An observational science is a science where it is not possible to construct controlled experiments in the area under study. For example, in astronomy, it is not possible to create or manipulate stars or galaxies in order to observe what happens. Other examples of necessarily observational sciences include geology, paleontology, epidemiology, and much of the social sciences.
Other fields of scientific study can have observational as well as experimental aspects. In high-energy physics, for example, some interactions involving energies higher than can be created in any experiment can be observed indirectly through astronomical observations.
To substitute for the inability to directly construct experiments as part of the scientific method, two main strategies are used. First, multivariate statistical techniques allow the approximation of experimental control with statistical control. Secondly, experimental observations of previously-unobserved phenomena can be used to suggest new hypotheses and test existing ones. This can be seen as making use of pre-existing "natural experiments".
In the social sciences, sociology and economics are generally held to be examples of observational sciences, because of the impracticality (not to mention dubious ethical status) of manipulating whole societies or economies for experimental purposes. However, microeconomics can be regarded as an experimental science, because it is possible to set up experimental micro-economies.
Sometimes fields of study can change from being observational to being experimental: for example, until the early 21st century, the study of comets was entirely observational -- it became experimental when the first man-made cometary collision was engineered in 2005.
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