The binomial test is a parametric hypothesis test that applies when the population can be divided into two classes: each observation of this population will belong to one or the other of these two categories.
MATHEMATICAL ASPECTS
We consider a sample of n independent trials. Each trial belongs to either the class C 1 or the class C 2. We note the number of observations n 1 that fall into C 1 and the number of observations n 2 that fall into C 2.
Each trial has a probability p of belonging to class C 1, where p is identical for all n trials, and a probability \( { q = 1-p } \) of belonging to class C 2.
Hypotheses
The binomial test can be either a two-sided test or a one-sided test. If p 0 is the presumed value of p, \( { (0 \leq p_0 \leq 1) } \), the hypotheses are expressed as follows:
- A: Two-sided case:
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$$ \begin{aligned} H_0\colon\enskip & p = p_0\:,\\ H_1\colon\enskip & p \neq p_0\:. \end{aligned} $$
- B: One-sided case:
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$$ \begin{aligned} H_0\colon\enskip & p \leq...
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Abdi, H.: Binomial distribution: Binomical and Sign Tests. In: Salkind, N.J. (ed.) Encyclopedia of Measurement and Statistics. Sage, Thousand Oaks (2007)
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© 2008 Springer-Verlag
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(2008). Binomial Test. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_36
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DOI: https://doi.org/10.1007/978-0-387-32833-1_36
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