SIZE OF PLOT AND NUMBER OF REPLICATIONS NECESSARY FOR VARIETAL TRIALS WITH WHITE PEA BEANS. ACKNOWLEDGMENTS The w r i t e r i s g r a t e f u l t o P r o f e s s o r E. E. Down an d Mr. H. M. Brown f o r g u id a n c e a n d a i d i n c o n d u c t i n g t h i s p r o b le m an d f o r review o f t h i s t h e s i s . SIZE OF PLOT AND NUMBER OF REPLICATIONS NECESSARY FOR VARIETAL TRIALS WITH WHITE PEA BEANS THESIS RESPECTFULLY SUBMITTED IN PARTIAL FULFILLMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY AT MICHIGAN STATE COLLEGE OF AGRICULTURE AND APPLIED SCIENCE CLARENCE M.‘ LOESELL 1936 ProQuest Number: 10008369 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10008369 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 06- 1346 TABLE I. OF CONTENTS SIZE OF PLOT AND NUMBER OF REPLICATIONS NECESSARY FOR VARIETAL TRIALS WITH WHITE PEA BEANS' II. - MATERIAL AND METHODS A. 2 EXAMPLE OF ANALYSIS OF VARIANCE FOR ENTIRE PLOT B. k EXAMPLE OF ANALYSIS OF VARIANCE FOR CENTER ROWS OF PLOT III. IV. V. V I. V II. V III. IX. 1 RESULTS AND DISCUSSION 6 7 STANDARD ERRORS IN PER CENT OF MEAN 11 NUMBER OF REPLICATIONS 15 COMPARATIVE IS LAND EFFICIENCY SUMMARY 22 CONCLUSIONS Zk LITERATURE CITED 26 103832 SIZE OF PLOT AND NUMBER OF REPLICATIONS NECESSARY FOR VARIETAL TRIALS WITH WHITE PEA BEANS. Many e x p e r i m e n t s have been c o n d u c t e d w i t h d i f f e r e n t f i e l d c r o p s t o d e t e r m i n e w hat s i z e o f p l o t a n d how many r e p l i c a t i o n s a r e n e c e s s a r y to g i v e r e l i a b l e r e s u l t s . Eco­ n o m i c a l a d m i n i s t r a t i o n o f f u n d s r e q u i r e s t h a t t h e p l o t s be s m a l l a n d r e p e a t e d a minimum number o f t i m e s . However, e f f i c i e n t p l o t t e c h n i q u e r e q u i r e s t h a t t h e p l o t s be o f s u f f i c i e n t s i z e and r e p e a t e d o f t e n enough to make t h e r e ­ su lts re lia b le . T h a t i n f o r m a t i o n o b t a i n e d f o r one crop u n d e r c e r t a i n c o n d i t i o n s can n o t be a p p l i e d t o a n o t h e r i s c l e a r l y shown by a r t i c l e s on t h e s u b j e c t . A co m p le te b i b ­ l i o g r a p h y (1) o f a r t i c l e s d e a l i n g w i t h p l o t t e c h n i q u e i n g e n e r a l was r e p o r t e d by a com m ittee o f t h e American S o c i e ­ t y o f Agronomy, f o r t h e s t a n d a r d i z a t i o n o f f i e l d e x p e r i ­ m ents. A d d i t i o n a l a r t i c l e s ( 2 ) were r e c e n t l y r e p o r t e d . A s e a r c h o f t h i s l i t e r a t u r e f a i l s t o r e v e a l any e x p e r i m e n t s o f t h i s n a t u r e w ith w hite p ea beans (P h aseo lu s v u l g a r i s , L .) . O dland an d G a r b e r (*l) i n t h e i r work w i t h s o y b e a n s , w hich comes n e a r e s t t o t h i s p a r t i c u l a r s u b j e c t , c o n c l u d e d t h a t u n ­ d e r c o n d i t i o n s e x i s t i n g w here t h e i r e x p e r i m e n t was c o n d u c t ­ e d , a l 6 - f o o t p l o t one row wide r e p l i c a t e d t h r e e t i m e s was t h e m o st s a t i s f a c t o r y when b o t h a c c u r a c y , and economy o f l a n d a n d o f l a b o r were t a k e n i n t o c o n s i d e r a t i o n . -2- The o b j e c t o f t h e s t u d y r e p o r t e d i n t h i s p a p e r was t o f i n d t h e p r o p e r s i z e o f p l o t an d t h e number o f r e p l i ­ c a tio n s of t h i s s iz e n ecessary fo r v a r i e t a l t r i a l s w ith w h i t e p e a b e a n s when t h e t r i a l s a r e c o n d u c t e d u n d e r con­ d i t i o n s s i m i l a r to th o se p r e v a i l i n g in t h i s experim ent. Due c o n s i d e r a t i o n s h o u l d be g i v e n t o t h e amount o f l a n d t o be u s e d a n d t o t h e c o n v e n i e n c e o f h a n d l i n g t h e p l o t s in a l l f i e l d o p e r a t io n s . MATERIAL AND METHODS The Robust v a r i e t y o f w h i t e p e a b e a n s i s u s e d as a s t a n d a r d o f c o m p ariso n i n v a r i e t y t r i a l s a t t h e M ic h ig an A g r i c u l t u r a l E x p e r im e n t S t a t i o n an d i s grown e x t e n s i v e l y throughout th e s t a t e . experim ent. C o n s e q u e n t l y , i t was u s e d in t h i s An a r e a o f Conover s o i l o f a p p r o x i m a t e l y one a n d t h r e e - q u a r t e r s ’ a c r e s , l o c a t e d i n one o f t h e r e g u l a r p l a n t - b r e e d i n g s e c t i o n s , was chosen f o r t h e p l a n t i n g . The b e a n s w ere p l a n t e d in rows t w e n t y - e i g h t i n c h e s a p a r t on June 1 5 , 193^> so s p a c e d t h a t t h e p l a n t s were ap­ p r o x i m a t e l y one t o two i n c h e s a p a r t . To i n s u r e a good s t a n d s i x t y pounds o f b e a n s were p l a n t e d to t h e a c r e i n ­ s t e a d o f t h e u s u a l r a t e o f f o r t y - f i v e p o u n d s. A fte r the l a s t c u l t i v a t i o n , an a r e a 210 f e e t l o n g a n d 210 f e e t w ide was chosen from t h e c e