The performance of parametric tests given data which are essentially normal but contain outliers is largely unknown. In this Monte Carlo study the robustness of validity and efficiency for the one-sample location problem are investigated. The Type I error rate and power of the one-sample t test given a normal underlying population are compared with the performance of this test 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. The robustness of validity results are explored using three sets of regression models. The first set of models is constructed using the parameters of the contamination model and is intended to inform the social science methodologist. The second set of models is constructed using skewness and kurtosis values. A third set of models is developed using an index of contamination proposed by Zumbo (1993). This set of models has practical relevance to the data analyst confronted with outlier contaminated data. Robustness of efficiency results are expressed using both power curves and a proposed fairly stringent criterion for power. In general, the results indicate that the one-sample t test demonstrates fairly stringent robustness of validity for all the 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.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/6629 |
| Date | January 1994 |
| Creators | Jennings, Martha. |
| Contributors | Zumbo, Bruno, |
| Publisher | University of Ottawa (Canada) |
| Source Sets | Université d’Ottawa |
| Detected Language | English |
| Type | Thesis |
| Format | 85 p. |
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