Table of Contents
What Is Continuity Correction?
Continuity correction is an adjustment of +/-0.5 applied when approximating a discrete probability distribution (like binomial) with a continuous one (like normal). Since discrete distributions assign probability to exact integers while continuous distributions assign probability to intervals, this adjustment bridges the gap and improves accuracy.
The correction was introduced by Frank Yates in 1934 and remains a standard technique in introductory statistics. Without it, the normal approximation systematically underestimates or overestimates probabilities, especially for moderate sample sizes.
The Correction Rules
Where Y is the normal random variable with the same mean and standard deviation as the binomial.
When to Use It
Use continuity correction when np ≥ 5 and n(1-p) ≥ 5, which are conditions for the normal approximation to be reasonable. For very large n, the correction has minimal effect. For small to moderate n, it significantly improves accuracy compared to exact binomial calculations.
Correction Table
| Desired Probability | Without Correction | With Correction |
|---|---|---|
| P(X = x) | Not computable | P(x-0.5 < Y < x+0.5) |
| P(X ≤ x) | P(Y ≤ x) | P(Y ≤ x+0.5) |
| P(X ≥ x) | P(Y ≥ x) | P(Y ≥ x-0.5) |
| P(X > x) | P(Y > x) | P(Y > x+0.5) |
Frequently Asked Questions
Is the correction always necessary?
No. For large sample sizes (n > 100), the correction makes negligible difference. Modern computing often makes exact binomial calculation feasible, eliminating the need for normal approximation altogether.
Does it apply to Poisson approximation?
Yes, the same principle applies when approximating any discrete distribution with a continuous one. The +/-0.5 adjustment converts integer boundaries to continuous intervals regardless of the underlying discrete distribution.
What is Yates' correction for chi-square?
Yates' correction subtracts 0.5 from each absolute observed-expected difference in a 2x2 chi-square test before squaring. It serves a similar purpose of correcting for the discrete-to-continuous approximation.