n t e r o f t h e f i e l d f o r t h e e x p e r i m e n t . A t o t a l o f 1^90 p l o t s was o b t a i n e d by d i v i d i n g t h i s a r e a - 3- i n t o t w e n t y - o n e t e n - f o o t s e r i e s , e a c h n i n e t y rows w ide. A c o u n t o f t h e number o f p l a n t s i n e a c h t e n - f o o t p l o t was made s h o r t l y b e f o r e h a r v e s t . At m a t u r i t y t h e p l a n t s were p u l l e d by h a n d an d a l l o w e d t o c u r e . The t e n - f o o t p l o t s w ere t h r e s h e d a n d t h e b e a n s a i r d r i e d i n a warm room b e ­ f o r e w eighing. F o r t u n a t e l y , t h e s e a s o n was f a v o r a b l e f o r b e a n s a n d a l l p l o t s had a good s t a n d w i t h o u t any s k i p s a l ­ t h o u g h a f a i r l y wide r a n g e i n t h e number o f p l a n t s p e r row o c c u r r e d . The c o e f f i c i e n t o f c o r r e l a t i o n betw een s t a n d a n d y i e l d was f o u n d to be . 1 0 + . 0 1 . T h is c o e f f i ­ c i e n t was to o s m a l l to make any c o r r e c t i o n i n t h e y i e l d s f o r v a r i a t i o n s in stand. The s t a t i s t i c a l c o n s t a n t s u s e d to s t u d y t h e p roblem w ere o b t a i n e d by making u s e o f t h e " a n a l y s i s o f v a r i a n c e " a s u s e d by Iramer ( 3) . The p r i n c i p l e s o f t h e method as s t a t e d by Immer a r e : I f the t o t a l v a r i a b i l i t y of the o b serv a­ t i o n s on a l l t h e p l o t s i s g i v e n i n s u i t a b l e te rm (sum o f s q u a r e s ) i t may l e g i t i m a t e l y be a p p o r t i o n e d t o v a r i o u s known c a u s e s , l e a v i n g a rem ain in g p o r t i o n a s c r i b a b l e to u n c o n t r o l l e d o r unknown c a u s e s . The l a t t e r w i l l t h e n s e r v e as a b a s i s f o r th e c a l c u l a t i o n of t h e . e r r o r of th e experim ent. The v a r i a n c e ( s t a n d ^ ' u e v i a t i o n s q u a r e d ) due t o any o f t h e known c a u s e s o r t o t h e u n c o n t r o l l e d o r unknown c a u s e s may t h e n be f o u n d by d i v i d i n g t h e sum o f s q u a r e s by t h e ap­ p r o p r i a t e number o f d e g r e e s o f freedom . The te rm " d e g r e e s o f freedom" i s h e r e u s e d i n t h e s e n s e o f " i n d e p e n d e n t c o m p a r i s o n s " . W ith N q u a n t i t i e s whose mean i s f i x e d , t h e r e a r e i n g e n e r a l N -l i n d e p e n d e n t co m p a r iso n s o r d e g r e e s o f fre edo m . - 4- The a s s u m p t i o n was made t h a t f i v e v a r i e t i e s o r t r e a t ­ m e n ts were t o be t e s t e d b y t h e a n a l y s i s a n d t h a t t h e a r ­ r a n g e m e n t o f t h e p l o t s w i t h i n e a c h r e p l i c a t i o n was a t r a n ­ dom. Thus, v a r i a t i o n b e t w e e n b l o c k s c o u l d b e removed l e g i t ­ i m a t e l y from t h e t o t a l v a r i a t i o n , by s u b t r a c t i n g t h e sum o f s q u a r e s due t o v a r i a t i o n betw e en b l o c k s from t h e t o t a l sum o f s q u a r e s o f a l l o f t h e p l o t s . to v a r ia tio n w ith in blocks. The r e m a i n d e r i s due The s t a n d a r d e r r o r , calcu lat­ e d from t h i s r e m a i n d e r , was u s e d a s t h e e r r o r o f t h e ex­ perim ent. T h is e r r o r w i l l be s m a l l e r th a n t h e s t a n d a r d e r ­ r o r a s c a l c u l a t e d from t h e t o t a l p o p u l a t i o n o n l y when t h e v a r i a t i o n b e tw e e n b l o c k s i s g r e a t e r t h a n t h a t w i t h i n b l o c k s . Example o f A n a l y s i s o f V a r i a n c e f o r E n t i r e P l o t An example o f t h e a n a l y s i s o f v a r i a n c e a s a p p l i e d to y i e l d s o f t h e 1 ,$ 9 0 p l o t s t e n f e e t l o n g and one row wide i s g iv e n i n T a b le 1 . TABLE 1 - A n a l y s i s o f V a r i a n c e o f Y i e l d o f Beans i n P l o t s Ten F e e t Long, One Row Wide, f o r 21 S e r i e s . Sum of Squares V a r i a t i o n Degrees of F r e e dorr Between blocks _ 377 W ithin b l o ck s _1& 2 T otal b e tw e en p lo ts 1 S&9 V ariance o r Mean Square S tandard Dev i a tion 6,967,077-18 19,678.4a 140.26 3 ,2 2 6 . 9 6 56.60 -JO 11 ,646., 2 ^ . 3 6 Mean (M) = 44S . 3S F* 6 .1 0 E rror i n fo o f Mean Y ield 12.67 6 , 2 7 1 . 1 6 _ 79 -20 *The r a t i o o f t h e l a r g e r mean s o u a r e to th e s m a l l e r . - 5- The f o r m u l a used, t o o b t a i n t h e t o t a l sum o f s q u a r e s 2 was S(X ) S(X)Mx w here X r e p r e s e n t s a v a r i a t e an d Mx the mean o f t h e po p u latio n . T h is f o r m u l a i s b r i e f e d to 2 S(X ) - 0 , w h e re 0 ( c o r r e c t i o n ) r e p r e s e n t s S(X)Mx . The f o r 2 m u la f o r t h e sum o f s q u a r e s be tw e e n b l o c k s was 8(B ) - 0 in 5 w h ich B was t h e sum o f t h e f i v e p l o t s i n a b l o c k an d C was t h e c o r r e c t i o n term S(X)Mx . The sum o f was d i v i d e d by 5 t o p l a c e t h e v a l u e on a s i n g l e p l o t b a s i s . The t o t a l sum o f s q u a r e s 11 ,£>^-6,235.3# was o b t a i n e d by s u b t r a c t i n g C or 3 7 9 , 9 6 6 , 0 6 2 . 