Alternative Approaches in the Behrens-Fisher Problem
Author : Sidney Irving Feurst
Publisher :
Page : 102 pages
File Size : 27,22 MB
Release : 1974
Category :
ISBN :
Author : Sidney Irving Feurst
Publisher :
Page : 102 pages
File Size : 27,22 MB
Release : 1974
Category :
ISBN :
Author : Joel Roger Geoffrey
Publisher :
Page : 182 pages
File Size : 32,32 MB
Release : 1969
Category : Mathematical statistics
ISBN :
Author : Tejas Desai
Publisher : Springer Science & Business Media
Page : 60 pages
File Size : 36,6 MB
Release : 2013-02-26
Category : Mathematics
ISBN : 1461464439
In statistics, the Behrens–Fisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an approach to the Behrens-Fisher problem. Since high-speed computers were not available in Fisher’s time, this approach was not implementable and was soon forgotten. Fortunately, now that high-speed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fisher’s approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case. In this monograph, we present the solution to the afore-mentioned multivariate generalization of the Behrens-Fisher problem. We start out by presenting a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate Behrens-Fisher problem. All methods proposed in this monograph will be include both the randomly-incomplete-data case as well as the complete-data case. Moreover, all methods considered in this monograph will be tested using both simulations and examples.
Author : Springer
Publisher :
Page : 64 pages
File Size : 44,12 MB
Release : 2013-02-25
Category :
ISBN : 9781461464440
Author : Basil M. De Silva
Publisher :
Page : 20 pages
File Size : 50,25 MB
Release : 2004
Category : Bootstrap (Statistics)
ISBN : 9780864593283
Author : Dolores Siu Kim Lam
Publisher :
Page : 0 pages
File Size : 38,85 MB
Release : 1974
Category : Statistical hypothesis testing
ISBN :
Abstract. This thesis studies the Behrens-Fisher test for the Behrens-Fisher problem. Fisher's hypotheses and his proposed methods of verification of the test are discussed. A sampling study on the actual size of the test based on Fisher's procedures is conducted. Actual sizes for different parameter values are obtained and tabulated. These results are discussed along with those obtained by other investigators. It is shown that the actual sizes as calculated using Fisher's proposed methods are close to the nominal sizes of the test. Furthermore, it is seen that the actual sizes for larger degrees of freedom agree more closely with the nominal sizes than those for smaller degrees of freedom. The test is thus recommended for use because it actually yields actual size close to the size specified by the user.
Author : Cong Cao
Publisher :
Page : pages
File Size : 33,73 MB
Release : 2019
Category : Analysis of covariance
ISBN :
The Behrens-Fisher Problem exists in many disciplines. The original problem aims to make inferences about the difference between the means of two normally distributed populations without assuming the equal variances. When the covariates are present, the treatment effects can be obscured. Existing analysis of covariance (ANCOVA) methods are typically based on the assumptions of a normal distribution and equal variances across the groups. These methods do not tend to control the type I error rate satisfactorily when the assumptions are violated. In this dissertation, we tackle this problem and derive group-specific unbiased variance estimators. These estimators are used to develop the new test statistic and compute the degree of freedom by Box-type approximation for a Behrens-Fisher Problem with covariates. Additionally, we generalize the new method to a broad range of factorial designs with covariates. Extensive simulation studies demonstrate the robustness of the new approaches, even for very small samples, moderately skewed distributions, unbalanced designs and under variance heteroscedasticity. The proposed methods are motivated and demonstrated by the real data sets.
Author : Joe C. Lundy
Publisher :
Page : 64 pages
File Size : 48,78 MB
Release : 1971
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ISBN :
Author : Gary Edwin Meek
Publisher :
Page : 66 pages
File Size : 50,96 MB
Release : 1965
Category :
ISBN :
Author : Samir Louis Saad
Publisher :
Page : 74 pages
File Size : 43,87 MB
Release : 19??
Category :
ISBN :