Statistical Aspects of Water Quality Monitoring, Proceedings by A.H. El-Shaarawi and R.E. Kwiatkowski (Eds.)

By A.H. El-Shaarawi and R.E. Kwiatkowski (Eds.)

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Sample text

A p r o b l e m t h a t a r i s e s when d a t a u n c e r t a i n t y i s accounted f o r i s how t o s t a t i s t i c a l l y a n a l y z e a sequence of d a t a , when e a c h d a t a p o i n t i s n o t a s p e c i f i c v a l u e , b u t a c t u a l l y is r e p r e s e n t e d by some d i s t r i b u t i o n t h a t a t t e m p t s t o e s t i m a t e t h e amount o f d a t a u n c e r t a i n t y . T h e p r o b l e m may b e f u r t h e r complicated s i n c e t h e d i s t r i b u t i o n parameters and/or t h e d i s t r i b u t i o n f u n c t i o n i t s e l f may c h a n g e a s t h e amount of t h e w a t e r v a r i a b l e changes.

The e f f e c t of t h e b i a s i s t o i n c r e a s e t h e r e g i o n of r e j e c t i o n a t t h e upper t a i l and d e c r e a s e t h e r e g i o n a t t h e l o w e r t a i l , w h e r e t h e amount o f c h a n g e i s a f u n c t i o n of o n l y t h e r a t i o of b i a s t o s t a n d a r d d e v i a t i o n (Cochran,l977). For example, when t h e b i a s e q u a l s 0 . 4 times t h e e s t i m a t e d s t a n d a r d d e v i a t i o n t h e p r o b a b i l i t y of e r r o r of more t h a n 1 .

The a f f e c t of n o t i n c l u d i n g an e s t i m a t e of n o n s a m p l i n g e r r o r w i t h s a m p l i n g e r r o r i s t o create an e s t i m a t e of v a r i a n c e s m a l l e r t h a n t h e a c t u a l amount. This could r e s u l t i n r e j e c t i n g a n u l l h y p o t h e s i s of e q u a l means o r v a r i a n c e s when i n r e a l i t y t h e r e i s no s t a t i s t i c a l d i f f e r e n c e . Hence, o n e i n c r e a s e s t h e l e v e l of Type I e r r o r .

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