Statistics Definitions > Continuity Correction Factor
Watch the video showing an example or read the article below:
What is the Continuity Correction Factor?
A continuity correction factor is used when you use a continuous function to approximate a discrete one. 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 size is large enough. The binomial distribution can be approximated with a normal distribution too, as long as n*p and n*q are both at least 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 .5 to the discrete x-value: use the following table to decide whether to add or subtract.
Continuity Correction Factor Table
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)
If P(X≥351), use P (X≥351-0.5)= P (X≥350.5)
Continuity Correction Factor Example
Sample problem: If n=20 and p=.25, what is the probability that X ≥ 8?
Step 1: Work out np and nq:
np = 20 * .25 = 5 (note: this is also the mean of the binomial distribution)
nq = 20 * .75 = 15
These are both over 5, so we can use the continuity correction factor.
Step 2: Figure out the variance of the binomial distribution:
n*p*q = 20 * .25 * .75 = 3.75
Set this number aside for a moment.
Step 3: Use the continuity correction factor on the X value.
X ≥ 8 becomes X ≥ 7.5.
Step 4: Find the z-score.
z = 7.5 – 5 / √3.75 = 1.29
Step 5: Look up Step 4 in the z-table.
1.29 = .4015.
Step 6: Subtract Step from 1 to get the area (as we are looking for the right tail):
1 – .4015 = 0.5985.
The probability that X ≥ 8 is 0.5985.
Why is the continuity correction factor used?
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