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Lecture 6 Basic Statistics Dr. A.K.M. Shafiqul Islam School of Bioprocess Engineering University Malaysia Perlis 28.09.2011

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CALIBRATION CURVE The straight-line equation given by where y = is the dependent variable x = is the independent variable m = is the slope of the curve b = is the intercept on the ordinate (y axis); y is usually the measured variable, plotted as a function of changing x.

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CALIBRATION CURVE

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The correlation coefficient is used as a measure of the correlation between two variables The closer the observed values to the most probable values, the more definite is the relationship between x and y. It gives numerical measures of the degree of correlation.

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CALIBRATION CURVE The Pearson correlation coefficient is one of the most convenient to calculate. This is given by where r is the correlation coefficient, n is the number of observations, s x is the standard deviation of x, s y is the standard deviation of y, x i and y j are the individual values of the variables, Y and y are their means.

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CALIBRATION CURVE The use of differences in the calculation is frequently cumbersome, This equation can be transformed to a more convenient form:

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CALIBRATION CURVE Correlation coefficient is calculated for a calibration curve to ascertain the degree of correlation between the measured instrumental variable and the sample concentration. General rule, 0.90 < r < 0.95 indicates a fair curve, 0.95 < r < 0.99 a good curve, and r > 0.99 indicates excellent linearity. An r > 0.999 can sometimes be obtained with care.

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Data for Example 3.19 Sample Your method(mg/dL) Standard method(mg/dL) XyXy A 10.2 10.5 B 12.7 11.9 C 8.6 8.7 D 17.5 16.9 E 11.2 10.9 F 11.5 11.1 CALIBRATION CURVE

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Solution CALIBRATION CURVE

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A more conservative measure of closeness of fit is the square of the correlation coefficient, r 2, and most statistical programs calculate this value An r value of 0.90 corresponds to an r 2 value of only 0.81, This is also called the coefficient of determination. CALIBRATION CURVE

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