ACCURACY, PRECISION, AND ERROR

 

ACCURACY, PRECISION, AND ERROR

•         In chemistry, the meanings of accuracy and precision are quite different.

•         Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.

•         Precision is a measure of how close a series of measurements are to one another, irrespective of the actual value.

To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.

To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

Darts on a dartboard illustrate the difference between accuracy and precision.

 

The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another corresponds to the degree of precision.

Errors
Three general types of errors occur in lab measurements:

                                      i.            random error,

                                   ii.            systematic error, and

                                 iii.            gross errors

1. Random (or indeterminate) errors are caused by uncontrollable fluctuations in variables that affect experimental results. For example, air fluctuations occurring as student’s open and close lab doors cause changes in pressure readings. A sufficient number of measurements result in evenly distributed data scattered around an average value or mean.

This positive and negative scattering of data is characteristic of random errors. The estimated standard deviation (the error range for a data set) is often reported with measurements because random errors are
difficult to eliminate. Also, a "best-fit line" is drawn through graphed data in order to "smooth out" random error.

2. Systematic (or determinate) errors are instrumental, methodological, or personal mistakes causing "lopsided" data, which is consistently deviated in one direction from the true value.
Examples of systematic errors:

       i.            an instrumental error results when a spectrometer drifts away from calibrated settings;

     ii.            a methodological error is created by using the wrong indicator for an acid-base titration; and,

  iii.            a personal error occurs when an experimenter records only even numbers for the last digit of buret volumes

Systematic errors can be identified and eliminated after careful inspection of the experimental methods, cross-calibration of instruments, and examination of techniques.

3. Gross errors are caused by experimenter carelessness or equipment failure. These "outliers" are so far above or below the true value that they are usually discarded when assessing data. The "Q-Test" (discussed later) is a systematic way to determine if a data point should be discarded.

Precision of a Set of Measurements
A data set of repetitive measurements is often expressed as a single representative number called the mean or average. The mean (M) is the sum of individual measurements (xi) divided by the number of measurements (N).

M = Σxi

            N              (mean)
 

Precision (reproducibility) is quantified by calculating the average deviation (for data sets with 4 or fewer repetitive measurements) or the standard deviation (for data sets with 5 or more measurements). Precision is the opposite of uncertainty Widely scattered data results in a large average or standard deviation indicating poor precision.

Accuracy of a Result
The accuracy of a result can be quantified by calculating the percent error. The percent
error can only be found if the true value is known. Although the percent error is usually
written as an absolute value, it can be expressed a negative or positive sign to indicate the direction of error from true value.

% Error = (true value - experimental value) x 100
                               true value

 

The Q-Test for Rejecting Data
As mentioned previously, outliers are data measurements occurring from gross errors.
Their value deviates significantly from the mean. The Q-Test can be used to determine whether an individual measurement should be rejected or retained. The quantity Q is the absolute difference between the questioned measurement (xq) and the next closest measurement (xn) divided by the spread (ω), the difference between the largest and smallest measurement, of the entire set of data.

Q= (xq - xn)
          ω

Q is compared to a specified confidence levels (the percent probability a measurement will fall into a range around the mean (x).) If Q is greater than the values listed below for a particular confidence level, the measurement should be rejected. If Q is less than the values in the table, the measurement should be retained.

•         Suppose you use a thermometer to measure the boiling point of pure water at standard pressure.

•         The thermometer reads 99.1°C. 

•         You probably know that the true or accepted value of the boiling point of pure water at these conditions is actually

•         100.0°C.

•         There is a difference between the accepted value, which is the correct value for the measurement based on reliable references, and the experimental value, the value measured in the lab.

•         The difference between the experimental value and the accepted value is called the error.

 

Determining Error

 

•         For the boiling-point measurement, the error is 99.1°C – 100°C, or –0.9°C.

•         The percent error of a measurement is the absolute value of the measured experimental value minus the accepted value divided by the accepted value, multiplied by 100%.

 

UNCERTAINTY IN MEASUREMENT

•         Definition.

The definition of the term uncertainty of
measurement is: “A parameter associated with the result of a
measurement that characterizes the dispersion of the values that could reasonably be attributed to be measured.

Uncertainty sources
In practice the uncertainty on the result may arise from many possible sources, including examples such as incomplete definition of the measurand, sampling, matrix effects and interferences, environmental conditions, uncertainties of masses and volumetric equipment, reference values, approximations and assumptions incorporated in the measurement method and procedure, and random variation.

Typical sources of uncertainty are
1. Sampling
Where in-house or field sampling form part of the specified procedure, effects such as random variations between different samples and any potential for bias in the sampling procedure form components of uncertainty affecting the final result

2. Storage Conditions

Where test items are stored for any period prior to analysis, the storage conditions may affect the results. The duration of storage as well as conditions during storage should therefore be considered as uncertainty sources

3. Instrument effects

Instrument effects may include, for example, the limits of accuracy on the calibration of an analytical balance; a temperature controller that may maintain a mean temperature which differs (within specification) from its indicated set-point; an auto-analyser that could be subject to carry-over effects.

4. Reagent purity

The concentration of a volumetric solution will not be known exactly even if the parent material has been assayed, since some uncertainty related to the assaying procedure remains. Many organic dyestuffs, for instance, are not 100 % pure and can contain isomers and inorganic salts. The purity of such substances is usually stated by manufacturers as being not less than a specified level. Any assumptions about the degree of purity will introduce an element of uncertainty.

5. Assumed stoichiometry

Where an analytical process is assumed to follow a particular reaction stoichiometry, it may be necessary to allow for departures from the expected stoichiometry, or for incomplete reaction or side reactions.

6. Measurement conditions

For example, volumetric glassware may be used at an ambient temperature different from that at which it was calibrated. Gross temperature effects should be corrected for, but any uncertainty in the temperature of liquid and glass should be considered. Similarly, humidity may be important where materials are sensitive possible changes in humidity.

7. Sample effects

The recovery of an analyte from a complex matrix, or an instrument response, may be affected by composition of the matrix. Analyte speciation may further compound this effect. The stability of a sample/analyte may change during analysis because of a changing thermal regime or photolytic effect. When a ‘spike’ is used to estimate recovery, the recovery of the analyte from the sample may differ from the recovery of the spike, introducing an uncertainty which needs to be evaluated.

8. Computational effects

Selection of the calibration model, e.g. using a straight line calibration on a curved
response, leads to poorer fit and higher uncertainty. Truncation and round off can lead to inaccuracies in the final result. Since these are rarely predictable, an uncertainty allowance may be necessary.

9. Blank Correction

There will be an uncertainty on both the value and the appropriateness of the blank
correction. This is particularly important in trace analysis.

10. Operator effects

Possibility of reading a meter or scale consistently high or low. Possibility of making a slightly different interpretation of the method.

11. Random effects

Random effects contribute to the uncertainty in all determinations. This entry should be included in the list as a matter of course.