In mathematics, a continuity correction is an adjustment made when a discrete object is approximated using a continuous object.
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}.
A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution.
Before the ready availability of statistical software having the ability to evaluate probability distribution functions accurately, continuity corrections played an important role in the practical application of statistical tests in which the test statistic has a discrete distribution: it had a special importance for manual calculations.
Where extreme accuracy is not necessary, computer calculations for some ranges of parameters may still rely on using continuity corrections to improve accuracy while retaining simplicity.