A Robust Alternative to the t - Test

t -test is a classical test statistics for testing the equality of two groups. However, this test is very sensitive to non-normality as well as variance heterogeneity. To overcome these problems, robust method such as F t and S 1 tests statistics can be used. This study proposed the use of a robust estimator that is trimmed mean as the central tendency measure in F t test and median as the central tendency measure in S 1 test when comparing the equality of two groups. The performance of the S 1 test with MAD n was able to give the most convincing result than the other methods. The F t with MAD n showed comparable results with the conventional methods. This study has shown some improvement in the statistical solution of detecting differences between location parameters. These modified methods may serve as alternatives to some other robust statistical methods which are unable to handle either the problem of non-normality, variance heterogeneity or unbalanced design.

[1]  G. Wetherill,et al.  Statistical Theory and Methodology in Science and Engineering. , 1962 .

[2]  K. M. L. Suxena,et al.  Introduction to Statistical Theory , 1976 .

[3]  F. Mosteller,et al.  Understanding robust and exploratory data analysis , 1985 .

[4]  S. Sheather,et al.  Robust Estimation and Testing , 1990 .

[5]  P. Rousseeuw,et al.  Alternatives to the Median Absolute Deviation , 1993 .

[6]  J. Booth,et al.  Resampling-Based Multiple Testing. , 1994 .

[7]  A ROBUST TEST FOR OMNIBUS ALTERNATIVES , 1996 .

[8]  Rand R. Wilcox.  "The goals and strategies of robust methods": Reply. , 1998 .

[9]  M. Puri,et al.  Robust One‐Way ANOVA under Possibly Non‐Regular Conditions , 1999 .

[10]  An invertible transformation two-sample trimmed t-statistic under heterogeneity and nonnormality , 2000 .

[11]  H. Keselman,et al.  Repeated measures ANOVA: some new results on comparing trimmed means and means. , 2000, The British journal of mathematical and statistical psychology.

[12]  H J Keselman,et al.  Testing treatment effects in repeated measures designs: trimmed means and bootstrapping. , 2000, The British journal of mathematical and statistical psychology.

[13]  H J Keselman,et al.  A generally robust approach to hypothesis testing in independent and correlated groups designs. , 2003, Psychophysiology.

[14]  H. Keselman,et al.  Modern robust data analysis methods: measures of central tendency. , 2003, Psychological methods.

[15]  A. R. Othman,et al.  Comparing measures of the 'typical' score across treatment groups. , 2004, The British journal of mathematical and statistical psychology.

[16]  A. R. Othman,et al.  Testing the Equality of Location Parameters for Skewed Distributions Using S 1 with High Breakdown Robust Scale Estimators , 2004 .

[17]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[18]  E. Ronchetti.  THE HISTORICAL DEVELOPMENT OF ROBUST STATISTICS , 2006 .

[19]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .