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How is the concept of Independence used in statistics?
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes . Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds ).
How to test that two continuous variables are independent?
Bin both variables and use Fisher’s exact test or G-test. Pro: use well-established statistical tests. Con: depends on binning. Estimate the dependency of X and Y: I ( X; Y) H ( X, Y) (this is 0 for independent X and Y and 1 when they completely determine each other). Pro: produces a number with a clear theoretical meaning.
How to write a paper about independent variables?
The variables should be outlined in the introduction of your paper and explained in more detail in the methods section. There are no rules about the structure and style for writing about independent or dependent variables but, as with any academic writing, clarity and being succinct is most important.
Which is the best Test to prove the independence?
In case of categorical variables, you can either perform a G -test or a X 2 -test of independence. If you do not have a lot of samples, you may consider performing Fisher’s exact test instead. Thanks for contributing an answer to Cross Validated!
Which is an example of mutual independence in probability theory?
This example shows that mutual independence involves requirements on the products of probabilities of all combinations of events, not just the single events as in this example. For another example, take to be empty and and to be identical events with non-zero probability. Then, since and are the same event,…
Is the term mutual independence the same as collective independence?
A similar notion exists for collections of random variables. The name “mutual independence” (same as “collective independence”) seems the outcome of a pedagogical choice, merely to distinguish the stronger notion from “pairwise independence” which is a weaker notion.
Can a mutually independent set of events be pairwise independent?
Note that it is not a single condition involving only the product of all the probabilities of all single events; it must hold true for all subsets of events. For more than two events, a mutually independent set of events is (by definition) pairwise independent; but the converse is not necessarily true.