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.