Continuity Correction
In probability theory, if a random variable X has a binomial distribution with parameters n and p, i.e., X is distributed as the number of "successes" in n independent Bernoulli trials with probability p of success on each trial, then
for any x ∈ {0, 1, 2, ... n}. If np and n(1 − p) are large (sometimes taken to mean ≥ 5), then the probability above is fairly well approximated by
where Y is a normally distributed random variable with the same expected value and the same variance as X, i.e., E(Y) = np and var(Y) = np(1 − p). This addition of 1/2 to x is a continuity correction.
A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. For example, if X has a Poisson distribution with expected value λ then the variance of X is also λ, and
if Y is normally distributed with expectation and variance both λ.
Read more about Continuity Correction: Applications
Famous quotes containing the words continuity and/or correction:
“Only the family, society’s smallest unit, can change and yet maintain enough continuity to rear children who will not be “strangers in a strange land,” who will be rooted firmly enough to grow and adapt.”
—Salvador Minuchin (20th century)
“There are always those who are willing to surrender local self-government and turn over their affairs to some national authority in exchange for a payment of money out of the Federal Treasury. Whenever they find some abuse needs correction in their neighborhood, instead of applying the remedy themselves they seek to have a tribunal sent on from Washington to discharge their duties for them, regardless of the fact that in accepting such supervision they are bartering away their freedom.”
—Calvin Coolidge (1872–1933)