ALL PAIRWISE COMPARISONS
91
of t h e l i n f c t c o m p o n e n t p r o d u c e d by g l h t (see S e c t i o n 3.3.1 g l h t objects). I n our example, R>
for d e t a i l s on
t(immer.mc$linfct)
P-M S-M T-M V-M S-P 0 0 0 0 (Intercept) 0 VarP 1 0 0 0 -1 1 0 1 VarS 0 0 VarT 0 0 0 1 0 VarV 0 0 0 1 0 LocD 0 0 0 0 0 LocGR 0 0 0 0 0 LocM 0 0 0 0 0 LocUF 0 0 0 0 0 LocW 0 0 0 0 0 attr( "type") [1] "Tukey"
T-P V-P 0 0 -1 -1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0
T-S v-s V-T 0 0 0 0 0 0 -1 -1 0 1 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
f
a n d we see t h a t t h e T u k e y c o n t r a s t s for the f o c u s factor V a r a r e specified i n rows 2 t h r o u g h 5; t h u s the l m a t . r o w s = 2 : 5 s p e c i f i c a t i o n i n t h e g l h t . m m c c a l l above. W i t h these p r e p a r a t i o n s , we c a n d i s p l a y the m e a n - m e a n m u l t i p l e c o m p a r i s o n plot for t h e t h e immer d a t a u s i n g R> p l o t (immer .nunc, r y = c ( 8 5 , 1 2 2 ) , + main = , main2 = " " )
x.offset
=
8,
w h e r e r y a n d x . o f f s e t are a r g u m e n t s to fine t u n e t h e a p p e a r a n c e of t h e plot; see t h e top g r a p h i n F i g u r e 4.7 for the r e s u l t s . T h e 9 5 % confidence i n t e r v a l s o n fix ~ M M , M T — Ms> d PT — Pv lie e n t i r e l y to t h e r i g h t of 0, w h i l e a l l other confidence i n t e r v a l s i n c l u d e 0. W e t h u s c o n c l u d e a t t h e 5 % level t h a t the average b a r l e y y i e l d for v a r i e t y T is larger t h a n t h e y i e l d for t h e v a r i e t i e s M, S , a n d V. N o further significances b e t w e e n t h e v a r i e t i e s a r e u n c o v e r e d , w h i c h reflects t h e test decisions o b t a i n e d from F i g u r e 4.4. a
n
E a c h of t h e s i m u l t a n e o u s confidence i n t e r v a l s for t h e 10 p a i r w i s e differences pi — fij i n F i g u r e 4.7 is centered a t a point w h o s e height o n t h e left y - a x i s is e q u a l to t h e average of t h e c o r r e s p o n d i n g m e a n s yi a n d yj a n d w h o s e l o c a t i o n a l o n g t h e rc-axis is a t d i s t a n c e yi — yj f r o m t h e v e r t i c a l line a t 0. N o t e t h a t t h e confidence i n t e r v a l s o n pp — ps a m d pv — M M a p p e a r a l m o s t at t h e s a m e height i n F i g u r e 4.7, l e a d i n g to a n i n f o r m a t i v e o v e r p r i n t i n g of the c o n t r a s t n a m e s a t t h e right y - a x i s . I n cases of o v e r p r i n t i n g , H e i b e r g e r a n d H o l l a n d (2006) suggested a tiebreaker plot of t h e s i m u l t a n e o u s confidence i n t e r v a l s s i m i l a r to F i g u r e 4.4, w h e r e the c o n t r a s t s a r e e v e n l y s p a c e d v e r t i c a l l y i n t h e s a m e o r d e r as i n t h e m e a n - m e a n m u l t i p l e c o m p a r i s o n plot a n d o n the s a m e h o r i z o n t a l s c a l e . T h e tiebreaker plot for t h e immer d a t a d i s p l a y e d a t t h e b o t t o m of F i g u r e 4.7 w a s o b t a i n e d w i t h t h e c o m m a n d R> p l o t . m a t c h M M C ( i m m e r . m m c $ m c a ,
main =
"")
T h e i s o m e a n s g r i d i n t h e center of F i g u r e 4.7 is p a r t i c u l a r l y useful w h e n