A COMPARATIVE STUDY ON THE EFFICIENCY OF TEST
STATISTICS IN TESTING THE DIFFERENCES BETWEEN
TWO DEPENDENT DATASETS
Unchalee Tonggumnead
Department of Mathematics and Computer Science
Rajamangala University of Technology Thanyaburi
THAILAND

Abstract

The purpose of the present study is to compare the efficiency of test statistics in testing the differences between two dependent datasets applying a regression framework with centered independent variable values. Comparisons of the efficiency of the test statistics, namely the $t_{b_0^*}^{RCM}$, the Wilcoxon matched-pairs signed-ranks test, and the Paired sample t-test, are made with the correlation coefficients, the sample sizes, and the ratio of mean different between the two datasets being varied. Simulations of the test statistics apply a Monte Carlo technique and are repeated 1,000 times. The research results show that the efficiency in controlling Type I errors of the Wilcoxon matched-pairs signed-ranks test and the Paired t-test is high under all scenarios, while that of the $t_{b_0^*}^{RCM}$ is high only in case the $r_{xy}$ is not excessively high, that is, under 0.80. In contrast, the power of the test of the latter is significantly higher than the former under all scenarios.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 1
Year: 2021

DOI: 10.12732/ijam.v34i1.2

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References

  1. [1] A. Gelman, and J. Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, Cambridge University Press (2006).
  2. [2] D.L. Street, Controlling extraneous variables in experimental research: A research note, Accounting Education, 6, No 2 (1995), 169-188.
  3. [3] D. Torgerson, Designing Randomised Trials in Health, Education and the Social Sciences: An Introduction, Springer (2008).
  4. [4] E.C. Hedberg, and S. Ayers, Controlling extraneous variables in experimental research: The power of a paired t-test with a covariate, Social Science Research, 50 (2015), 277-291.
  5. [5] E. Marsden, and C.J. Torgerson, Single group, pre-and post-test research designs: Some methodological concerns, Oxford Review of Education, 38, No 5 (2012), 583-616.
  6. [6] F.J. Samaniego, Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists, Chapman and Hall/CRC (2014).
  7. [7] H.J. Keselman, R. Cribbie, and B. Holland, Controlling the rate of Type I error over a large set of statistical tests, British Journal of Mathematical and Statistical Psychology, 55, No 1 (2002), 27-39.
  8. [8] J. Hox, and J.K. Roberts, Handbook of Advanced Multilevel Analysis, Psychology Press (2011).
  9. [9] J. Miles, and M. Shevlin, Applying Regression and Correlation: A guide for Students and Researchers, Sage (2001).
  10. [10] P.D. Mehta, Control Variables in Research (2015).
  11. [11] R.H. Myers, and J.S. Milton, A First Course in the Theory of Linear Statistical Models, Kent Publishing Company (1991).
  12. [12] R.W. Robins, R.C. Fraley, and R.F. Krueger, Handbook of Research Methods in Personality Psychology, Guilford Press (2009).
  13. [13] S.D. Oman, Easily simulated multivariate binary distributions with given positive and negative correlations, Computational Statistics and Data Analysis, 53, No 4 (2009), 999-1005.
  14. [14] T.W. MacFarland, and J.M. Yates, Wilcoxon matched-pairs signed-ranks test, In: Introduction to Nonparametric Statistics for the Biological Sciences Using R, Springer, Cham (2016).
  15. [15] W.R. Shadish, T.D. Cook, and D.T. Campbell, Experimental and QuasiExperimental Designs for Generalized Causal Inference, Boston, Houghton Mifflin (2002).