6 2 from S(X2 ) or 3 9 1 ,8 1 2 ,2 9 6 .0 0 . The sum o f s q u a r e s betw een t h e 37$ b l o c k s o f t h e f i v e ad­ j a c e n t p l o t s a d d e d s i d e w i s e o f t h e s e r i e s was o b t a i n e d in a s i m i l a r way e x c e p t t h e summation was d i v i d e d by f i v e , to p l a c e v a l u e s on t h e b a s i s o f a s i n g l e p l o t , b e f o r e s u b t r a c t 2 in g the c o r r e c t io n f a c t o r s . Thus S(B ) - 0 became 5 1 , 9 ^ , 6 6 5 , 6 9 9 .0 0 - 379 ,9 6 6 ,0 6 2 .62 w hich gave 6 , 9 6 7 , 0 7 7 . 1 $ . The sum o f s q u a r e s due t o v a r i a t i o n w i t h i n b l o c k s was t h e d i f f e r e n c e b e t w e e n t h e t o t a l sum o f s q u a r e s a n d t h a t p o r t i o n due t o v a r i a t i o n b e t w e e n b l o c k s . S in c e t h e t o t a l o f 1£>90 p l o t s was c o n s i d e r e d , t h e r e were 1669 ( N - l) degrees of f r e e ­ dom a t t r i b u t a b l e t o t h e t o t a l sum o f s q u a r e s . T here w ere 37B b l o c k s ( o f f i v e p l o t s each) a n d c o n s e q u e n t l y 377 ( N - l ) d e g r e e s o f freedom due t o b l o c k s . The d i f f e r e n c e o f 1512 was t h e number o f d e g r e e s o f freedom due t o v a r i a t i o n be­ tw een t h e f i v e p l o t s w i t h i n e a c h o f t h e 37S b l o c k s . Each - 6- sum o f s q u a r e s was d i v i d e d by i t s r e s p e c t i v e number o f de­ g r e e s o f f re e d o m t o g i v e t h e mean s q u a r e . The s t a n d a r d e r ­ r o r i s t h e s q u a r e r o o t o f t h e mean s q u a r e , a n d , c a l c u l a t e d from t h e r e m a i n d e r was 5 6 . &0 grams o r 1 2 . 6 7 p e r c e n t o f t h e mean y i e l d o f W 6 . 3 6 grams. The s i g n i f i c a n c e o f t h e d i f f e r e n c e betw een t h e v a r i ­ a n c e b e tw e en b l o c k s a n d t h a t w i t h i n b l o c k s was d e t e r m i n e d by t h e F - t e s t d e v e l o p e d by S nedec or ( 5 ) . The v a l u e s o f F i n t h e s e t a b l e s a r e g iv e n f o r two d i f f e r e n t l e v e l s o f s i g ­ n i f i c a n c e , t h e f i v e p e r c e n t and t h e one p e r c e n t p o i n t s f o r s e l e c t e d numbers o f d e g r e e s o f fre ed o m . The fo rm e r i s e x p e c t e d t o be e x c e e d e d i n random s a m p l i n g from a homogene­ ous p o p u l a t i o n f i v e t i m e s i n one h u n d r e d t r i a l s , o n ly once. the l a t t e r The f i v e p e r c e n t p o i n t i s t a k e n a s a c o n v e n i­ e n t minimum l e v e l o f s i g n i f i c a n c e . I n T a b le 1 t h e o b s e r v e d v a l u e o f F e x c e e d s t h e one p e r c e n t p o i n t a n d i t can be con­ c l u d e d t h a t rem oval o f t h e v a r i a t i o n between b l o c k s was w orthw hile. Example o f A n a l y s i s o f V a r i a n c e f o r C e n t e r Rows o f P l o t The s t a n d a r d e r r o r o f a t h r e e - r o w p l o t was d e t e r m i n e d , w i t h t h e o u t e r rows d i s c a r d e d to e l i m i n a t e p o s s i b l e c o m p e ti­ t i o n from o t h e r p l o t s . each three-row p lo t. T a b le 2 . The c e n t e r v a l u e s were u s e d from The a n a l y s i s of v a r i a n c e i s g iv e n in - 7- TABLE 2 - A n a l y s i s o f V a r i a n c e o f Y i e l d o f Beans i n T h r e e Row P l o t s , Ten F e e t Long, o f w h ic h o n l y t h e C e n t e r Row was U sed, f o r Tw enty-one S e r i e s . V a r i a t i o n D egrees of Freedom Between b locks W ithin blocks T otal be tw e e n p lo ts Sum of Squares V ariance o r Mean S q u are S tandard Dev i a tio n 125 2 , 2 7 7 , 8 2 9 .6 5 1 8 , 2 2 2 .6 4 504 1 .887 l2 73_._6o 3 , 7 4 4 .5 9 6 1 .1 9 4 , 1 6 5 , 1 0 5 . 25 6 , 7 0 7. 64 8 1.90 629. . I 3 4 i93_ F Error in $ of Mean Y ield . . 4 .8 7 1 3 .4 0 M = 4-56. 73 The number o f d e g r e e s o f freedom a t t r i b u t a b l e to t o t a l v a r i a t i o n was 629, s i n c e t h e r e were 630 t h r e e - r o w p l o t s i n t h e e n t i r e f i e l d o f IS90 s i n g l e r o w s , t e n f e e t l o n g . b l o c k o f f i v e th e n r e q u i r e d f i f t e e n rows. Each The 63O t h r e e - row p l o t s s u b d i v i d e d i n t o b l o c k s o f f i v e c o n t r i b u t e d 125 de­ g r e e s o f f r e e d o m , l e a v i n g 504- d e g r e e s o f freedom a t t r i b u t a b l e t o v a r i a t i o n b etw e en p l o t s w i t h i n b l o c k s . The o b s e r v e d v a l u e o f F e x c e e d e d t h e one p e r c e n t p o i n t a n d i t was c o n c l u d e d t h a t t h e rem oval o f t h e v a r i a t i o n b e­ tw een b l o c k s was w o r t h w h i l e . The s t a n d a r d e r r o r o f a s i n g l e p l o t was 61 .1 9 grams o r 1 3 . ^ 0 p e r c e n t o f t h e mean y i e l d ( 4-5 6 .7 3 grams) o f a l l t h e c e n t r a l rows i n t h e t h r e e - r o w p l o t s i n t h e f i e l d . RESULTS AND DISCUSSION The w e i g h t s i n grams o f c l e a n e d bea n s f o r t h e IS90 p l o t s a r e g i v e n i n T ab le 3. of p l o t s 1 , 2 , 3, A n a l y s e s were made o f t h e f i e l d s 5 , 6 , 9 an d 1$ rows wide a n d 1 0 , 2 0 , 3 0 , ^0 a n d 50 f e e t i n l e n g t h , r e s p e c t i v e l y . A t o t a l of 10$ d i f f e r e n t s i z e s a n d s h a p e s o f p l o t s were s t u d i e d , 72 o f t h e s e i n v o l v e d t h e e n t i r e p l o t w h i l e t h e o t h e r 36 u s e d o n l y t h e c e n t e r r o w s , t h e o u t s i d e o r b o r d e r rows b e i n g d i s ­ c a r d e d t o e l i m i n a t e c o m p e t i t i o n b e tw e e n p l o t s . C ertain of t h e s e c o m b i n a t i o n s c o u l d n o t be b a s e d on t h e e n t i r e a r e a o f 21 s e r i e s a n d 90 rows w ide. T h is was p a r t i a l l y due t o t h e o r i g i n a l assum ption in v o lv in g f iv e v a r i e t i e s or tre a tm e n ts . The f o u r - r o w a n d f i v e - r o w p l o t s c o u l d n o t u s e a l l 90 rows b e c a u s e 90 i s n o t d i v i s i b l e by f o u r , n o r c o u l d t h e 1$ p l o t s f i v e rows w ide be s u b d i v i d e d i n t o b l o c k s c o n t a i n i n g f i v e p l o t s each. A l s o , 21 s e r i e s c o u l d n o t be s u b d i v i d e d i n t o p l o t s 2 0 , *4-0, o r 50 f e e t i n l e n g t h , b u t c o u l d be d i v i d e d i n ­ t o p l o t s 30 f e e t i n l e n g t h . To overcome t h e s e l i m i t a t i o n s , v a l u e s w ere c a l c u l a t e d f o r a r e a s 21 a n d 20 s e r i e s in l e n g t h c o n t a i n i n g 90 , $0 , a n d 75 rows i n w i d t h . In o r d e r t o com­ p a r e t h e v a l u e s o b t a i n e d w i t h p l o t s f o u r an d f i v e rows wide w i t h t h o s e 1 , 2 , 3, 6, 9» rows w i d e , t h e s t a n d a r d e r r o r s were a l s o c a l c u l a t e d f o r t h e a r e a s 21 and 20 s e r i e s l o n g , a n d $0 an d 75 rows w id e , r e s p e c t i v e l y . The same con­ d i t i o n s h o l d t r u e f o r t h e p l o t s h a v i n g t h e b o r d e r rows d i s ­ carded. S i m i l a r c a l c u l a t i o n s were made w henever n e c e s s a r y . TABLE 3 - Y i e l d o f Beans i n grams from IS90 3 in g le -R o w P l o t s Each Ten F e e t Long. ’ S eries - P l o t Number - f “> / 2 3 3 < ? 334 343 373 433 468 365 467 430 446 474 470 384 438 353 465 502 376 500 468 387 490 600 347 488 482 510 425 330 340 416 7 r 438 450 527 333 570 270 348 50 5 473 602 545 485 520 415 416 440 360 515 540 315 465 430 450 480 490 530 465 0 305 351 605 435 465 556 373 425 518 404 535 600 614 430 520 467 418 538 470 470 440 225 470 582 555 418 476 531 430 487 5 370 557 516 605 481 438 602 433 590 467 498 425 386 538 417 443 438 3. 470 520 455 435 440 382 511 430 367 435 370 450 540 405 390 53 0 398 412 304 485 381 7 312 407 410 4 9 v is- /C / 7 / r /r 20 361 533 6 Ji /£. /3 /d v5“ 480 462 404 520 550 626 433 516 320 413 301 425 440 456 440 54 5 585 562 670 478 516 495 417 460 435 460 465 440 557 457 504 586 491 460 551 395 295 528 457 420 502 381 488 440 506 590 415 438 510 542 425 431 465 410 475 435 560 550 530 490 402 432 444 490 424 528 450 425 402 482 446 488 519 376 480 498 460 405 525 453 455 475 461 557 530 10 334 387 613 490 575 532 472 11 305 400 619 564 550 480 480 481 12 390 415 590 567 517 612 430 465 415 432 535 522 432 421 535 437 486 448 483 509 485 13 301 37 8 565 486 588 457 492 486 450 364 554 426 410 420 485 468 419 423 575 570 550 14 456 482 546 482 53 5 500 450 471 485 477 523 494 512 431 600 535 462 536 552 560 556 15 420 495 475 448 593 406 516 445 470 370 408 554 445 440 440 364 488 530 445 565 525 16 390 473 445 521 479 470 458 515 380 443 565 360 370 460 575 560 323 490 470 470 405 17 402 495 570 455 498 520 518 570 540 432 519 494 414 441 450 415 470 498 495 630 523 10 380 507 431 562 476 432 480 359 515 334 424 524 449 426 548 456 496 437 490 480 415 19 362 523 448 455 478 500 474 425 470 464 474 488 381 400 562 495 507 400 410 435 366 20 360 470 512 457 466 598 443 470 385 464 420 533 480 515 476 558 456 442 535 640 455 21 405 598 441 425 495 437 579 474 432 389 410 431 375 470 545 360 555 518 505 525 445 22 339 483 452 450 465 420 500 505 512 490 540 400 390 360 475 468 450 480 418 440 462 458 23 398 470 406 452 468 583 507 572 42 0 526 460 450 473 385 618 474 507 472 52 5 530 24 287 443 451 444 389 612 508 424 573 515 505 394 338 438 577 485 512 550 517 463 400 25 517 445 458 450 530 561 494 585 492 504 486 410 463 448 656 446 620 560 405 385 400 452 445 26 467 472 440 510 540 525 484 555 545 475 505 400 374 354 634 488 490 450 557 27 386 492 449 506 495 512 495 474 645 399 457 399 462 480 425 591 390 490 454 512 400 28 475 44 5 410 560 450 565 490 556 509 453 513 445 485 520 521 605 485 545 512 415 370 29 450 455 460 519 537 504 425 540 505 534 483 430 505 474 535 612 30 4 473 376 447 380 30 404 412 412 393 414 540 452 481 460 470 430 460 479 473 621 530 498 506 400 410 414 31 475 435 458 586 