Calibration Methods: Regression & Correlation. Calibration Methods: Regression & Correlation

Transcription

1 Calbraton Methods: Regresson & Correlaton Calbraton A seres of standards run (n replcate fashon) over a gven concentraton range. Standards Comprsed of analte(s) of nterest n a gven matr composton. Matr Wh s the composton of the matr mportant? Slope & Intercept Eplan the dfferences. *Fgures used n sldes from: Mller and Mller, 5 1 Calbraton Methods: Regresson & Correlaton Ke Questons: 1. Is the graph lnear? If t s a curve, what s the form of the curve?. What s the best straght lne on the curve? Do we force the lne thought zero 3. Assumng lneart, what are the errors and confdence lmts for the slope & ntercept of the lne. How do we show the errors?. When the calbraton plot s used for the analss of a test materal, what are the errors and confdence lmt for the determned concentraton? 5. What s the lmt of detecton of the method? How do we determne? 1

2 Calbraton Methods: Regresson & Correlaton Determnng Concentraton from Calbraton Curve Basc steps: (1) Make a seres of dlutons of known concentraton for the analte. () Analze the known samples and record the results. (3) Determne f the data s lnear. () Draw a lne through the data and determne the lne's slope and ntercept. (5) Test the unknown sample n duplcate or trplcate. Use the lne equaton to determne the concentraton of the analte: m + b Conc analte readng ntercept slope 3 Calbraton Methods: Regresson & Correlaton A closer look at lneart: slope / ntercept formula m + b where m slope, b -ntercept, concentraton of unknown. What s? Ponts on the lne: ( 1, 1 ) normall the blank readng (, ), ( 3, 3 ) (, ) The mean of the -value s termed. The mean of the -value s termed. How s lneart assessed? (, ) centrod of all ponts

3 Calbraton Methods: Regresson & Correlaton Lneart s addressed b the product-moment correlaton coeffcent, r. r s gven b equaton 5. and represented vsuall as b: r-value of 1 perfect negatve correlaton between and. r-value of +1 perfect postve correlaton between and. r-value of no correlaton between and. 5 Calbraton Methods: Regresson & Correlaton 6 3

4 Calbraton Methods: Regresson & Correlaton The lne of regresson of on : Devatons wll occur both negatve and postve. We then need to mnmze the sum of squares of the resduals. Ths eplans the use of: Slope of least squares lne: b Intercept of least square lne: a b {( )( )} ( ) Eample 5..1 Interpretaton of results See Fgure 5.3 for vsual representaton 7 Calbraton Methods: Regresson & Correlaton 8

5 5 9 Errors n the slope and ntercept of the regresson lne. Wh mportant? Frst calculate the statstc, s / whch estmates the random errors n the -drecton: (5.6) Calbraton Methods: Regresson & Correlaton Calbraton Methods: Regresson & Correlaton ) ˆ ( / n s 1 Then calculate: Calbraton Methods: Regresson & Correlaton Calbraton Methods: Regresson & Correlaton b s s / ) ( a n s s / ) (

6 Calbraton Methods: Regresson & Correlaton 11 Calbraton Methods: Regresson & Correlaton Eample Estmate the lmt of detecton for the fluorescen determnaton studed n the prevous sectons. We use equaton (5.1) wth the values of B (a) and S B (S / ) prevousl calculated. The value of at the lmt of detecton s found to be ,.e..8. Use of the regresson equaton then elds a detecton lmt of.67 pg ml -1. Fgure 5.8 summarzes all the calculatons performed on the fluorescen determnaton data. 1 6

7 Calbraton Methods: Regresson & Correlaton 13 Calbraton Methods: Regresson & Correlaton Eample Standard aqueous solutons of fluorescen are eamned n a fluorescence spectrometer and eld the followng fluorescence ntenstes (n arbtrar unts)? Fluorescence ntenstes: Concentraton, pg ml -1 :

8 Calbraton Methods: Regresson & Correlaton ( ) ( ) ( )( ) Sums: The fgures below the lne at the foot of the columns are n each case the sums of the fgures n the table: note that ( ) and ( ) are both zero. Usng these totals n conjuncton wth equaton (5.), we have: r Calbraton Methods: Regresson & Correlaton Use of regresson lnes for comparng analtcal methods 16 8

9 Outlers Treatment of Outlers 1. Re-eamne for Gross Errors. Estmate Precson to be Epected 3. Repeat Analss f Tme and Suffcent Sample s Avalable. If Analss can not be Repeated, Perform a Q-Test 5. If Q-Test Indcates Retenton of Value, Consder Reportng the Medan 17 Calbraton Methods: Regresson & Correlaton Lmt of Detecton (LOD) - lowest amount of analte n a sample whch can be detected but not necessarl quanttated as an eact value. - mean of the blank sample plus or 3 tmes the SD obtaned on the blank sample (.e., LOD mean blk + Zs blk ) LOD calculaton - alternatve Data requred: (1) calbraton senstvt slope of lne through the sgnals of the concentraton standards ncludng blank soluton () standard devaton for the analtcal sgnal gven b the blank soluton LOD 3 SD blank sgnals slope of sgnals for std' s 18 9