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What Is 'Margin of Error'?

Margin of Error is an estimate of how much you can trust your conclusions from a given set of observed Samples.

Small sample sizes can lead to misleading measurements. Always collect the largest samples you can to ensure better results.

Josh Kaufman Explains 'Margin of Error'

Suppose you purchase a trick coin from a magician's shop, and you want to be sure the coin is actually biased to land on heads most of the time.

How can you be sure you didn't buy a dud? You start flipping the coin, of course.

Let's assume that in the first five flips, you get two heads and three tails. Should you ask for a refund? A Confidence Interval is the probability a particular analysis is correct.

It's probably worthwhile to make sure your results are accurate before jeopardizing the magician's good name.

How can you be sure the coin isn't a dud? The more samples you take, the higher the confidence interval of your measurement.

Each coin flip is a sample of all of the possible times you could flip the coin.

The larger your sample, the more confidence you can have in the accuracy of your measurements.

Since you only flipped the coin five times, you can't be too sure it's a dud-your sample size is very small.

If you flip the coin 1,000 times and it comes up tails 2/3 of the time, you can be relatively sure that the coin is biased, but not in the way you expected.

Since a non-loaded coin should come up heads 1/2 the time, your large sample size makes it very likely the magician gave you a tails-loaded coin by mistake.

The math behind how to calculate confidence intervals is beyond the scope of this book, but it's relatively easy once you get the hang of it, particularly if you use a spreadsheet or database for your analysis.

If you need to calculate confidence intervals, I recommend picking up Principles of Statistics by M.G.

Bulmer for an in-depth primer.

Beware of misleading measurements based on small sample sizes.

Whenever you're presented with an average or a percentage based on data you're not familiar with, it always pays to investigate the size of the sample and how it was collected.

Sample sizes that are too small can significantly influence the final results.

When it comes to analytical confidence, more data is always better-collect the largest samples you can.

Questions About 'Margin of Error'

• How confident are you in the quality of your measurements and analysis?
• Is it possible to increase your sample size to add confidence to your assessment?

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"Everyone generalizes from one example. At least, I do."

Steven Brust, science fiction author

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