525 520 453 500 482 685 430 485 525 450 500 550 485 515 438 497 462 32 392 431 410 572 568 583 530 520 470 625 606 485 505 422 465 565 497 439 445 443 380 33 394 455 412 256 440 535 505 458 570 603 438 465 435 417 512 544 476 480 454 377 444 34 396 440 385 508 660 515 415 521 475 547 555 456 453 38 0 640 470 435 494 350 36 5 435 405 558 465 35 390 425 355 420 61 0 560 556 510 540 419 455 538 520 570 457 470 360 450 36 305 445 340 455 560 510 516 484 505 451 596 475 430 393 430 430 465 430 375 407 417 37 352 360 395 519 548 557 587 600 485 486 505 532 365 455 654 488 488 495 494 396 420 625 518 620 605 475 38 38 0 425 335 414 645 507 564 638 495 545 590 544 521 562 384 430 39 368 440 410 448 580 600 500 568 390 480 440 608 402 415 517 481 437 563 525 400 403 40 387 485 420 558 575 460 478 492 478 555 445 580 458 405 575 555 690 597 550 495 334 540 645 414 570 41 336 446 380 488 545 472 440 560 557 476 596 59 0 662 557 562 456 455 42 324 465 421 390 596 630 507 419 390 535 486 457 352 376 572 600 555 468 575 420 452 - 423 39 2 408 482 490 620 492 450 555 476 468 550 38 5 334 426 557 61 5 556 50 7 405 368 d 370 490 447 460 645 577 626 445 68 2 470 526 584 377 432 605 532 466 455 385 364 -•8 413 418 535 609 492 530 362 586 479 53 0 466 39 5 640 61 5 507 458 505 580 4' \ -1 0 - TABLE 3 — ( c o n t i n u e d ) 350 608 390 / 348 452 405 48 330 404 325 355 587 468 410 565 565 475 507 660 305 605 550 534 385 386 472 445 490 372 402 505 557 546 390 555 487 330 345 373 430 545 505 400 470 447 385 365 463 360 440 392 417 465 383 429 502 437 342 420 458 302 437 450 380 460 400 530 560 425 555 440 371 396 462 49 417 386 402 421 614 566 548 350 48 5 556 50 510 405 360 550 570 703 375 345 485 580 468 446 402 412 530 5 1 5 462 425 360 357 385 51 405 345 370 495 541 567 470 320 382 513 474 503 483 410 563 340 426 446 420 320 298 52 265 548 505 450 420 424 450 415 498 385 466 532 410 324 437 370 350 300 53 461 394 355 510 455 545 4 1 0 437 368 445 500 427 435 351 512 466 348 393 356 425 300 54 340 392 315 446 520 391 531 315 440 39 2 516 360 318 290 448 402 401 385 420 354 328 55 348 4 4 5 370 580 470 451 343 400 395 395 435 370 318 444 412 305 390 439 366 386 534 410 490 400 419 217 434 375 286 378 395 370 260 370 435 388 434 450 373 345 415 419 270 303 350 365 315 425 425 475 353 365 352 448 366 430 415 387 375 393 500 422 435 384 377 354 265 355 541 450 250 310 377 431 392 392 473 389 344 440 340 386 455 350 260 373 393 480 440 3 4 4 365 373 373 306 332 367 290 420 335 240 312 420 400 465 : 56 57 58 59 364 335 353 420 335 392 318 314 350 392 343 422 520 453 332 578 437 432 500 461 487 390 468 367 350 405 484 418 296 377 300 335 430 302 330 285 267 434 437 62 252 330 404 570 400 410 345 375 377 411 395 422 325 407 508 430 345 383 613 487 420 63 372 390 394 555 565 400 405 450 368 338 466 442 350 403 440 445 357 354 540 483 350 64 310 450 380 448 340 455 4 6 2 335 466 360 334 314 405 481 452 358 374 358 450 362 365 60 61 375 411 414 295 3 8 4 400 375 65 341 320 388 490 448 440 399 4 3 5 455 364 332 420 365 392 470 426 338 434 426 555 300 66 287 268 425 485 480 444 370 4 6 6 590 435 292 332 334 384 405 428 380 436 442 355 352 67 368 332 382 490 456 545 4 4 4 567 390 474 358 400 388 344 446 427 274 325 312 386 356 337 406 524 475 510 560 530 540 522 335 425 517 463 387 4 1 5 410 335 340 310 475 69 300 325 358 475 515 432 3 8 2 490 458 440 356 440 436 430 455 392 352 226 310 352 453 70 352 354 325 540 405 478 4 2 9 420 465 345 425 415 555 503 415 440 410 373 290 400 470 68 310 71 375 354 388 482 555 426 4 6 8 506 465 418 345 571 437 420 485 430 376 228 260 398 492 72 306 320 432 417 475 512 475 440 436 500 456 438 516 445 564 534 348 337 329 365 555 73 375 387 242 390 458 431 363 455 438 520 509 551 494 485 660 407 404 329 331 487 406 74 75 76 355 345 370 365 444 348 440 483 4 1 9 377 460 530 490 460 525 552 540 47 3 455 367 294 409 523 425 395 370 436 556 515 4 9 2 525 511 571 523 454 467 575 435 441 319 340 345 531 377 425 4 8 1 415 473 420 595 511 510 509 416 492 468 370 339 385 534 454 570 470 331 451 374 258 528 420 415 371 77 414 366 325 400 401 367 416 370 550 425 485 413 515 78 316 287 311 312 305 364 431 407 483 509 404 408 550 444 525 420 400 372 275 380 464 79 289 286 376 345 400 452 392 366 540 380 533 355 407 452 458 460 485 335 270 276 385 425 435 470 512 490 565 316 528 456 435 80 335 336 343 325 375 442 351 338 475 53 3 460 81 395 335 336 424 365 532 420 432 520 485 467 388 400 430 610 440 405 408 398 355 428 82 323 394 355 420 405 450 ' 458 443 625 570 548 475 450 375 515 490 490 414 475 350 395 83 400 380 280 460 473 530 370 498 5 65 435 510 405 362 586 500 395 331 371 380 390 450 84 370 410 260 402 470 525 4 5 6 292 565 524 451 435 339 386 610 548 410 412 483 405 290 85 354 390 246 415 534 473 568 475 473 440 390 440 408 468 590 49 5 365 329 452 404 £95 86 365 406 380 344 435 505 449 510 525 438 453 432 485 505 603 532 450 400 375 365 450 37 350 357 357 320 435 573 520 4 6 0 562 393 414 439 452 543 635 530 402 376 334 410 475 4 7 0 545 543 88 300 278 509 451 524 583 462 645 520 445 427 440 350 465 335 256 3 4 8 325 381 350 468 375 474 495 542 492 445 470 464 495 498 562 627 4 5 2 376 420 392 396 40? 