# What is the difference between the confidence interval and margin of error?

Jun 9, 2018

The margin of error is how far from the estimate we think the true value might be (in either direction).

The confidence interval is $\text{the estimate " +- " the margin of error.}$

#### Explanation:

You might hear people say things like:

"It'll be an hour, give or take 10 minutes."

Or perhaps,

"His approval rating was 59 percent, plus or minus 3 percentage points."

These phrases, "give or take" and "plus or minus", indicate a margin of error (or $\text{ME}$). It's like the furthest away from the estimate that we expect the true value to be, at a given significance level $\alpha .$ It could be 10 minutes less than an hour, 10 minutes more than an hour, or anywhere in between, but it'll likely be no more than 10 minutes out, either way. Ten minutes (or 3 percentage points) is our margin of error.

The confidence interval gives us the actual low and high limits of the estimate at a given significance level $\alpha .$ These limits are one $\text{ME}$ below the estimate and one $\text{ME}$ above it. For the above examples, the confidence intervals are

50 minutes to 1 hour, 10 minutes

and

56 percent to 62 percent.

Notice the use of "at a given significance level $\alpha$." If we want to be more sure that the unknown value is within one $\text{ME}$ of the calculated estimate, we need a better significance level.

The value of $\alpha = 0.05$ is a common one; it means there's only a 5% chance our confidence interval will not capture the true value. Using $\alpha = 0.01$ would mean there's only a 1% chance. Of course, there's a trade-off. If we want increased confidence, we have to take a wider interval.