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Margin of Error

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Hi. This tutorial covers margin of error. So let's start with an example. A national polling organization tracks public opinion for the upcoming presidential race. The poll shows the Republican candidate is attracting 47% of the vote. And the Democratic candidate is attracting 45% of the vote. The organization gave a 3% margin of error in polling.

So both of these statistics were taken from samples. And each time you quote a sample statistic, it's important to also include a margin of error. So their margin of error was 3%. So basically, what that means is if we look at the Republican candidate, if you do 47%, and with a margin of error, that margin of error could be 3% less than 47% or 3% above 47%. So what that leaves us is the Republican candidate really could be anywhere between 44% and 50%.

Now, the Democratic candidate had 45% plus or minus 3%. So the sample concluded that 45% of the sample supported the Democratic candidate. But that could be off either above or below 45% by 3%. So this now, it could be anywhere between 42% and 48%.

So would you definitively conclude that the Republican has the lead? Well, certainly looking at the sample data, we can see that the Republican has the lead in the sample. But if we're thinking about the entire population, no. I wouldn't definitively conclude that the Republican had the lead.

Because the Republican could be all the way down to 44% of the population, or the Democrat could be all the way up to 48%. So there actually could be a pretty strong lead by the Democrat just looking at one of these margins of error.

So would you definitively conclude that the Republican has the lead? No. So the 47% and the 50%-- or 45% are estimates of the true proportions of voters supporting each candidate. Most good surveys provide a margin of error to accompany each estimate like that one did.

So the formal definition of margin of error is a way of measuring the random sampling error in a survey's results. An estimate with a margin of error is called a confidence interval. So 47% plus or minus 3% and 45% plus or minus 3% are both called confidence intervals.

The confidence interval again is the estimate plus or minus the margin of error. This confidence interval like we said before could also be written as 45% comma 50%. Or if we're writing it as a proportion, could be 0.44, 0.50.

So kind of in conclusion, when two outcomes are close, it can be misleading to order the outcomes without first considering the margins of error. So if we were just, again, just to order them without considering the margins of error, yes, it does look like the Republican has the lead.

But by looking at the margin of error and creating a confidence interval, we can see, well, it's possible that the Democrat actually has the lead in terms of the entire population rather than just the sample. So that is the tutorial on margin of error. Thanks for watching.