Autocorrelation corrected standard error for two sample t-test under serial dependence

Year 2017, Volume: 46 Issue: 6, 1199 - 1210, 01.12.2017

Ayfer Ezgi Yılmaz Serpil Aktas

Abstract

The classical two-sample t-test assumes that observations are independent. A violation of this assumption could lead to inaccurate results and incorrectly analyzing data leads to erroneous statistical inferences. However, in real life applications, data are often recorded over time and serial correlation is unavoidable. In this study, two new autocorrelation corrected standard errors are proposed for independent and correlated samples. These standard errors are replaced by the classical standard error in the presence of serially correlated samples in two samples t-test. Results based upon the simulation show that the proposed standard errors gives higher empirical power than other approaches.

Keywords

Hypothesis testing, Two sample tests, t-test, Serial dependence, Autocorrelation

References

• Box, G.E.P, Hunter, W.G and Hunter, J.S. Statistics for experimenters: An introduction to design, data analysis, and model building (John Wiley and Sons, 1978).
• Box, G.E.P and Jerkins, W.G. Time series analysis: Forecasting and control (San Francisco: Holden-Day, 1976).
• Chen, B. and Gel, Y.R. A sieve boostrapt two-sampe t-test under serial correlation, Journal of Biopharmaceutical Statistics 21, 1100-1112, 2011.
• Katz, R.W. Statistical evaluation of climate experiments with general circulation models: A parametric time series approach, Journal of the Atmospherie Sciences 39, 1446-1455, 1982.
• Seitshiro, M.B. Two-sample comparisons for serially correlated data. Dissertation Thesis for Master of Science in Statistics, School of Computer, Statistical and Mathematical Sciences, North-West University, Potchefstroom, South Africa, 2006.
• Thiébauz, H.J and Zwiers, F.W. The interpretation and estimation of effective sample size, Journal of Applied Meteorology and Climate 23, 800-811, 1984.
• Wilks, D.S. Resampling hypothesis tests for autocorrelated fields, Journal of Climate 10, 65-82, 1997.
• Zimmerman, D.W. Correcting two-sample z and t tests for correlation: An alternative to one-sample tests on difference scores, Psicológica 33, 391-418, 2012.