Analysis of Experimental Reliability
prepared by R. F. Schneider (Rev 12/06)
measurement, intrinsic precision, average (= arithmetic mean = mean), average
deviation, absolute value, percent, percent deviation, random errors, systematic
errors, homogeneous, heterogeneous, significant figures
An essential part of any quantitative laboratory measurement is an understanding of the
of the measurement.
Powerful statistical methods exist for the analysis of
The exercises conducted in the introductory chemistry laboratory will utilize
procedures and apparatus with well known limits of accuracy and precision.
measurements will be replicated several times in order to establish the reliability of those
quantities reported as conclusions of exercises (and on which a substantial part of the
earned grade will depend).
The number of repetitions of a measurement will typically be
relatively small (3-4 repetitions). Simple statistical concepts suffice to represent the
reliability of measurements that are replicated small numbers of times.
Measures of Reliability
We use two quantities to characterize the reliability of a series of experimental
Accuracy measures the extent to which
measurements agree with a known or “true” value.
Precision measures the consistency of
measurements with each other, independent of their accuracy.
Fig 1 demonstrates accuracy and precision. It shows the result of a series of attempts to
hit the bullseye of a circular target with a bow and arrow.
The objective of this exercise
(i.e., its known value) is to have each arrow strike the center of the target.
circles on the target mark areas which are successively further from the objective.
distance from the center of the bullseye represents the error in an attempt.
shows great consistency in the part of the target that the arrows strike, but they are all
distant from the center of the target.
The data are precise, but not accurate.
shows inconsistency in the location of the arrows on the target, but there are about as
many of them on the right as on the left and on the top of the target as on its bottom.
archer demonstrates some measure of accuracy, but with low precision.
demonstrates both accuracy and precision.
How does accuracy play a role in experiments whose results are
? If on the
basis of a series of experimental results, a sample is asserted to be potassium iodide, the
assertion is accurate (i.e.
) if the material was, in fact, potassium iodide.
material was another substance, the assertion is inaccurate, which in this case means
If the data from which the identity was concluded does not permit distinguishing
potassium iodide from sodium iodide, asserting that the substance may be one