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.
An alternative robust method for testing the equality of central tendency measures was developed by integrating H Statistic with adaptive trimmed mean using hinge estimator, HQ. H Statistic is known for its ability to control Type I error rates and HQ is a robust location estimator. This robust estimator used asymmetric trimming technique, where it trims the tail of the distribution based on the characteristic of that particular distribution. To investigate on the performance (i.e. robustness) of the procedure, some variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Bootstrap method was used to test the hypothesis. The integration seemed to produce promising robust procedure that is capable of addressing the problem of violations to the assumptions. About 20% trimming is the appropriate amount of trimming for the procedure, where this amount is found to be robust in most conditions. This procedure was also proven to be robust as compared to the parametric (AN0vA) and non parametric (Kruskal-Wallis) methods.
The classical procedures of comparing two groups, such as t-test are, usually restricted with the assumptions of normality and equal variances. When these assumptions are violated, the rates of the Type I errors of the independent samples t-test are affected, particularly when the sample sizes are small. In this situation, the bootstrap procedure has an advantage over the parametric t-test. In this study, the performances of the bootstrap procedure and the independent sample t-test were investigated. The investigation focused on the power of both the test procedures to compare the two groups under different design specifications for normal and chi-square distributions. The results showed that the bootstrap procedure has a slight edge over the conventional t-test in term of the rate of achieving the benchmark level for both the distributions. In fact, the bootstrap procedure consistently outperformed the conventional t-test across all the combinations of the test conditions.