STUDIES IN RESEARCH METHODOLOGY. VI. THE CENTRAL LIMIT EFFECT FOR A VARIETY OF POPULATIONS AND THE ROBUSTNESS OF Z, T, AND F.
Abstract
The robustness of Z, t and F tests was studied by obtaining 1220 empirical sampling distributions (some of which were later combined) each consisting of 10,000 values of the test statistic obtained under a unique combination of sampling conditions. Conditions investigated, both alone and in combination, were: population shapes (nonnormal, normal, or some nonnormal and others normal), population variances (all sigma squared, or some sigma squared and others sigma squared/4), relative sample sizes (for two-sample tests N,N; 2N,N; 3N,N; or 2N,2N; for other multi-sample tests N,N,N; 2N,N,N; or N,N,N,N), and absolute sample size (N assumed values of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and in four special cases 2048 and 4096). Robustness at nominal significance levels of .05, .01, and .001 was examined for both left-, right- and two-tail tests. The Central Limit effect upon means of samples from populations differing considerably in shape and 'degree of nonnormality' was revealed in the robustness of certain Z statistics.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1964
- Accession Number
- AD0612886
Entities
People
- James V. Bradley