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

2. 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.

3. CALIBRATION CURVE

4. 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.

5. 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.

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

7. 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.

8. 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

9. Solution CALIBRATION CURVE

10. 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

11. Thank you