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Statistics in a Nutshell by Sarah Boslaugh, Paul Andrew Watters

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Chapter 7. Inferential Statistics

Statistical inference is the science of characterizing or making decisions about a population using information from a sample drawn from that population. Most of the practice of statistics is concerned with inferential statistics, and many sophisticated techniques have been developed to facilitate this type of inference.

The name “inferential statistics” derives from the term “inference,” given two definitions by the Merriam-Webster online dictionary (http://www.m-w.com/dictionary/inference):

a) the act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former

b) the act of passing from statistical sample data to generalizations (as of the value of population parameters) usually with calculated degrees of certainty

The second meaning, which is specific to statistics, is clearly related to the first. Inference in general is a method of making suppositions about an unknown, drawing on what is known to be true. Statistical inference is a refinement of ordinary inference, and is a process of making generalizations about unmeasured populations using data calculated on measured samples. Statistical inference has the additional advantage of quantifying the degree of certainty for a particular inference.

People sometimes get confused about the difference between descriptive statistics (covered in Chapter 4) and inferential statistics, partly because in many cases the statistical ...

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