387 314 3 4 0 395 352 506 574 438 485 330 416 400 387 413 430 480 540 548 535 427 - 11 - STANDARD ERRORS IN PER CENT OF MEAN The s t a n d a r d d e v i a t i o n s , a s o b t a i n e d by a n a l y s i s o f v a r i a n c e f o r t h e p l o t s o f v a r y i n g l e n g t h s an d w i d t h s , were e x p r e s s e d i n p e r c e n t a g e o f t h e i r r e s p e c t i v e means an d a r e shown i n T a b l e s ^ a n d 5 * B e f o r e t h e s e t a b l e s a n d a l l sub­ s e q u e n t t a b l e s can be d i s c u s s e d , i t i s n e c e s s a r y t o d e t e r ­ mine w h e t h e r t h e v a l u e s o b t a i n e d f o r t h e p l o t s f o u r and f i v e rows w ide can be compared w i t h t h o s e o b t a i n e d f o r o t h ­ e r w idths. The v a l u e s a r e c o n s i d e r e d to be c o m p a r a t i v e i n t h i s an d in a l l f u t u r e t a b l e s b e c a u s e s i m i l a r c a l c u l a t i o n s from 1 , 2 , a n d p l o t s f o r t h e a r e a s o f 50 and 75 rows in w id th , r e s p e c t i v e l y , a re in c lo s e agreement w ith th o se c a l c u l a t e d f o r t h e e n t i r e a r e a o f 90 rows. These v a l u e s a r e a l s o shown i n T a b l e s K a n d 5 * C onsidering the e n t i r e p l o t s , t h e s t a n d a r d e r r o r in p e r c e n t o f t h e mean, d e c r e a s e d a s t h e l e n g t h o f t h e p l o t was i n c r e a s e d . The g r e a t e s t r e d u c t i o n s come when t h e p l o t s w ere i n c r e a s e d from 10 t o 20 f e e t in l e n g t h . C onsiderable f u r t h e r r e d u c t i o n i n p e r c e n t a g e e r r o r o c c u r s when t h e p l o t s w ere i n c r e a s e d t o 30 f e e t i n l e n g t h , b u t when t h e l e n g t h o f t h e p l o t was i n c r e a s e d t o *K) o r 50 f e e t , f u r t h e r r e d u c t i o n does n o t co m p en sa te f o r t h e i n c r e a s e in l a n d u s e d . I n c r e a s i n g t h e w i d t h o f t h e p l o t from one row t o two rows shows a g r e a t r e d u c t i o n i n p e r c e n t a g e e r r o r , compare.- o' \© o VO •r-t OQ 4-3 o 1— 1 Ph Vt o Number Series Plots End to of of Used End +3 Ti •i— f S& CO o> l— rH O d h Iso ft o©| N 50 »— 1 00 0 N *9 CO I-1 d dt LO r-~ • ^0 O' ft r— © N co o cr> rH 50 \<5 av LO d !? N ro LO ro to CO CO dr CO o> rH LO d LO rLO 50 50 k? fd K' O CO C Oft rCO O' d r rH ft • rr^r— eo O 1O — 1 i— 1 © 0 0 0 0 0 < \ (N n H H K> rH K> ro O' o dr ro LO dr o- r—o cr> O' o 00 5} CO dr r— • d a> d d d 50 r—vO d d d d o o o L j <0 <0 n % f r y ro oo — 1 CO rH a> ro CO 50 a> O•' 50 50 S Is-« lo!CO oo 50 O 'o • CO LOLO cr>a> Is- r- d 00 oo d a> o 1— 1 i 5> c © v>: o Q § > § O 50 r- 50 i— i r- LO 50 K>00 aS 00 O 50 K>o C r— r^- Is■ — i co CO =t- K•" 50• C3>O' COCOCO vo OV 50 ft ft • co COC\J COCOCO COO' O' r- r- r- Is- d Is- d d d (— 1 °6 °SSt 06 °s st 04 O 1£ $ rHSt 03St Ss/ *&r-t 6 (— 0 -P CO • COT3 o i— 1 Jh 0 O -H ■ci! & o CO rH CO o rH r- LO rdr O CO oro 2 oLO ♦Small her CO o ffi d 1— 1 i? *0 K> rHft a> \0 LO CO o rH V 50 50 =* 50 th e ^0 LO CVI O' O' 5 indicate ON LO Is-• oS iso d 12— figures in each compartment of Tables 4 and of plots side to side across the f i e l d . 50 rH Length I of Plot in Eeet. i TABLE k - Standard Errors of Plots Varying Single Plots in Percentage of the Mean, of Yields in Size and Shape, when Entire Plot was Used. of — o 1— 1 Number of Series of Plots Used End to End ; Across th e 1 F ield. 3 o> LO r^- vO rH 0 CO o> 0 • f—1 0 \ \0 cvj 1—1 H O K' § CVJ fA % rH OJ rH O O' rH X) =3r LTV X) pd- CFS <50 r-~ X) X) \0 5 • rH rH rH 1—1 b is X • 0 b O cr O CVJ H CVJ 1—1 CVJ « rH 1—1 ro i—1 & Vo r ■d~ — X) C>> <50* 50 N U N 0 n x> X> =J* CVJ 0 rH 0 <0 Vo O O CVJ rH O CVJ C) X rH 1—1 =J50 • o> CVJ p- 0 =t p K> X ) * 50 O 1—1 0 p( N pJ p ~- O O fO x> ro cr> rH <30 \ rH O cr> a> 50 x> x> .6 b b b b l* OJ <50 JO P• p- r p - rH x> O O IO $ 50 50 SO p p l h 0 «) O 0 ro PLTV O ro S b 0 PI 0 pj 0 Pp- * u Ct compartment of Tables k and 5 i n d i c a t e side to side across the f i e l d . X> Small figures in each the number of plots Width of P l o t in Rows. Number of Rows U sed. 5 - Standard Errors of Single P l o t s , in Percentage of the Mean, of Y i e l d s of Plots Varying in Size and Shape, when Border Rows were Removed. L ength of P l o t in F e e t . TABLE -1 3 - 0 O LTV i -14— b l e t o i n c r e a s i n g t h e l e n g t h from 10 t o 20 f e e t . Increas­ i n g t h e w i d t h o f p l o t s to t h r e e rows r e d u c e s t h e p e r c e n t a g e e r r o r s l i g h t l y w h i l e f u r t h e r i n c r e a s e s i n w i d t h change t h e r e s u l t s but very l i t t l e . When t h e b o r d e r rows a r e d i s c a r d e d and o n l y t h e c e n t e r rows u s e d i n t h e c a l c u l a t i o n s , t h e r e s u l t s a r e s i m i l a r t o t h o s e o b t a i n e d when t h e e n