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Margins of Error
We have all read the stories on polls in the news.  The President's popularity is rising or falling.  This week, 50% of the registered voters in the U.S. believe that the President is doing a good job, last week it was 53%.  Typically, that "50%" will be accompanied by a margin of error which, in a poll of this type, will usually be 3-4%.  What does this mean?  It means that 50% is an estimate.  How accurate this estimate is will depend on the true size of the population and the size of the sample that we obtain from it.

The margin of error is computed to give us an idea of the range within which the true population statistics are likely to lie.  The narrower the range, the more accurate our estimates are thought to be.  A margin of error of +3 percentage points in the above example would suggest that the true percentage of people who believe the President is doing a good job is somewhere between 47% and 53%.  Obviously, we want tight margins of error because we want accurate estimates.  It is hard to show strengths and weaknesses or to track changes over time when our estimates are subject are imprecise.

Confidence Intervals
When we estimate averages within a sample, we are also trying to estimate a true statistic in a population.  In this case, we use confidence intervals such as the 95% confidence interval  to define the range in which the true average is likely to lie.  When our measures are more accurate and our samples are larger, the confidence intervals, like the margins of error, will tend to be narrower.  In the case of a 95% confidence interval, what we are really saying is that if we were to collect these data 100 times, we would expect 95% of the averages we obtain in our samples to be within the range defined by the confidence interval.

In both of these cases, it is important to remember that these are margins of error or confidence intervals for individual estimates.  Margins of error or confidence intervals for differences between groups will be larger than for estimates of a single percentage.  This is because difference scores include the errors in measurement associated with both estimates that you wish to compare.  One advantage to working with experienced research professionals is that we can help to advise on which of the differences you see in your findings are likely to be meaningful and which are not. 

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