 
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 3branch 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.