t i r e p l o t i s u s e d . A g r e a t reduc­ t i o n i n p e r c e n t a g e e r r o r was n o t e d when t h e l e n g t h o f p l o t was i n c r e a s e d from 10 t o 20 f e e t a n d a s t i l l f u r t h e r r e d u c ­ t i o n when i n c r e a s e d t o 30 f e e t , b u t v e r y l i t t l e was n o t e d beyond t h a t . difference I n c r e a s i n g t h e w i d t h of t h e p l o t from t h r e e rows to f o u r rows r e s u l t e d in a s l i g h t d e c r e a s e i n t h e p e r c e n t a g e e r r o r b u t when t h e w i d t h was i n c r e a s e d t o f i v e rows a c o n s i d e r a b l e r e d u c t i o n was o b s e r v e d . Increasing t h e w i d t h o f t h e p l o t t o s i x an d n i n e rows showed v e r y l i t ­ tle change one way o r t h e o t h e r . The s t a n d a r d e r r o r was i n a l l b u t one c a s e g r e a t e r th a n when a l l t h e rows o f t h e same s i z e d p l o t s w ere u s e d i n t h e c a l c u l a t i o n s . I n c r e a s in g the s i z e o f p l o t t o a l l o w f o r t h e d i s c a r d i n g o f t h e b o r d e r rows r e s u l t e d i n some i n c r e a s e i n t h e p e r c e n t a g e o f t h e s t a n d a r d e r r o r i n a l l b u t t h r e e c a s e s where a c o r r e s p o n d i n g number o f rows w ere h a r v e s t e d . T h is means t h a t t h e r e was g r e a t e r v a r ­ i a b i l i t y b e t w e e n t h e p l o t s o f a b l o c k when o n l y t h e c e n t e r rows w ere h arv ested th a n when t h e e n t i r e number o f h arv ested rows was u s e d . p l o t o f t h e same -15- NUMBER OF REPLICATIONS The t h e o r e t i c a l number o f r e p l i c a t i o n s r e q u i r e d by an y g i v e n s i z e o f p l o t t o r e d u c e t o f o u r p e r c e n t t h e s t a n d a r d e r r o r o f t h e mean o f t h a t number o f r e p l i c a t i o n s may be o b t a i n e d by d i v i d i n g t h e s t a n d a r d e r r o r p e r c e n t ­ a g e s , a s g i v e n i n T a b le k- and T ab le 5 > ing th e se q u o tie n ts . in Tables 6 and 7 - f o u r and s q u a r ­ The v a l u e s t h u s o b t a i n e d a r e g iv e n The v a l u e o f f o u r p e r c e n t was chosen becau se n o rm a lly t h i s is the approxim ate s i z e of the s t a n d a r d e r r o r o f n i n e r e p l i c a t i o n s o f bean p l o t s a t t h e M ic h ig a n S t a t i o n . The t h e o r e t i c a l number o f r e p l i c a t i o n s f o r t h e e n t i r e p l o t t e n d e d t o d e c r e a s e a s t h e l e n g t h o f t h e p l o t was i n ­ creased. The g r e a t e s t d i f f e r e n c e i n number was o b s e r v e d when t h e p l o t was i n c r e a s e d from 10 t o 20 f e e t , t h e number o f r e p l i c a t i o n s f o r t h e 2 0 - f o o t p l o t s b e i n g n e a r l y on eh a l f o f t h a t f o r t h e 1 0 - f o o t p l o t i n t h e two n a r r o w e s t w idth p l o t s . There was a f u r t h e r n o t i c e a b l e d e c r e a s e when t h e l e n g t h o f t h e p l o t i s i n c r e a s e d from 20 t o 30 f e e t b u t s c a r c e l y any when i n c r e a s e d b eyond t h a t . When t h e w i d t h o f t h e p l o t was i n c r e a s e d from one row t o two rows t h e r e was a l s o a d e c i d e d d e c r e a s e i n t h e num­ b e r of r e p l i c a t i o n s r e q u i r e d b ut f u r t h e r in c r e a s e in the number o f rows p e r p l o t made v e r y l i t t l e change i n t h e t h e o - O O' LO 0 LO LO • cr d cr d LO LO CV•J LO CT> d 1— 1 d =1OJ* fO OJ* «— 1 d so id JO .6 OJ LO vO VO ■O •iH CQ J-3 O rH a* 60 rH OJ• LO -= y O += •*H 16 - 6.0 CO P 0* LO fo O* LO =t LO vd LO d OJ LO O0 OJ OJ vO.6 cr ro cr rH 0 OJ LO fo CVJ d rH h- r— =JIO OJ* C\J 0J O« 0 10 50 60 ro d d =J“ OJ* 60 a> o> CT CT*> O LO LO LO LO LO d OJ 0- 60 0J OJ ♦ OJ*OJ vO CVJ 1 0 — 0J OJ Number Series Plots End to 1 Across F ield. of of Used End the LO • ou*LO • LO<0LO o> o> cr to 10 OJ 60 cr 50 1—1O* O 0 O cr cr CO LOLOLO ro ro I'd K>ro d 0J OJ OJ 1— 11— ! rH Length of P l o t in F e e t . TABLE 6 - T heoretical Number of R e p lic a tio n s Needed to Reduce the Standard of the Mean to Four Per Gent, when Entire Plot was Used. Error - rH OJ 0 OJ O 1— t O 1— 1 0- LO OJ O 0ro § O LO Number o f Series of Plots Used End to End Across th e Field. Width, of P l o t in Rows. Number of Rows Used. 1 3 VO r^ * cu 7.6 6.2 45 ro cvj fO • I t— i i— 1 H i— • 1 1 .2 LO Is- 1— 1 o> CVJ t- l o1—1 45 • CVJ o 4> 45 • CVJ o 45 ro =J*• = ± O• =t I—1 O 60 r— Is- CT> 45 =J- ro ro • Is-♦ 60 • =t O rH r— O o ro 45 CVJ* — ■■— rH * 60 =h to Is- LO ro CVJ* CVJ CVJ* O• =J- o =h ro 5 ro • LO oLO -13- r e t i c a l number o f r e p l i c a t i o n s n e c e s s a r y to r e d u c e t h e s t a n d a r d e r r o r o f t h e mean t o f o u r p e r c e n t . P r a c t i c a l l y t h e same t h i n g i s t r u e when t h e b o r d e r rows w ere d i s c a r d e d an d o n l y t h e c e n t e r rows u s e d in t h e calcu latio n s. The g r e a t e s t d e c r e a s e was n o t e d i n t h e t h r