# Continuity Correction Calculator

Created by Tibor Pál, PhD candidate
Reviewed by Anna Szczepanek, PhD and Steven Wooding
Last updated: Dec 21, 2022

With the continuity correction calculator (or binomial probability continuity correction calculator), you can quickly check how to restate a binomial probability problem by applying normal distribution to approximate a binomial distribution.

In the following article, continuity correction is explained, and you can read about:

• What is the role of the central limit theorem in continuity correction?
• How to do continuity correction?
• When to use continuity correction?
• How to apply the continuity correction calculator?

If you would like to learn more, you may like to check our normal approximation calculator, where you can get more insight into this subject. Also, our normal distribution calculator is an excellent source to get familiar with the connected theoretical background.

## What is continuity correction?

The continuity correction factor is applied when a continuous probability distribution is used for approximating a discrete probability distribution. The continuity correction factor is the bridge between the continuous normal distribution and the discrete binomial.

It is an addition or subtraction of 0.5 to the discrete x-value following the rules summarized in the following continuity correction table.

Using binomial distribution

Continuity correction

P(X = n)

P(n – 0.5 < X < n + 0.5)

P(X > n)

P(X > n + 0.5)

P(X ≤ n)

P(X < n + 0.5)

P (X < n)

P(X < n – 0.5)

P(X ≥ n)

P(X > n – 0.5)

## What is the role of the central limit theorem in continuity correction?

According to the central limit theorem, the sample mean of a distribution becomes approximately normal when the sample size is large enough. In the case of the normal approximation to binomial continuity correction, the approximation can be applied to a normal distribution if the product of the number of samples and the probability of events, n × p and n × (1 - p), are at least 5.

## How to apply the continuity correction calculator

You need to set the following three variables to run the continuity correction calculator.

• Number of trials (N);
• Number of successes (n); and
• Probability of success (0 < p < 1).

After this simple specification, you will obtain the continuity correction table, which lists all possible problem statements and the associated continuity corrections and approximated probabilities.

## FAQ

### When to use continuity correction?

You need to use the continuity correction with normal distribution when you would like to approximate a discrete probability distribution by applying the continuous probability distribution.

### How do I perform continuity correction?

For applying the continuity correction, you need to take the following steps:

1. Find the sample size (the number of occurrences or trials).
2. State the problem with the number of successes.
3. Choose the appropriate continuity correction factor:
• if x = n then n - 0.5 < x < n + 0.5;
• if x ≤ n then x < n + 0.5;
• if x < n then x < n − 0.5;
• if x ≥ n then x > n − 0.5; or
• if x > n then x > n + 0.5.

### What is the continuity correction factor for an event occurring at most 60 times?

The continuity correction factor is 0.5, and you need to deduct from the number of events if you would like to find the probability event occurring at most 60 times: if P(x < 60) then P(x < 59.5).

### Can the continuity correction factor be zero?

No. The continuity correction factor is always 0.5, and you need to add it to or subtract it from the number of occurrences according to your problem statement.

Tibor Pál, PhD candidate
Problem setup
Number of trials (N)
Number of successes (n)
Probability of success (0<p<1)
Continuity corrections
 Using binomial distribution Continuity correction Approximated probability P(x = 60) P(59.5 < x < 60.5) 0.9821 - 0.9713 = 0.0109 P(x ≤ 60) P(x < 60.5) 0.9821 P(x < 60) P(x < 59.5) 0.9713 P(x ≥ 60) P(x > 59.5) 1 - 0.9713 = 0.0287 P(x > 60) P(x > 60.5) 1 - 0.9821 = 0.0179
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