Simultaneous confidence intervals for two linear functions of population means when population variances are not equal

1970 ◽  
Vol 67 (2) ◽  
pp. 365-370 ◽  
Author(s):  
Saibal Banerjee
Keyword(s):  
Confidence Intervals ◽  
Linear Functions ◽  
Simultaneous Confidence Intervals ◽  
Population Means

AbstractIt is shown that given k samples of nj units from it is possible to construct simultaneous confidence intervals for two given linear functions of population means, (where cij are known constants), when population variances are not equal.

Simultaneous Confidence Intervals for the Linear Functions of Expected Mean Squares Used in Generalizability Theory

1986 ◽  
Vol 11 (3) ◽  
pp. 197-205
Author(s):  
John F. Bell
Keyword(s):  
Linear Model ◽  
Confidence Intervals ◽  
Random Effects ◽  
Variance Components ◽  
Generalizability Theory ◽  
Linear Functions ◽  
Simultaneous Confidence Intervals ◽  
Balanced Design ◽  
Expected Values ◽  
Bonferroni's Inequality

This paper demonstrates a method, derived by Khuri (1981) , of constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model. The method may be applied to obtain confidence intervals for the variance components and other linear functions of the expected mean squares used in generalizability theory, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient. The Khuri intervals are compared with the approximate intervals obtained by using Satterthwaite’s (1941 , 1946) method in conjunction with Bonferroni’s inequality.

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