Document 91o1L2yVLEKnyGK4eQExqbwG7

m M em o to: D r. K ehoe From : B iom etrics O ctober 30, 1959 1. C o n c e r n in g T a b le 5 th e m e a n fo r P h a s e III e q u a ls to 6 . 9 7 a n d th e standard deviation to 5. 38. The coincidence b etw een the old m ean and standard deviation,b ased on 445 c a s e s , and the new m ean and standard deviation, b a sed on 952 c a s e s .would in d icate ex trem e r e liab ility of the m ethods of m easu rem en t. An o v era ll te st of sig n ifica n ce, testin g the h yp oth esis that the m eans o f P h a se I, P h a s e II, and P h a se III h ave b e e n draw n fr o m a com m o n population of m easu rem en ts m ust be rejected . The a n a ly sis of variance gives a value of F = 20.78 ( d egrees of freedom 2 and 1, 765 ) - th e p r o b a b ility o f o b ta in in g a n F of th a t m a g n itu d e , o r . g r e a te r , by ch an ce alon e is e x tr e m e ly sm a ll ( le s s than 1/1?000, 000). T estin g the d iffere n c e b etw een P h a se I and P h a se II by Students t, one ob tain s a valu e fo r t = 3 .8 4 ( d e g r e e s o f fr e e d o m 815 ) w h ich a g a in in d ica tes that the d ifferen ce b etw een P h a se I and P h a se II a r e r e producable w ith a high d egree of relia b ility . C o n c e r n in g T a b le 1, th e h y p o th e s is w a s t e s t e d th a t th e m e a n s fo r P h a se I, P h a se II, and P h a se III, obtained at the F u elin g Island, w ere drawn fro m a com m on population of m ea su rem en ts. The an a ly s is of v a r ia n c e g iv e s the v a lu e of F = 154. 27 ( d e g r e e s of free d o m 2 and 185 ) 4 g a in the p ro b a b ility of obtaining F of that m agn itu d e, or g r e a te r , by ch an ce alon e is ex tre m e ly sm a ll ( le s s than 1 /1 ,0 0 0 , 000). A v a lu e of t co m p u ted b e tw e e n th e m e a n s o f P h a s e I and P h a s e II taken at the F u elin g Island equals to 49.17 ( d eg rees of freed om 94 ) w h ich a g a in in d ic a te s th at the d iffe r e n c e b etw een P h a s e I and P h a se II a r e rep rod u cab le w ith a high d eg ree of r e lia b ility . , If the rela tio n b etw een tem p eratu re and hum idity on one hand and lead on the other is taken into co n sid era tio n one w ould expect d ifferen ces b e tw een Phase>I, II, and III to be in the sa m e o rd er in w h ich th ey w ere ob served , h ow ever, the m agnitude of the d ifferen ce would not b e a s g r e a t ( ,, 26 b e tw e e n P h a s e s I and II, ,,34 b e tw een P h a s e s II and III. T hese figu res w ere estim ated on the assum ption that the relationship found fo r the la s t th r e e w e e k s of P h a se III h eld throughout the stud y. ) kF One other item of note is the sm a ll standard erro r of the ob served d ifferen ces. F or in stan ce, for T able 1 the standard erro r of diffe re n c e b etw een th e m e a n s of P h a s e s I and II eq u a ls to . 012. That m ean s that a d ifferen ce as sm a ll a s . 05, b etw een the m ean s of P h a se s I and II, w ould h ave y ie ld e d a h ig h ly sig n ific a n t s ta tis tic a l d iffe r e n c e ( i. e . t w ould h ave eq u a led to 4 ). T h is r a is e s the q u estion w hether the ob serv ed sta tistic a l d ifferen ces can be r e fated to p ractical d ifferen ces. S tatistical an alysis cannot answ er this question w ith the p resen t data. 4. B ecau se of the sm all error of m easu rem en t the sin gle deviating value of P h ase I can be elim inated as an accident. , 'Y ;' ' Y Y Y 'Y Y ; y y ' syr'-' ^'Y.Y ; .-.Y' ,.Y;: y ..... ' i. ' . . . .,<. ' '' ' : . ' . . YY'Y Y?. .-: ./YYv ', : Y: Yy y ".' .';YY V Y 1 . , Y Y Y -- ? :V';'Y Y ' ,Y; Y ' ' "i ... . ' ' . . . " : . : -:. . Y/'Y' . ' . .. Y Y Y 'Y y Y'. Y i.V'-Y'- ' .