Question

Describe the continuity correction (covered in an earlier course unit), and explain how, when, and why it is used in statistics. Don't limit your thinking to the most common example given of this corrective step: approximation of binomials using the Normal distribution. While that is an example of such a correction, it is only one example. (Hint: You could compare the development of this correction logic for discrete distributions to the use of integration against continuous distributions.) Discuss the more general case and how it affects probabilities you might need to calculate as an engineering working on a project.

Answer 1

In probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.

For example, when you want to approximate a binomial with a normal distribution. According to the Central Limit Theorem, the sample mean of a distribution becomes approximately normal if the sample sizeis large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p and n*q are both greater than equal to 5.

The continuity correction factor a way to account for the fact that a normal distribution is continuous, and a binomial is not. When you use a normal distribution to approximate a binomial distribution, you’re going to have to use a continuity correction factor. It’s as simple as adding or subtracting 0.5 to the discrete x-value: use the following table to decide whether to add or subtract.

If   P(X=n) use   P(n – 0.5 < X < n + 0.5)
If   P(X>n) use   P(X > n + 0.5)
If   P(X?n) use P(X < n + 0.5)
If P (X<n) use   P(X < n – 0.5)
If P(X ? n) use   P(X > n – 0.5)

Example:
If P(X?351), use P (X?351-0.5)= P (X?350.5)

On the other hand, when the normal approximation is used to approximate a discrete distribution, a continuity correctioncan be employed so that we can approximate the probability of a specific value of the discrete distribution.