TITLE:
Comparison of Two Sample Tests Using Both Relative Efficiency and Power of Test
AUTHORS:
Edith Uzoma Umeh, Nkiru Obioma Eriobu
KEYWORDS:
Asymmetric, Symmetric, Nonparametric Test, Two Sample Tests, Power of Test, Relative Efficiency
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.2,
April
27,
2016
ABSTRACT: 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.