Experimental Errors

1

• Experimental Errors
• All science is based on the results of
  experimental measurements
• Mathematical statements of natural laws
• Measurements in support of theories
• One of the purposes of our study of analytical
  chemistry is to determine how precisely the
  available apparatus can be used
• Usually little extra effort required to
  accomplish this
• Measuring the position of a meniscus to ?0.02 mL
  is not much more time consuming than reading it
  to ?0.1 mL
• Distinguish this from the indiscriminate pursuit
  of the ultimate precision when it is not
  necessary
• Analytical determinations often involve several
  measurements
• Combined in a calculation to produce the reported
  analytical result
• Each measurement may involve several manual or
  instrumental manipulations
• The uncertainties in each step can add or
  subtract in such a way as to produce scatter in
  the final calculated result
• See Figure 2.1, page 12 FAC7, for the
  determination of ppm Fe in aqueous solution

2

• Experimental Errors
• The result of a measurement is not useful without
  some statement of its reliability
• Statistics will allow a statement about the
  limits of uncertainty associated with a result
• Even not very accurate data are useful if it can
  be determined where the true value associated
  with the data lies with a certain probability
• Usually analysists make multiple, replicate
  measurements in the same way on fractions of a
  sample and report a best value from the data
• Some measure of the central value of the data set
  is reported
• Such a central value is a more reliable measure
  of the true value than a single measurement
• Averaging the results of replicates averages out
  the effects due to the accumulated
  uncertainties
• The variability in the results of replicate
  analyses can give a measure of the uncertainty
  associated with the central value of the data set

3

• Experimental Errors
• Measures of Central Value
• Mean arithmetic average
• Median the middle value in a sized-ordered
  arrangement of the individual replicates
• For a data set containing an even number of
  values, the median is the average of the middle
  two replicates
• Example Figure 2.1, page 12 FAC7

4

• Experimental Errors
• Precision is the reproducibility of a measured
  result when measured in the same way. We will
  use the term uncertainty to describe less than
  perfect precision
• Absolute measures of precision

5

• Experimental Errors
• Absolute measures of precision
• w maximum value - minimum value spread
• Relative measures of precision involve dividing
  the absolute measure of precision by the mean
  of a data set

6

• Experimental Errors
• Accuracy is how close a measurement is to the
  true or accepted value. We will use the term
  error to describe less than perfect accuracy.
• Measures of Accuracy

7
Experimental Errors Example Find the statistics
for the data in FAC7, page 29