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221-chapter-5 - Calibration Methods Introduction 1 Graphs...

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Calibration Methods Introduction 1.) Graphs are critical to understanding quantitative relationships One parameter or observable varies in a predictable manner in relationship to changes in a second parameter 2.) Calibration curve : graph showing the analytical response as a function of the known quantity of analyte Necessary to interpret response for unknown quantities Time-dependent measurements of drugs and metabolites in urine samples Generally desirable to graph data to generate a straight line
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Calibration Methods Finding the “Best” Straight Line 1.) Many analytical methods generate calibration curves that are linear or near linear in nature (i) Equation of Line: where: x = independent variable y = dependent variable m = slope b = y-intercept b mx y + = m x y slope = =
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Calibration Methods Finding the “Best” Straight Line 2.) Determining the Best fit to the Experimental Data (i) Method of Linear Least Squares is used to determine the best values for “m” (slope) and “b” (y-intercept) given a set of x and y values Minimize vertical deviation between points and line Use square of the deviations deviation irrespective of sign ) b ) x ( m y ( ) y y ( d i i i i + - = - = 2 i i 2 i 2 i ) b ) x ( m y ( ) y y ( d + - = - =
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Calibration Methods Finding the “Best” Straight Line 4.) Goodness of the Fit (i) R 2 : compares the sums of the variations for the y-values to the best-fit line relative to the variations to a horizontal line. R 2 x 100: percent of the variation of the y-variable that is explained by the variation of the x-variable. A perfect fit has an R 2 = 1; no relationship for R 2 0 99.5% of the y-variation is due to the x-variation 53.0% of the y-variation is due to the x-variation What is the other 47% caused by? Very weak to no relationship Strong direct relationship R 2 based on these relative differences Summed for each point
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Calibration Methods Calibration Curve 1.) Calibration curve : shows a response of an analytical method to known quantities of analyte Procedure: a) Prepare known samples of analyte covering convenient range of concentrations.
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