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Introducton of the Evaluaton of Epermental Error and Stattc ()
Lnear Leat Square Regreon Stattcal anal of multple obervaton for the SAME meaurement and the SAME ample. Stattcal anal of the mathematcal relatonhp between varable a+b e.g. Optcal aborpton-beer law AεbC Bear' Law [Ca+] A.607 0.04 5.3 0.08 0.46 0.65 5.639 0.38 6.065 0.399 Take.607 mmol tandard oluto and put nto 5 cell, take the meaurment for each cell cell A 0.04 0.044 3 0.04 4 0.04 5 0.04 mean 0.048 SD 0.00483
Bear' Law [Ca+] A.607 0.04 5.3 0.08 0.46 0.65 5.639 0.38 6.065 0.399 Slope 0.05 Intercept 0.003 A 0.45 0.4 0.35 0.3 0.5 0. 0.5 0. 0.05 0 0 5 0 5 0 5 30 concentaton ( mmol )
How relable the fttng? Doe the two varable ha lnear correlaton? Correlaton Coeffcent, R: R cloe to or - trong correlaton; R cloe to 0 no correlaton. The percentage of one varable coupled wth another varable Coeffcent of determnaton, R Standard Devaton of the vertcal devaton ( ) Standard Devaton of lope. Standard Devaton of ntercept. Confdence Level for lope and ntercept.
+ ) ( ) ( ) ( nt tan tan ) ( tan b m n D where D ercept of Devaton dard S D n lope of Devaton dard S b m d where n d of Devaton dard S σ
SUMMARY OUTPUT Regreon Stattc Multple R 0.99986678 R Square 0.999733475 Adjuted R Square 0.999644633 Standard Error 0.00670455 Obervaton 5 R R ANOVA df SS MS F Sgnfcance F Regreon 0.08048606 0.08048606 5.9655.84685E-06 Redual 3.394E-05 7.333E-06 Total 4 0.0807 Coeffcent Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.008875 0.000935.3784333 0.68783-0.00377777 0.0095388 X Varable 0.0589095 0.0004385 06.0799957.8468E-06 0.0473345 0.0564477 lope RESIDUAL OUTPUT b m Obervaton Predcted Y Redual 0.044807-0.0004807 0.08063504-0.00063504 3 0.64456 0.003755744 4 0.4045007-0.0045007 5 0.3987865 0.0003489
The SD for the unknown If the lnear regreon ued for the tandard or calbraton curve, the regreon anal tell u the relablt of the curve. The queton remanng what the tandard devaton of the meaurement ometme onl one meaurement done for the unknown. S tan dard k m where n + + k D D n Devaton ( ( D ) ( of ) D ) where m lope number of replcate meaurement of the the calculated X value for the unknown unknown
Error Propagaton for random error Addton or ubtracton: a+b+cd a-b-cd S d (S a +S b +S c ) Multplcaton or dvon a*bc a/bc (S c %) (S a %) +(S b %) where S a %(S a /a)*00
Student t tet Determne f two et of data are tattcall dfferent or not. (cae two n Harr book page 70) Calculate t cal compare wth t 95% f t cal > t 95% then wth 95% confdence, two et of data are tattcall dfferent. f t cal StDev pooled nn n + n the ame for both et of meaurement{ where f pooled tan dard ( n ) + ( n n + n devaton ) dfferent for both et of meaurement t cal n + n Degree of freedom { ( ( ( + ) n n ) ( ) n n + n + n + }
F tet to compare StDev To determne f there gnfcantl dfferent from each other. F cal If F cal > F table, then the dfference gnfcant. Larger one to enure F
I a data pont a bad data? Q Tet Q cal gap/range If Q cal >Q table, then the data hould be dcarded
Important Stattcal Tool Not n the cope of the lab Student t tet Gauge R&R F tet Q tet Confdent Level Control chartng DOE