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Margin of Error

Margin of Error

Author: Jonathan Osters

Determine the estimate, margin of error, and confidence interval in studies.

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In this tutorial, you're going to learn about margin of error. You probably have seen this term before, maybe in the newspaper where maybe it says that a political candidate leads the field by 5%, and there's maybe a 3% margin of error in the poll. We'll talk a little bit deeper into what exactly that means a little bit later in this tutorial.

But here are the basics of margin of error. When we do surveys, we want to collect the right amount of data. We want to answer the question correctly. Suppose that the question that we're trying to ask is what percent of a school is left handed. Maybe 10% of students in the school are left handed, but when we take our sample, even though we were very diligent about the way that we collected the data, maybe we only got 8%. So we were wrong.

It's possible that the data we obtain is not exactly the same as what the population would have obtained. Maybe we got 8% left handed people and the population actually contains 10% percent left handed people. We didn't do anything wrong. But samples might be inherently just off through the random selection process.

Samples therefore are often reported with something called a margin of error, meaning that we're off by a little bit maybe, but we can quantify how far off we think we might be. It explains to the reader that we're not really sure that we have the right answer, but we think we're close.

Here's an example. So suppose a newspaper polled 500 voters and said that 48% were going to vote for candidate X in the upcoming election. Now, the paper doesn't know this, but suppose that on election day only 46% of people are going to vote for candidate X. The newspaper might print a margin of error along with that 48% mark-- that maybe the margin of error is four percentage points.

It's not particularly important how this 4% was calculated, but there's a margin of error that they report along with the percent value. What that means when they say four percentage points is the margin of error, they mean that they're pretty confident that the true amount of people that will vote for Candidate X is within 4% of 48, which means that it could be as low as 44% or as high as 52% or anywhere in between.

Between 44% and 52% of voters will vote for Candidate X is what they're pretty sure when they report a value of 48% with a 4% margin of error. This idea of creating some wiggle room on either side of 48% is called a confidence interval. And guess what? The right answer-- the one that the paper doesn't know is actually going to happen on election day-- this 46% mark is within that range of 44% to 52%. So the pole is in fact close enough to the right answer.

Think about this statement here. As the sample size of a poll goes up, the margin of error for the poll-- think about it-- does it go up, does it go down, or does it stay about the same? As the sample size goes up the margin of error goes down. Think about when we were talking about sample size. A larger sample size gives a more accurate portrait of the population. Which means the more people we survey, the more sure we are that our number is close to the right answer. Which means we don't need to get ourselves as much wiggle room on each side.

And so to recap, most statistical results are reported alongside a margin of error. If the data are well collected, then it's likely that the true population value is within the confidence interval created by the value that we have, plus or minus the margin of error. And it's a bad idea to compare two values, like the 47% and 43% percent the previous page, if they're within the margin of error of each other. That would be a statistical dead heat. So the terms we used were margin of error and confidence interval, which is the interval created by the actual value that we got from our sample and plus or minus the margin of error. Good luck and we'll see you next time.

Terms to Know
Confidence Interval

A range of potential values that the true value could be. It is obtained by adding and subtracting the margin of error from sample mean.


The mean value obtained from the sample. If the sample was well-collected, the estimate should be reasonably close to the true value.

Margin of Error

An amount by which we believe our sample's mean may deviate from the true mean of the population.