FUTA JOURNAL OF RESEARCH IN SCIENCE

VOLUME 13 NUMBER 2 2017

Paper Details

  • Title :A STUDY ON SENSITIVITY AND ROBUSTNESS OF MATCHED-PAIRS INFERENTIAL TEST STATISTICS TO OUTLIERS
  • Author(s) : 1*Adegoke S. Ajiboye, 2Taiwo Joel Adejumo and 1Kayode Ayinde,
  • Abstract:

Outliers are data points that are different from others. Their presence may affect the robustness and the sensitivity of test statistics used for inferential purposes. Test statistics that are meant for the purpose of inference have been developed which include: Paired t-test, Distributional Wilcoxon Sign Test (DST), Asymptotic Wilcoxon Sign Test (AST), Distributional and Asymptotic Wilcoxon Signed rank Test (DWST and AWST), t-test for rank transformation (Rt-test) and Trimmed t-test statistics (Tt-test). Consequently, the effect of outliers on these test statistics needs to be investigated so as to determine the one that is sensitive and robust. The experiment was conducted five thousand (5000) times using Monte Carlo experiments at eight (8) levels of sample sizes namely: 10, 15, 20, 25, 30, 35, 40 and 50 by generating data from normal distribution with the aid of R- statistical programming codes. Also, in order to exhibit different degree of correlations between the paired samples, the levels of correlations reconsidered are; 0, 0.3, 0.6, 0.9, 0.95 and 0.99. At each sample size, 10% and 20% of the generated data were invoked with twenty-one (21) various magnitude (k) of outliers (-10, -9, -8, ...8, 9, 10). The three (3) commonly used preselected levels of significance used were 0.1, 0.05 and 0.01. The Type 1 error rate of the inferential test statistics was determined when there was no outlier in the data sets. While, to assess the sensitivity and robustness of the test statistics hence, the Power rate was determined. A test is considered robust if its estimated error rate approximates the true error rate and has the highest number of times it approximates the error rate when counted over the levels of significance otherwise sensitive. With different levels of correlation, results revealed that the Type 1 error rate of the paired t- test and AWST are good; and that AST, Rt-test and DST, and Tt-test statistics are respectively robust to outliers at 0.1, 0.05 and 0.01 levels of significance.
Keywords: Outliers, Power rate, Sensitivity, Robustness, Inferential Test Statistics, Monte Carlo