Errors in Analysis

• Determinate or systematic error–errors that can be determined or eliminated. It affects the accuracy of results.
• Systematic errors have a definite value, an assignable cause, and are of the same magnitude for replicate measurements made in the same way. They lead to bias in measurement results.
• Bias– the deviation from the target value measures the systematic error associated with an analysis. It has a negative sign if it causes the results to be low and a positive sign otherwise.
• Instrumental Errors– are caused by non-ideal instrument behavior, by faulty calibrations, or by use under inappropriate conditions.
• Method Errors– arise from non-ideal chemical or physical behavior of analytical systems.
• Personal Errors– result from the carelessness, inattention, or personal limitations of the experimenter.
• Constant errors– errors that are independent of the size of the sample being analyzed. Here the value of absolute error is constant with sample size, but the relative error varies when the sample size is changed
• Proportional errors– errors that decrease or increase in proportion to the size of the sample. Here the value of absolute error varies with sample size, but the relative error stays constant when the sample size is changed.
• Indeterminate or random error– errors that can not be determined or controlled. It affects precision.
• Random errors are the cumulative effect of many small,

  uncontrollable variables and personal judgments that lead to

  uncertainty in a measured value.
• Replicates are samples of about the same size that are carried through an analysis in exactly the same way.
• In order to improve the reliability and to obtain information about the variability of results, two to five portions (replicates) of a sample are usually carried through an entire analytical procedure.
• Individual results from a set of measurements are seldom the

  same, so we usually consider the “best” estimate to be the central value for the set.
• Mean– sum of numbers divided by numbers of measurements
• Median– the middle value in a set of data that has been arranged in numerical order.
• The median is used advantageously when a set of data contain an outlier, a result that differs significantly from others in the set. An outlier can have a significant effect on the

  mean of the set but has no effect on the median.
• Accuracy– describes the nearness of an experimental value or a mean to the true value. Although true value can never be known exactly, accepted value is often used. Statistically measured through absolute or relative error
• Precision– refers to the agreement between values in a set of data. It describes the reproducibility of measurements. Statistically measured through standard deviation, variance, coefficient of variation
• Absolute Error– The absolute error of a system is equal to the difference between the actual reading, and the true (or accepted) value, bears a sign.
• Relative Error– describes the error in relation to the magnitude of the true value, and may, therefore, be more useful than considering the absolute error in isolation
• Sample standard deviation– describes the spread of data around the mean data point for a set of replicate measurements.
• Significant figures– are all of the certain digits plus the first uncertain digit.
• The amount of uncertainty depends both upon the skill of the measurer and the quality of the measuring tool.
• The degree of uncertainty in physical measurements can be indicated by means of significant figures.