Methods to test for equality of two normal distributions

被引:0
作者
Julian Frank
Bernhard Klar
机构
[1] Karlsruhe Institute of Technology (KIT),Department of Mathematics
来源
Statistical Methods & Applications | 2016年 / 25卷
关键词
Fisher combination method; Minimum combination method ; Likelihood ratio test; Two-sample model;
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摘要
Statistical tests for two independent samples under the assumption of normality are applied routinely by most practitioners of statistics. Likewise, presumably each introductory course in statistics treats some statistical procedures for two independent normal samples. Often, the classical two-sample model with equal variances is introduced, emphasizing that a test for equality of the expected values is a test for equality of both distributions as well, which is the actual goal. In a second step, usually the assumption of equal variances is discarded. The two-sample t test with Welch correction and the F test for equality of variances are introduced. The first test is solely treated as a test for the equality of central location, as well as the second as a test for the equality of scatter. Typically, there is no discussion if and to which extent testing for equality of the underlying normal distributions is possible, which is quite unsatisfactorily regarding the motivation and treatment of the situation with equal variances. It is the aim of this article to investigate the problem of testing for equality of two normal distributions, and to do so using knowledge and methods adequate to statistical practitioners as well as to students in an introductory statistics course. The power of the different tests discussed in the article is examined empirically. Finally, we apply the tests to several real data sets to illustrate their performance. In particular, we consider several data sets arising from intelligence tests since there is a large body of research supporting the existence of sex differences in mean scores or in variability in specific cognitive abilities.
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页码:581 / 599
页数:18
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共 39 条
  • [1] Aspin AA(1949)Tables for use in comparisons whose accuracy involves two variances, separately estimated Biometrika 36 290-296
  • [2] Welch BL(1979)Asymptotically optimal methods of combining tests Journal of the American Statistical Association 74 812-814
  • [3] Berk RH(2007)Brother-sister differences in the Intelligence 35 451-456
  • [4] Cohen A(1972) factor in intelligence: analysis of full, opposite-sex siblings from the NLSY1979 J Psychol 80 351-363
  • [5] Deary IJ(2009)An additive method for combining probability values from independent experiments Stat Sci 24 343-360
  • [6] Irwing P(1983)The impact of Levene’s test of equality of variances on statistical theory and practice Metrika 30 1-13
  • [7] Der G(1979)On the convolution of logistic random variables Ann Statist 7 592-598
  • [8] Bates TC(1971)On asymptotic optimality of likelihood ratio tests for multivariate normal distributions Biometrika 58 213-217
  • [9] Edington ES(1958)A combination of Wilcoxon’s and Ansari–Bradley’s statistics Magyar Tudományos Akadémia Matematikai Kuatató Intezetenek Kozlemenyei 3 1971-1977
  • [10] Gastwirth JL(2004)On the combinationn of independent tests Comput Stat Data Anal 47 467-485