Analytical skill is the ability to visualize, articulate, and solve
complex problems and concepts, and make decisions that make sense based
on available information. Such skills include demonstration of the
ability to apply logical thinking to gathering and analyzing
information, designing and testing solutions to problems, and
formulating plans.

To test for analytical skills one might be asked to look for
inconsistencies in an advertisement, put a series of events in the
proper order, or critically read an essay. Usually standardized tests
and interviews include an analytical section that requires the examinee
to use their logic to pick apart a problem and come up with a solution.

Critical thinking consists of mental processes of discernment, analysis
and evaluation. It includes possible processes of reflecting upon a
tangible or intangible item in order to form a solid judgment that
reconciles scientific evidence with common sense. In contemporary usage
"critical" has a certain negative connotation that does not apply in the
present case. Though the term "analytical thinking" may seem to convey
the idea more accurately, critical thinking clearly involves synthesis,
evaluation, and reconstruction of thinking, in addition to analysis.
Critical thinkers gather information from all senses, verbal and/or
written expressions, reflection, observation, experience and reasoning.
Critical thinking has its basis in intellectual criteria that go beyond
subject-matter divisions and which include: clarity, credibility,
accuracy, precision, relevance, depth, breadth, logic, significance and
fairness.
-wiki



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