This tutorial will explain margin of error by focusing specifically on:
You have have seen the term “margin of error” in the newspaper stating that a political candidate leads the field by 5%, and there's maybe a 3% margin of error in the poll. What does this mean?
When surveys are done, collecting the right amount of data is important to ensure the answer is correct. Samples are often reported with something called a “margin of error”, meaning that the results may be off by a little bit, but it can be estimated by how much it’s off. It explains to the reader that right answer is not 100% accurate, but it’s close.
Suppose you are an administrator of a school and you need to determine the overall percentage of left handed students. Maybe 10% of students in the school are left handed, but when you take a sample, even though you were diligent about the way data was collected, you got 8%.
The answer was not accurate. What happened?
It's possible that the data obtained was not exactly the same as what the population would have obtained. Maybe only 8% of left handed people were in the sample, but the population actually contains 10% percent left handed people. You didn't do anything wrong, but samples might be inherently off the mark due to random selection process.
Suppose a newspaper polled 500 voters and 48% responded that they were going to vote for candidate X in the upcoming election. The newspaper might print a margin of error along with that 48% mark; maybe they use four percentage points as their margin of error. 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 does a 4% margin of error mean? It means the researchers are 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.This idea of creating some wiggle room on either side of 48% is called a “confidence interval”. And guess what? On election day, 46% of the people voted for candidate X. Since this falls into the range of 44% to 52%, it is close enough to the right answer.
As the sample size of a poll goes up, does the margin of error for the poll go up, down, or does it stay about the same? How would a larger sample impact the margin of error?
As the sample size goes up, the margin of error goes down. A larger sample size gives a more accurate portrait of the population. What’s happening is that you cast a wider net to include people that may be closer to representing the actual population. If you had a sample size of 4 people and you want to generalize the findings to a population of 200 people, it’s unlikely that that just those 4 people have enough of the characteristics to represent the population.
However, when the sample size is increased, you get closer to achieving a representative sample, which means the confidence interval can be lower; in other words, the higher the sample size, the less wiggle is needed room on each side of the measurement.
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 reported value, plus or minus the margin of error. It's a bad idea to compare two values within the same confidence interval, since both would be accurate enough to be correct. That would be a statistical dead heat.
Source: Adapted from Sophia tutorial by Jonathan Osters.
The mean value obtained from the sample. If the sample was well-collected, the estimate should be reasonably close to the true value.
A range of potential values that the true value could be. It is obtained by adding and subtracting the margin of error from the value in the sample.
An amount by which we believe our sample's mean may deviate from the true mean of the population.