Development of a Regression Model for Estimating the Effects of Assumption Violations on Type I Error Rates in the Student's T-Test: Implications for Practitioners.
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| Title: | Development of a Regression Model for Estimating the Effects of Assumption Violations on Type I Error Rates in the Student's T-Test: Implications for Practitioners. |
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| Language: | English |
| Authors: | Newman, Isadore, Hall, Rosalie J., Fraas, John |
| Peer Reviewed: | N |
| Page Count: | 25 |
| Publication Date: | 2003 |
| Document Type: | Reports - Research Speeches/Meeting Papers |
| Descriptors: | Estimation (Mathematics), Monte Carlo Methods, Multiple Regression Analysis, Regression (Statistics) |
| Abstract: | Multiple linear regression is used to model the effects of violating statistical assumptions on the likelihood of making a Type I error. This procedure is illustrated for the student's t-test (for independent groups) using data from previous Monte Carlo studies in which the actual alpha levels associated with violations of the normality assumption, homogeneity of variance, or unbalanced designs were determined. The observed Type I error rates were recorded, along with information coding the type and extent of statistical assumption violation. The resulting linear models had R squared values of 0.88 to 0.91 and adjusted R squared values of 0.87 to 0.90. The results of the suggested methodological approach: (1) reveal the feasibility of developing multiple linear regression models to predict actual Type I error rates based on various assumption violation conditions for the independent groups-t-test; (2) suggest that alpha inflation is rarely larger than a factor of 2; and (3) provide a template for the development of assumption violation models for other types of statistical tests. (Contains 3 tables and 27 references.) (Author/SLD) |
| Entry Date: | 2004 |
| Accession Number: | ED476919 |
| Database: | ERIC |
| Abstract: | Multiple linear regression is used to model the effects of violating statistical assumptions on the likelihood of making a Type I error. This procedure is illustrated for the student's t-test (for independent groups) using data from previous Monte Carlo studies in which the actual alpha levels associated with violations of the normality assumption, homogeneity of variance, or unbalanced designs were determined. The observed Type I error rates were recorded, along with information coding the type and extent of statistical assumption violation. The resulting linear models had R squared values of 0.88 to 0.91 and adjusted R squared values of 0.87 to 0.90. The results of the suggested methodological approach: (1) reveal the feasibility of developing multiple linear regression models to predict actual Type I error rates based on various assumption violation conditions for the independent groups-t-test; (2) suggest that alpha inflation is rarely larger than a factor of 2; and (3) provide a template for the development of assumption violation models for other types of statistical tests. (Contains 3 tables and 27 references.) (Author/SLD) |
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