluated under various spectrums of non-normal distributions and different sample sizes. The results showed that the Shapiro-Wilk test is the best normality test because this test rejects the null hypothesis of normality test at the smallest sample size compared to the other tests, for all levels of skewness and kurtosis of these distributions.