The Robustness of Validity and Efficiency of the Related Samples t-Test in the Presence of Outliers

• Main Authors: James F. Joula, Bruno D. Zumbo, Martha J. Jennings
• Format: Article
• Language: English
• Published: Sciendo 2002-01-01
• Series: Psicológica
• Online Access: http://www.redalyc.org/articulo.oa?id=16923209

The performance of the related samples t-test (a one-sample t-test applied
 to the difference scores) given data which are essentially normal but
 contain outliers is largely unknown. In this Monte Carlo study the
 robustness of validity and efficiency for both the paired and one-sample ttests
 are investigated. The Type I error rate and power of these tests
 given a normal underlying population are compared with the performance
 of these tests given a systematic range of outlier contamination in the
 underlying population. Sample sizes of 8, 16, 32, 64, and 128 are
 included in the design. Robustness of validity results are explored using
 regression models. Robustness of efficiency results are expressed using a
 proposed fairly stringent criterion for power. The results indicate that the
 t-test demonstrates fairly stringent robustness of validity for the range of
 symmetric contamination explored. When contamination is asymmetric
 the Type I error rate becomes inflated as the proportion of contamination
 increases. If robustness of validity is intact, power is not greatly affected
 when medium or large effect sizes are examined. This is not necessarily
 true for small effect sizes and the problems are further exacerbated when
 sample sizes are also small. Finally, a model with practical relevance for
 data analysts confronted with outlier contaminated data is developed using
 a novel index of contamination. This model is compared with a model
 using skewness and kurtosis values as disributional measures.