- We have just learned about populations, samples, and random samples. However, you may have deduced that each random sample that we take from the population will, by chance, be slightly different than every other random sample that we take. This matters because we're trying to use random samples to make inferences about the population. So how do we account for the fact that each random sample is slightly different? The answer is the margin of error. In this video, we will cover the very basic intuition behind the margin of error. For more advanced discussions about the margin of error, please see the resources in this module. After the video, you should be able to explain the basic intuition behind the margin of error. Think about an election poll. One news agency takes a random sample of voters from the population of all voters and asks them who they will vote for in the upcoming presidential election. Another news agency also takes a random sample and asks voters who they will vote for in the upcoming presidential election. The first news station tells us that in their poll 49% of voters support Biden while only 42% support Trump. At the same time, the second news station tells us that in their poll 51% of voters support Biden and 41% support Trump. How do we make sense of this? Well, think about this. Each time that we take a random sample from a population, the random sample will be slightly different than the population and than other random samples. How big or small the difference is between the sample and the population is called the margin of error. The margin of error tells us the expected difference between the sample and the population. In other words, it tells us how confident we can be about making inferences from our sample to the population. Think about our two news agencies and their election polls. While their numbers are slightly different, we need to take into consideration the margin of error. As you can see here, the margin of error for each election poll is plus or minus 4%. This means that we can be fairly confident that the actual percent of people supporting one candidate or the other is off by plus or minus 4% in the polls. So take the first poll as an example. We can be fairly confident that the actual percent of people supporting Biden is between 45 and 53% while the actual number of people in the population supporting Trump is between 38 and 46%, while in the second poll we can be fairly confident that the actual percentage of people in the population that support Biden is between 47 and 55% while that supporting Trump is between 37 and 45%. As you can see here, taking the margin of error into consideration means that these two polls, while the numbers are slightly different, are completely consistent with each other. Now there's two very important things to note here. One, as the size of our random sample increases, the margin of error will decrease. That is, if we have a bigger random sample, we will be able to be more confident about our inferences about the population. The second thing to note is that if our sample is not a probability sample, that is, if our sample is a non-probability sample, the margin of error tells us nothing. And if we wanted to make inferences about the population, we will have wasted our money and time. In the resources below, you can explore more deeply how the margin of error is calculated, how confident we can be in the margin of error, and why the margin of error is so important to understand.