The robustness to non-normality of significance levels of the t and F tests

A statistical test is called"robust" if it is insensitive to departures from the underlying assumptions, this term was introduced by Box (4). Theoretical study made by Gayen (13), (14) and (15) showed that"Student's" t-test and the closely related F-test of analysis of variance are insensitive to departures from normality. But the F-test on the equality of two variances is very sensitive to such departures. Empirical studies made by Norton (19) and Boneau (3) agree with Gayen's theoretical conclusions. Norton studied the effect of non-normality on the F-test of analysis of variance,and showed that the form of the sampled population had very little effect on this test. For example, for the case of three groups of sample sizes 3, for the 5% level, the percentages exceeding the theoretical limits were 7.83 and 4.77% respectively for sampling from a leptokurtic and an extremely skewed population. Such property of robustness to non-normality on the F-test of analysis of variance is also possessed by t-test. Boneau's empirical study on the effect of non-normality on the two-sample t-test showed that for two samples of size 5, the significance level is respectively 3.1 and 5.1% for the empirical distribution of t’s from the exponential and uniform distribution compare to the nominal 5% value. The discrepancy is decreased when sample size is increased.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1965

Author dc:creator

• Ho, Tsau-yi

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/74602

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/74602