Properties of Umass Boston

Transcription

1 Fle name hould be LatName_labNumber.doc or LatName_labNumber.doc.l. 0 pont wll be taken for wrong fle name. Follow the format of report and data heet. Both are poted n the web. MS Word and Ecel 003 format. Onl two fle n one e-mal.

2 Introducton of the Evaluaton of Epermental Error and Stattc ()

3 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 Take.607 mmol tandard oluto and put nto 5 cell, take the meaurment for each cell cell A mean SD

4 Bear' Law [Ca+] A Slope 0.05 Intercept A concentaton ( mmol )

5 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.

6 + ) ( ) ( ) ( 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

7 SUMMARY OUTPUT Regreon Stattc Multple R R Square Adjuted R Square Standard Error Obervaton 5 R R ANOVA df SS MS F Sgnfcance F Regreon E-06 Redual 3.394E E-06 Total Coeffcent Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Varable E lope RESIDUAL OUTPUT b m Obervaton Predcted Y Redual

8 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

9 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

10 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 + }

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12 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

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14 I a data pont a bad data? Q Tet Q cal gap/range If Q cal >Q table, then the data hould be dcarded

15 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