Lesson 2 : Errors

• We do not use data obtained when gross error has occurred during collection.
• Steps in a Typical Quantitative Analysis include Select method, Obtain a representative sample, Prepare a laboratory sample, Define replicate samples, Dissolve the samples, Eliminate interferences, Measure property of the analyte, Calculate results, and Estimate the reliability of results.
• Data of unknown quality is useless, as all laboratory measurements contain experimental error.
• Experimental uncertainties, also known as error, are deviations from the "true" values of the quantities being measured.
• Replicates are two or more determinations on the same sample.
• The mean is an average or arithmetic mean.
• The median is the middle value of replicate data, if an odd number of replicates, the middle value of replicate data, if an even number of replicates, the middle two values are averaged to obtain the median.
• Precision describes the reproducibility of measurements, how close are results which have been obtained in exactly the same way, the reproducibility is derived from the deviation from the Mean: Deviation from the mean, Standard deviation, Variance, Coefficient of variation.
• Absolute Deviation (D) of an element of a data set is the absolute difference between that element and a given point, typically the point from which the deviation is measured is the value of either the median or the mean of the data set.
• Average absolute deviation or Average deviation or mean absolute deviation is the average of the absolute deviations and is a summary statistic of statistical dispersion or variability.
• Standard Deviation is a measure of the dispersion of a collection of numbers, it measures the spread of the data about the mean value, it is useful in comparing sets of data which may have the same mean but a different range.
• Variance is a measure of statistical dispersion, it is the average squared deviations about the mean, thus, variance is the square of the standard deviation.
• Coefficient of Variation (CV) is a normalized measure of dispersion of a probability distribution, it is defined as the ratio of the standard deviation to the mean.
• Systematic or determinate errors affect accuracy.
• Method errors include slow or incomplete reactions, unstable species, nonspecific reagents, side reactions, and can be corrected with proper method development.
• Gross errors or blunders lead to outlier’s and require statistical techniques to be rejected.
• Random or indeterminate errors affect precision.
• The effect of systematic error is normally "biased” and often very "reproducible".
• Random errors give rise to a normal or Gaussian curve, and results can be evaluated using statistics.
• Examples of gross error are an obviously "overrun end point” (titration), instrument breakdown, loss of a crucial sample, and discovery that a "pure" reagent was actually contaminated.
• Constant errors in systematic error are of the same magnitude, regardless of the size of the measurement, and can be minimized when larger samples are used.
• Relative Error (Er) is the absolute error corrected for the size of the measurement or expressed as the fraction, %, or parts-per-thousand (ppt) of the true value.
• Random errors are caused by uncontrollable variables which normally cannot be defined, accumulate over time, and cause replicate measurements to fluctuate randomly around the mean.
• Proportional errors in systematic error occur when Es increases or decreases with increasing or decreasing sample size, respectively, and the relative error remains constant.
• Gross errors cause an experimental value to be discarded, lead to outlier’s and require statistical techniques to be rejected.
• Absolute Average Error (AAE) = ∑ (xi − xt).
• Personal errors occur where measurements require judgment, result from prejudice, color acuity problems, and can be minimized or eliminated with proper training and experience.
• Accuracy is the closeness of the measurement to the true or accepted value, this "closeness" is called the error: absolute or relative error of a result to its true value.
• Potential instrument errors include variation in temperature, contamination of the equipment, power fluctuations, component failure, and can be corrected by calibration or proper instrumentation maintenance.
• Outlier is an Occasional error that obviously differs significantly from the rest of the results.
• Precision: Described by the standard deviation, the variance and the coefficient of variation (all are functions of the deviation from the mean).
• Accuracy: Described by the absolute and relative error.
• Range: Calculated by diminishing the highest value to the lowest value.
• Absolute Error (E) is the difference between the experimental value and the true value.