e e - r o w p l o t s when t h e l e n g t h o f t h e p l o t was i n c r e a s e d from t e n t o t w e n t y f e e t . I n c r e a s in g th e l e n g t h of the p l o t s t o t h i r t y f e e t t e n d e d t o r e d u c e t h e number s t i l l more b u t when i n c r e a s e d t o f o r t y a n d f i f t y f e e t t h e r e d u c t i o n i n t h e o r e t i c a l number o f r e p l i c a t i o n s was s m a l l . When t h e two c e n t e r rows o f t h e f o u r - r o w p l o t s o r t h e t h r e e c e n t e r rows o f t h e f i v e - r o w p l o t s were u s e d i n s t e a d o f t h e c e n t e r one o f t h e t h r e e - r o w p l o t s , t h e t h e o r e t i c a l number o f r e p l i c a t i o n s was a p p r e c i a b l y d e c r e a s e d , b u t a f u r t h e r i n c r e a s e i n number o f rows t o s i x an d n i n e d i d n o t r e d u c e t h e number g r e a t l y . COMPARATIVE LAND EFFICIENCY T a b l e s 6 an d 7 i n d i c a t e t h a t a s t h e p l o t was i n c r e a s e d i n l e n g t h , a n d , t o some e x t e n t , i n w i d t h t h e number o f r e p ­ l i c a t i o n s n e e d e d t o p u t t h e s t a n d a r d e r r o r to t h e common b a s i s o f f o u r p e r c e n t o f i t s mean was r e d u c e d . t h e l a r g e r p l o t s r e q u i r e d more l a n d . However, To d e t e r m i n e , t h e n , w h ic h s i z e a n d s h a p e o f p l o t u s e d t h e l a n d most e f f e c t i v e l y t h e c o m p a r a t i v e l a n d e f f i c i e n c y v a l u e s f o r t h e 103 s i z e s -19- a n d s h a p e s o f p l o t s were o b t a i n e d . I t was assum ed t h a t a p l o t t e n f e e t l o n g a n d one row wide h a d an e f f i c i e n c y o f 1 0 0 .0 p e r c e n t . A c c o r d i n g t o T ab le 6 , a p l o t t e n f e e t l o n g a n d two rows w ide r e q u i r e d 6 .2 r e p l i c a t i o n s t o r e d u c e t h e s t a n d a r d e r r o r o f t h e mean t o f o u r p e r c e n t . S in c e t h e p l o t was two rows w i d e , 6 . 2 was m u l t i p l i e d by two and t h i s p r o d u c t d i v i d e d i n t o 1 0 . 0 ( t h e t h e o r e t i c a l number o f r e p l i c a t i o n s n e e d e d f o r a p l o t t e n f e e t l o n g and one row w ide) , t h e n m u l t i p l i e d by 100 to g i v e p e r c e n t . Thus 1 0 . 0 x 100 s _ , -g -g ^-----2* = SO. 6 p e r c e n t . V a l u e s f o r l a n d e f f i c i e n c y c a l c u l a t e d i n t h i s way a r e g i v ­ en i n T a b l e s 3 a n d 9 I t w i l l be n o t e d i n T able S t h a t when t h e l e n g t h o f t h e p l o t was i n c r e a s e d from t e n to tw e n t y f e e t t h e p e r c e n t ­ a g e o f l a n d e f f i c i e n c y was m a t e r i a l l y d e c r e a s e d b u t when t h e l e n g t h o f p l o t was i n c r e a s e d from tw e n t y t o t h i r t y f e e t the la n d e f f i c i e n c y p ercen tag e v alu e d id n o t decrease. When t h e l e n g t h o f p l o t was i n c r e a s e d s t i l l f u r t h e r t h e r e was a c o n s i d e r a b l e d e c r e a s e i n t h e p e r c e n t a g e o f l a n d e f f i ­ ciency. An i n c r e a s e i n t h e num ber o f rows p e r p l o t from one t o two c a u s e d a d e c r e a s e i n p e r c e n t a g e o f l a n d e f f i c i ­ ency. S t i l l f u r t h e r d e c r e a s e s i n l a n d e f f i c i e n c y were n o t ­ e d when t h e number o f rows p e r p l o t was i n c r e a s e d t o t h r e e , t o f i v e a n d so on t o e i g h t e e n . - Shape, and Size in LO OJ o o> i—1 OJ OJ LO OJ OJ of Plots ,c i -p 3 •H ro x> r— o 60 =J- OJ • LO ro rH rH rH o (7s G> X> OJ 60 OJ OJ OJ rH h- OJ 60 X) ro xh OJ oj’ OJ X> OJ* O'­ LO =h o> * xi1 LO e r rH LO O rH rH h- r- rH « xh OJ ro 60 X ) r o 60 xj- xh LO xh xh K> xh “ "I 1Ch» xh o• o O* xj- O r- 0s Is- 1— o o o ro xh LO LO 50 60 o> rH Ol o 1o—1o 50 50 50 60 50 50 vO x> Length of P l o t in F e e t . Number Series Plots End to Across Field. of of Used End the 1100-0 Lioo.o X) X) o 50 OJ OJ OJ =t LO • xh i—1 LO Irs-o Is- CT" Is— ro ro Ch rH OJ 50 • • OJ xh 50 50 * Is— LO r o O ro, 50 50 1100.0 50 rH LO OJ i—i OJ* o 1 : CVI X> LO cr> • rH i—1 rH =3r 50 « 50 rH LO LO =h cr> • OJ Is. oro =1* • «H o vO 50 » xh ov zj- xh •—1 * xt* rH o> lo a •H CQ -P O i—1 P-i TABLE S - Percentage E ffic ienc y in Use of when Entire Plot was Used. 6o • CO £ o Land Varying vo 50 O * LO 2*£ X> OJ 150 • rH CTn O' 20 - i—i cu O OJ o rH o O- LO O O ro 3 xh rH OJ oLO - H ito 0 (SI •rH CO VO Pi &0 PI *H R cd > • 40 ro LO 0 +3 o * * o> O «H r— r<> o* CM p -t CM in H K' CM 50 • * K"' <50 CM • r<> LO t" - 43 60 <6 CM rH . Ph *o 0 o o 53 0 PS §tu H 0 R 0 o £ 0 0 0 & £3 O ffi PI •H R 0 > j T3 O R PS O 0 PQ •H O 0 •h 43 CM -R CQ CO P-i P4 ,Q pci O $5 R £ O 0 o o> rH CM * PM rH rCM m K> CM CM CM CM o> 60 lO r«A60 o>60 iH CM 60 * 0 H *H PJ 3 19 2 S . S n ed eco r, 0*. W ., C a lc u la t io n s and I n t e r p r e t a t io n s o f A n a ly s is o f V a ria n ce and C o v a ria n ce. Ames, Iowa: C o lle g ia t e P r e s s , I n c . , 193^*