This paper, comparison of two sample tests, is motivated by the fact that in the test of significant difference between two independent samples, numerous methods can be adopted; each may lead to significant different results; this implies that wrong choice of test statistic could lead to erroneous conclusion. To prevent misleading information, there is a need for proper investigation of some selected methods for test of significant difference between variables/subjects most especially, independent samples. The paper examines the efficiency and sensitivity of four test statistics to ascertain which test performs better. Based on the results, the relative efficiency favours median test as being more efficient than modified median test for both symmetric and asymmetric distributions. In terms of power of test, median test is more sensitive than Modified Median (MMED) test since it has higher power irrespective of the sample sizes for both symmetric and asymmetric distribution. In terms of relative efficiency for asymmetric distribution Modified Mann-Whitney U test is more efficient than Mann-Whitney U test (MMWU), and then for symmetric distribution, Mann-Whitney U test (MMWU) is more efficient than Modified Mann-Whitney in sample size of 5; but for other sample sizes considered Modified Mann-Whitney U test (MMWU) is better than Mann-Whitney. Using power of test for both symmetric and asymmetric distributions, Mann-Whitney is more sensitive than Modified Mann-Whitney U test (MMWU) because it has higher power.

Outlier detection is an important data screening type. RIM is a mechanism of outlier detection that identifies the contribution of data points in a regression model. A BIC-based RIM is essentially a technique developed in this work to simultaneously detect influential data points and select optimal predictor variables. It is an addition to the body of existing literature in this area of study to both having an alternative to the AIC and Mallow's C p Statistic-based RIM as well as conditions of no influence, some sort of influence and perfectly single outlier data point in an entire data set which are proposed in this work. The method is implemented in R by an algorithm that iterates over all data points; deleting data points one at a time while computing BICs and selecting optimal predictors alongside RIMs. From the analyses done using evaporation data to compare the proposed method and the existing methods, the results show that the same data cases selected as having high influences by the two existing methods are also selected by the proposed method. The three methods show same performance; hence the relevance of the BIC-based RIM cannot be undermined.

Abstract:Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.