Abstract
Over the years, non-parametric test statistics have been the only solution to solve data that do not follow a normal distribution. However, giving statistical interpretation used to be a great challenge to some researchers. Hence, to overcome these hurdles, another test statistics was proposed called Rank transformation test statistics so as to close the gap between parametric and non-parametric test statistics. The purpose of this study is to compare the conclusion statement of Rank transformation test statistics with its equivalent non parametric test statistics in both one and two samples problems using real-life data. In this study, (2018/2019) Post Unified Tertiary Matriculation Examinations (UTME) results of prospective students of Ladoke Akintola University of Technology (LAUTECH) Ogbomoso across all faculties of the institution were used for the analysis. The data were subjected to nonparametric test statistics which include; Asymptotic Wilcoxon sign test and Wilcoxon sum Rank (both Asymptotic and Distribution) using Statistical Packages for Social Sciences (SPSS). In the same vein, R-statistical programming codes were written for Rank Transformation test statistics. Their P-values were extracted and compared with each other with respect to the pre-selected alpha level (α) = 0.05. Results in both cases revealed that there is a significant difference in the median of the scores across all faculties since their type I error rate are less than the preselected alpha level 0.05. Therefore, Rank transformation test statistics is recommended as alternative test statistics to non-parametric test in both one sample and two-sample problems.
Highlights
In social, behavioural and physical sciences, studies have shown the usefulness of statistical analysis in arriving at conclusions in problems solving Odukoya, Omonijo, Olowookere, John & Atayero, 2019; Olowookere, Omonijo, Odukoya & Anyaegbunam, 2020)
It is very imperative to apply some of these test statistics to real life data and compare whether the conclusion statement of rank transformation test statistics by Conover and Iman (1981) in one sample and two samples problems is the same with the already existing non-parametric test statistics
While to assess the sensitivity and robustness of the test statistics Power rate was determined. In their study, they affirmed that a test was examined to be robust if its estimated type I error rate approximately equal to the true error rate and it has the highest number of times it approximates the error rate when counted over the preselected alpha level otherwise sensitive. Their results revealed that paired t-test and Asymptotic wilcoxon sign test have better Type I error rate across different categories of correlation and that Asymptotic sign test, Rank transformation test and distribution sign test, and Trimmed t-test statistics are respectively robust to outliers at all alpha levels
Summary
Behavioural and physical sciences, studies have shown the usefulness of statistical analysis in arriving at conclusions in problems solving Odukoya, Omonijo, Olowookere, John & Atayero, 2019; Olowookere, Omonijo, Odukoya & Anyaegbunam, 2020). It is very imperative to apply some of these test statistics to real life data and compare whether the conclusion statement of rank transformation test statistics by Conover and Iman (1981) in one sample and two samples problems is the same with the already existing non-parametric test statistics. To accomplish this task the scores of post Unified Tertiary Matriculation Examination (Post-UTME) 2018/2019 academic session prospective students of Ladoke Akintola University of Technology (LAUTECH) across all faculties of the institution were collected and used for the analysis
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