ABSTRACT
Approximate one-sided confidence intervals for the proportions of variability PA = <r11(<r1 + <T~ + <Tl) and Ps = <rll(<r1 + <T~ + <Tl) were proposed by Graybill and Wang ( 1979). Based on these results, an approximate two-sided 1 - 2et confidence interval on PA is
(5.2.8)
• The approximate two-sided 1 - 2et confidence interval on p8 is
where
L - ~ - F <X:"z ·"'S~S~ - (F <X:n2•"J - F <X:n2,oo)F Q:''2·"JS1, 8
- F <X:n1,,,srs~ + (JK - 1 )F <X:n1,ooS~S~
(5 .2.9)
and
Since 0 =s p8 =s 1, any bound greater than one in (5.2. 9) is defined to be one. In addition, if Si!Sj =s F cx:n
zero. If S~!Sj < F l-cx:"z·">' both bounds are defined to be zero. The lower bound in (5.2.9) was proposed by Graybill and Wang (1979). The upper bound results from replacing a with 1 - a in the lower bound.
