Oracle Corporation et al v. SAP AG et al

Filing 836

Declaration of Scott W. Cowan in Support of 835 Memorandum in Opposition, filed bySAP AG, SAP America Inc, Tomorrownow Inc. (Attachments: # 1 Exhibit A, # 2 Exhibit B, # 3 Exhibit C, # 4 Exhibit D, # 5 Exhibit E, # 6 Exhibit F, # 7 Exhibit G, # 8 Exhibit H, # 9 Exhibit I, # 10 Exhibit J, # 11 Exhibit K, # 12 Exhibit L, # 13 Exhibit M, # 14 Exhibit N, # 15 Exhibit O, # 16 Exhibit P, # 17 Exhibit Q)(Related document(s) 835 ) (Froyd, Jane) (Filed on 9/9/2010)

Oracle Corporation et al v. SAP AG et al

Doc. 836 Att. 14

EXHIBIT N

Dockets.Justia.com

Sampling o f Populations
M e t h o d s a n d Applications

Fourth Edition

P a n l S. L e v y
RTf Intemational S t a t i s t i c a l Research Division Research Triangle Parle, North Carolina

S t a n l e y Lemeshow
The Ohio Sta te University C o l l e g e 0 1 P u b l i c Health C o l u m b u s , Ohio

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Levy. P u l S. S a m p l i n g o f p o p u J d O N : mClhods 000 lIpplic 110Il5/ P ul , L e v y . tanlcy Lerncsho . - 41h cd. p.em. l n e l u d e s bLbliographical r e f e r e n c a nd Index. ISB 97 � 0 - 4 7 0 - 0 0 7 - 2 ( c l o t b ) 1. Po ulario I I b s t i I methods. ~. a m p l i n (Slllli les) 1 Lcme.sho ,S~nky. 11. T i l l e . HB 4 9 . 4 9 . L 4 2008 200 004 J4 J04.60I'SI9S2--dc.2I Pnnl.ed .n Ihe nited les o A m e n c a .

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2.4 C H A R A C f E R I S T I C S O F ESTIMA T E S O F POPULA T I O N P A R A M E T E R S

35

T a b l e 2.9 D a t a f o r t b e B u r o A r e a E s t i m a t e s
Student Dave Don Virginia Mean ( % ) 37 42 50 Variance (%)1 64 9 9

w h e r e z i s the s t a n d a r d normal d e v i a t e . D o n ' s burn m e a s u r e m e n t s a r e usually high, but it is n o t o f t e n that he w o u l d be m o r e than 10 p e r c e n t a g e p o i n t s away from the true value. F o r Don

Pr(X>47)+Pr(X<27)=Pr ( z>

47-42

J9

) =1.67 + P r ( z < - 5 . 0 0 ) = . 0 5 .

F i n a l l y , a s r e f l e c t e d by h e r l a r g e M S E , the probabililY t h a t V i r g i n i a m i s s e s t h e t a r g e t b u r n a r e a by more than 10 p e r c e n t a g e p o i n t s is q u i t e high:

Pr(X>47)+Pr(X>27)=Pr ( z>

47-50

J9

) =-1 +Pr(z<-7.67)=.84.

W e h a v e s e e n in this e x a m p l e that, w h e n e v a l u a t i n g p a r t i c u l a r e s t i m a t e s , it is imp o r t a n t to e x a m i n e both bias a n d variance. Both e n t i t i e s play i m p o r t a n t roles in d e t e r m i n i n g the s i z e o f the m e a n s q u a r e error.

2.4.3 Validity, Reliability, a n d Accuracy
In e a r l i e r s e c t i o n s , we s p o k e o f the d e s i r a b i l i t y o f using s a m p l e d e s i g n s that y i e l d reliable a n d valid e s t i m a t e s . H o w e v e r , we h a v e n e v e r d e f i n e d j u s t w h a t the t e r m s " r e l i a b l e " a n d " v a l i d " m e a n in t e r m s o f c h a r a c t e r i s t i c s o f e s t i m a t e s . W e n o w h a v e d e v e l o p e d e n o u g h c o n c e p t s and n o t a t i o n c o n c e r n i n g e s t i m a t e s t o b e a b l e t o d e f i n e t h e s e t w o t e r m s a s weIl a s a t h i r d t e r m , t h e " a c c u r a c y " o f a n e s t i m a t e , w h i c h we will s e e is d e r i v e d f r o m t h e v a l i d i t y and r e l i a b i l i t y . T h e reliability o f an e s t i m a t e d p o p u l a t i o n c h a r a c t e r i s t i c r e f e r s to h o w reprod u c i b l e the e s t i m a t o r is o v e r r e p e t i t i o n s o f the p r o c e s s y i e l d i n g the e s t i m a t o r . I f we a s s u m e that there is n o m e a s u r e m e n t e r r o r in the s u r v e y , then the r e l i a b i l i t y o f an e s t i m a t o r c a n be stated in t e r m s o f its s a m p l i n g v a r i a n c e o r , e q u i v a l e n t l y , its s t a n d a r d e r r o r . T h e s m a l l e r t h e s t a n d a r d e r r o r o f a n e s t i m a t o r , t h e g r e a t e r i s its rel iabil ity. T h e validity o f an e s t i m a t e d p o p u l a t i o n c h a r a c t e r i s t i c r e f e r s to h o w the m e a n o f t h e e s t i m a t o r o v e r r e p e t i t i o n s o f the p r o c e s s y i e l d i n g the e s t i m a t e , d i f f e r s f r o m the true v a l u e o f the p a r a m e t e r being e s t i m a t e d . A g a i n , i f w e a s s u m e t h a t there is n o m e a s u r e m e n t e r r o r , t h e validity o f an e s t i m a t o r c a n be e v a l u a t e d by e x a m � n i n g the bias o f the e s t i m a t o r . T h e s m a l l e r t h e bias, the g r e a t e r is the validity.