The Margin of Error
Even if you aren't familiar with confidence intervals, you've probably unknowingly run across them. You've probably heard the term "Margin of Error" used along with the results of a survey of, say, a presidential poll.

After polling 1000 eligible voters, the Star-Tribune Newspaper reported that 55% of Americans would vote for James Bean and 45% for John F Daniels +/- 3%.

That plus or minus disclaimer is the margin of error. In other words, the margin of error means that James Bean could be favored by as much as 58 to 42 percent (55 + 3) or as low as 52 to 48 percent (55 - 3)-- a six percentage point spread (58-52 = 6). This spread is the confidence interval. U

Samples Vary
Of course, the Star-Tribune Newspaper didn't ask everyone in the US who they were going to vote for; instead, they sampled a portion of the total voting population. Since most polls only sample a portion of a larger population, another sample of 1000 people might provide slightly different results. Instead of 55 to 45, another sample might provide 54 to 46. The margin of error is a way to describe this variability.

This same principle applies in many settings. Consider another example:

Cash Fast, a manufacturer of ATM machines, hired a research firm to find out how long it took people to withdraw money. This firm watched 20 people go to an ATM and withdraw money. They kept track of how long each person took and reported an average time of 2 minutes +/- 30 seconds.

There's our friend the Margin of Error. It can be used whenever samples are taken and an estimate is made about a larger population.U Did you also notice that the margin of error is half the confidence interval? So an easy way to know the confidence interval if all you know is the margin of error is to multiply the margin of error times two.

So remember the confidence interval = 2 times the margin of error.

Smaller Samples Vary More
There's another important point that's worth noting: The smaller the sample, the more variable the responses will be and the bigger the margin of error. U Let's say the population was going to vote 55% for Jim and 45% for John and the Star Tribune only asked five people instead of 1000. With a smaller sample, they increase the chance that they are getting a result that's different than the whole population.

Imagine if the Star-Tribune took the same poll as in the example above but only asked 5 people instead of 1000 people. Let's say they took the poll six times. The results might look something like this:

Result of Star-Tribune Poll done 6 times with only 5 Users

Look at the poll results above. Notice how the results are all over the place? We know that the population will vote 55% for Jim and 45% for John; but if the newspaper reported the results with only 5 people, they could be way off. By sampling more people they will reduce their chances of being way off.

The important point is that as samples get larger, the amount of variability goes down: Larger samples have a smaller margin of error (less variability) and smaller samples have a higher margin of error (more variability). This is a point that will continue to appear in confidence intervals.