ABSTRACT
The proportions of variability PA = cr11-y, p8 = crj!-y, and PAB = crkl-y, where -y = cr~ + cri + crk + cr~ are other important ratios that cannot be written in the general form presented in Section 3.4.2. For example, PA = I(61 - 63)/[/61 + 162 + (/J - I - 1)63 + IJ(K - 1)64] and 63 appears in both the numerator and denominator of the ratio. Leiva and Graybill (1986) considered this special form and derived approximate intervals for all three proportions of variability. Their approximate 1 - 2a confidence interval on PA is
(6 .2 .6)
where
St - F a:n.,n3S~ LA = ------------~------~~------------~ I(K - l)Fa:n,.oo S~ + Fa:n.,n2S~ + (I - l)Fa:n, ,oo Sj and
Sy - Fl-a:n ,,n3S~ VA = --------------~------~~--------------~ l(K - l)Ft-a:n.,oo S~ + Fl-a:n, .n2S~ + (I - l)FI-a:n,,oo S~.
