Binomial distribution

Summary

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q=1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric d

Official source

https://en.wikipedia.org/wiki/Binomial_distribution

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Variance stabilizing transformations for meta-analysis of binary data

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The binary data are often used in the medical field or in social sciences to study an effect between two groups. It can be for example the effect of a treatment between a treated and a control group. The outcome will be the number of successes and the total number of trials in each group. Let us call X1, X2 the successes and n1, n2 the number of trials, then X1 and X2 are binomial random variables with probabilities p1 and p2 respectively. The difference between these two probabilities will attest the difference of the effect between the two groups. Several statistics may be used to compare two probabilities.

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