Concept:
In statistics, statistical inference is the process of drawing conclusions
from data that are subject to random variation, for example, observational
errors or sampling variation.[1] More substantially, the terms statistical inference,statistical
induction and inferential statistics are used to describe systems of
procedures that can be used to draw conclusions from datasets arising from
systems affected by random variation,[2] such as observational errors, random
sampling, or random experimentation.[1] Initial requirements of such a system
of procedures for inference and induction are that the system should produce
reasonable answers when applied to well-defined situations and that it should
be general enough to be applied across a range of situations. Inferential
statistics are used to test hypotheses and make estimations using sample data.
The outcome of statistical inference may be an answer
to the question "what should be done next?", where this might be a
decision about making further experiments or surveys, or about drawing a
conclusion before implementing some organizational or governmental policy.
The conclusion of a statistical
inference is a statistical proposition.
Some common forms of statistical proposition are:
·
an estimate;
i.e., a particular value that best approximates some parameter of interest,
·
a confidence interval (or set estimate);
i.e., an interval constructed using a dataset drawn from a population so that,
under repeated sampling of such datasets, such intervals would contain the true
parameter value with the probabilityat the stated confidence
level,
·
a credible interval; i.e., a set of values
containing, for example, 95% of posterior belief,
·
rejection
of a hypothesis[3]
·
clustering or classification of data points into
groups
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