The Binomial Distribution The Binomial and Sign Tests Summary: The Binomial Distribution The Binomial and Sign Tests Hervé Abdi1 1 Overview The binomial distribution models repeated choices between two alternatives. For example, it will give the probability of obtaining 5 Tails when tossing 10 coins or the probability for a rat to choose 10 times out of 20 the correct branch of a 3-branch maze. The bino- mial test uses the binomial distribution to decide if the outcome of an experiment using a binary variable (also called a dichotomy) can be attributed to a systematic effect. The sign test is applied to before/after designs and uses the binomial test to evaluate if the direction of change between before and after the treatment is sys- tematic. 2 Binomial distribution The binomial distribution models experiments in which a repeated binary outcome is counted. Each binary outcome is called a Ber- noulli trial, or simply a trial. For example, if we toss 5 coins, each 1 In: Neil Salkind (Ed.) (2007). Encyclopedia of Measurement and Statistics.