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### + or – 5%: Fun with Math

February 26th, 2016 by John

So it’s election time and poll numbers abound. Pundits will talk about virtual ties and margins of error and the like – but what does that actually mean and how is it calculated? And as a marketer, where can you be confident that the decisions you are making are valid?

Margins of error and confidence levels have quite a bit of actual math behind them (SCARY) but they are actually a simple idea. Margins of error simply tell you how many percentage points in one way or another that your stats can be trusted. Confidence levels are how many times that number will be right. In other words, a 5% margin of error at the 95% confidence level means that if you ran the same study 100 times, 95 of those studies would have your stats falling in that 5% range.

Which brings me to the question we’re asked often – “How many completed surveys will we need?” Well, the standard for a public opinion marketing research study is 400 completes. You’ll rarely need more than that. In fact, you get diminishing returns (dollar wise) because, well, math. And in any case, 400 gets you to the magic 5% + or –.

Of course there can always be variables like the ultimate size of your audience (for all of you that want left-handed, blue-eyed engineers that studied at a Jesuit college), the amount of segmentation you’ll want to do with the data, or the confidence level you want to achieve.

An easy way to get your approximate margin of error is the following formula on any old calculator or app: 100 ÷ the square root of your number of completes. In other words, the square root of 400 is 20. 100 ÷ 20 = 5. It’s not exact but it’s close. Or you can always find a calculator online.