Statistics

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Along with probability, upon which it is mostly based, statistics is a mathematical discipline which provides techniques for drawing conclusions from observed data. It is heavily relied upon in most scientific fields (experiments and observational studies), as well as in business and industry (marketing, operations management, economic analysis, quality control) and government (public polling, policy analysis).

Statistics can be divided into two large subfields, descriptive statistics and inferential statistics:

Descriptive statistics 
Numerical and graphical summaries of data — i.e., "charts and graphs". These are more in the public eye (think USA Today), but they can be used by unscrupulous sorts to mislead ("lies, damned lies, and statistics").
Inferential statistics 
Probability-based analysis used to infer something about a larger, mostly unobserved, population based on what is seen in a sample from that population. While the results of statistical analyses are often reported in the mainstream media (medical studies and the like), the details of the statistics behind them are usually left out and can often only be found in academic journals.

Significance and inference

A central idea in inferential statistics that is widely misunderstood is statistical significance. In an experiment to test, say, whether a new drug to treat a disease is more effective than the old, standard treatment, the degree of improvement the new drug provides is said to be statistically significant if it is so large as to be unlikely to have occurred by chance alone. Please see the statistical significance article for more information.

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