Analytical numbers are often given with a plus (+) and minus ( -) and, therefore, can have a lot to do with how we interpret our data.
Dear Paul, precision is the tightness or clustering of data around the same number, i.e., it is "the degree or agreement or uniformity of repeated measurements of a quantity... It is the deviation of a set of estimates or observations from their mean." [AGI Glossary, 1972].
The accuracy is the closeness of the observations or data to the 'truth.' It is best for both the precision and the accuracy to be as high as possible. I was taught that the precision was like an archer whose arrows were all in a tight cluster but off of the target (low accuracy) and that what you wanted was a tight cluster around the bullseye (the truth, if known in data sets).
AGI Glossary has for accuracy: "closeness to true value or to a value accepted as being true; the degree of perfection attained in a measurement, computation, or estimate, or the degree of conformity to some recognized standard value..." "Accuracy relates to the quality of a result, as distinguished from precision."
Usually, when we report a mean and a standard deviation, what we are reporting is the precision which is related to the quality of the data collection method/instrument and the care of the operator(s).
best, Ken
I agree with Ken, when measuring quantities in physical sciences "precision" is the consistency of multiple measurements and "accuracy" is the degree to which an estimate corresponds with the true value. I also agree with Ken that the number following the +/- is normally a measure of precision in sciences (especially physical sciences, but not always, especially in social sciences). "Precision" and "accuracy" are analogous to "reliability" and "validity" respectively in measures from sciences that rely more on statistics (e.g., psychology). I don't know if there are any established conventions on exactly what the number following the +/- means. I often use it, for both physical & social science data, to show "mean +/- standard deviation" (especially in data tables). In contrast, when we see election poll data, the +/- is the margin of error, and when you look closer that's almost always defined as the 95% confidence interval. That is, 95% of time, if the election were held "today," the results of the election (true value) would be within the range given by the poll. Complicating things, that's actually a claim of accuracy / validity for the poll (assuming no systematic error measurement). Hope this is helpful Paul! ~ Kevin
Dear Kenneth and Kevin,
Thank you for very much for your cogent responses to my question.
I would like to offer my colleagues a fictitious example of precision and accuracy from the single-crystal zircon dating of a Pennsylvanian tonstein:
Pb207/Pb206 311,9 +- 1.0 Ma
Pb207/U235 312.7 +-0.7 Ma
Pb206/U238 312.5 +-0.4 MA
The values +=1.0, 0.7, and 0.4 Ma represent the precision (2 sigma) of the age measurements.The value Pb206/U238 312.5 +-0.4 Ma is the most precise age and is the most robust with respect to analytical biases and, therefore, is considered the most accurate age.
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