Home Reading Skoog et al. Fundamental of Analytical Chemistry. Chapters 5 and 6

Errors SystematicRandom Caused by nonideal instrument behavior, faulty calibration, or by use under inappropriate conditions Caused by fluctuation of experimental conditions, fluctuation of sample composition, or by fluctuation of instrumental function Gross Caused by carelessness and inattention of an experimenter or by significant defects of an instrument.

Errors SystematicRandom Gross Systematic deviations are biases. Sometimes they can be corrected by a proper calibration. They are invariant throughout the whole series of measurement and cannot be reduced by replication. Systematic deviations are biases. Sometimes they can be corrected by a proper calibration. They are invariant throughout the whole series of measurement and cannot be reduced by replication. Random deviations fluctuates with time. They change in magnitude and sign from measurement to measurement. They can be reduced by replication Random deviations fluctuates with time. They change in magnitude and sign from measurement to measurement. They can be reduced by replication Gross errors are usually large deviations that cannot be explained by physical reasons. Minimization of gross errors requires self- discipline and a proper care about equipment. Gross errors are usually large deviations that cannot be explained by physical reasons. Minimization of gross errors requires self- discipline and a proper care about equipment.

p(x) – probability distribution  x - centroid x p(x)p(x) x x N – number of experiments x is an estimation of  x  x characterizes the whole population whereas the characterizes a part of this population selected by random sampling Random deviations

Statistical estimations Mean value Standard Deviation Standard Error of the Mean Relative Standard Deviation Coefficient of Variation

Confidence interval Corresponding integration intervals and levels of significance Normal (Gauss) distribution

Confidence interval Corresponding integration intervals and levels of significance Normal (Gauss) distribution 68.3%

Confidence interval Corresponding integration intervals and levels of significance Normal (Gauss) distribution 90.7%

Confidence interval is an interval that includes a measured value with a given probability P. It is a characteristic of uncertainty of a result of measurement Results of measurements are always reported with confidence intervals t P,N is the Student coefficient Assumption: Normal distribution of errors

Table of Student t-coefficients Degree of Freedom = N - 1

Rounding convention In any report issued by an analytical chemist, results must be rounded so that they content only significant figures. Significant figures in a number are all of the digits known with certainty plus the first uncertain digits. 1.Rounding must be postpone until the computation is completed. Round only the final result, not intermediate results! 2.The number of significant figures is limited by error. So, the last significant digit of a result is the first significant digit of the confidence interval (or standard deviation). 3.We usually keep one, seldom two and never three or more significant figures in an confidence interval (or standard deviation) value.

Rounding convention Example 2  x = = x = ± 300 x = ± 280 x = ± Correct: Allowed: Not correct: Average measured value: Confidence interval:

Rounding convention Example 2  x = = x = ± 0.03 x = ± x = ± Correct: Allowed: Not correct: Average measured value: Confidence interval:

Example: Calculation of a mean value, standard deviation, and confidence interval X.XXX 0.XXX 0.XXX 0.XXX 0.XXX 0.XXX 0.XXX 0.XXX 0.XXX 0.XXXX 0.XX0.XX0.XX X.X0.X

Accuracy and Precision Accuracy is the closeness of the measurement to true value of the measurand* [ISO ] Precision characterizes agreement among results of successive measurements of the same measurand*. *Measurand is a quantity or property that is measured

x True value Accuracy Precision Accuracy characterizes the systematic component of the measurement error and Precision characterizes the random component of the measurement error. Precision does not relate to the true value. Accuracy and Precision

Reproducibility is the precision achieved in the measurement of the same value under changed conditions of measurement. The changed conditions include: principle of measurement, method of measurement, observer, measuring instrument, reference standards, location, conditions of use, and time. According to the International Standard [ISO ] two kind of precision are distinguished: Repeatability is the precision under conditions that include: the same measurement procedure, the same observer, the same measuring instrument, used under the same conditions, the same location, and repetition over a short period of time. Reproducibility and Repeatability