An enumerative study is focused on judgment of results. These studies are meant to enumerate (explain, evaluate, describe) the condition that exists with the existing population.
On the other hand, an analytic study is focused on improvement of the process which created the results and which will continue creating results in the future.
An enumerative study should be used only when you are studying an unchanging situation or a snapshot at one moment in time. Unfortunately we often use the methods which are proper for an enumerative study when we are in fact studying the process over time. When we are studying a process that we aim to improve over time we should apply the methods appropriate for an analytic survey.
One of the topics discussed by Mike Tveite in his presentation, Deming 101, at the 2012 annual conference of The W. Edwards Deming Institute was enumerative and analytic surveys.
“Dr. Deming stated that the purpose of any statistical study should be to provide a rational basis for taking action.”
Mike made an interesting point about how quite a few of the points from Deming’s 14 points and diseases from the 7 deadly diseases can be seen as eliminating an “enumerative practice” or instituting an “analytic practice.”
Mike references Dr. Deming’s paper, On Probability As a Basis For Action, (7 page article from The American Statistician, 1975) in the talk. Also see, On the Distinction Between Enumerative and Analytic Surveys by W. Edward Deming (12 page paper, published in the Journal of the American Statistical Association in 1953).
Statistical methods such as hypothesis tests, CIs and probability statements are appropriate to analyse and report data from enumerative studies.
Because the population of interest is open and continually shifts over time, random samples from that population cannot be obtained in analytical studies, and traditional statistical methods are therefore not useful. Rather, graphical methods of analysis and summary of the repeated samples reveal the trajectory of system behaviour over time, making it possible to predict future behaviour. Use of a Shewhart control chart to monitor and create learning to reduce infection rates in an intensive care unit is an example of a simple analytical study.
The ‘gold standard’ of analytical studies is satisfactory prediction over time.
The related links included below (as well as the complete articles sited above) provide a great deal of additional detail and thoughts on this topic.
Related: Some Theory of Sampling , book by W. Edwards Deming – Assumptions for Statistical Inference – Statistics and Reality – Analytic and Enumerative Studies by John Dowd – ASQ – A Primer for Enumerative vs. Analytic Studies: Using Caution in Statistical Inferences