Margin of Error - Definition, Usage, and Calculator | Zoho Survey (2024)

What's the margin of error?

From helping market research to coming up with valuable insights about countries and economies, let's admit, without statistics we'd still be in the dark in many ways.

However, there's a catch—statistics can never be 100% accurate, and the same applies for your survey results. Estimation is the very nature of surveys, so when we decide to study a huge population, there are a few things we have to keep in mind.

To put it simply, the margin of error means the degree of uncertainty that your survey results might have. The larger the margin of error is, the more likely it is to be further away from the "true figures" for the whole population.

Margin of error is only used when you can't record responses from every person you want to survey. Polling the entire population of New York isn't feasible, so instead, you pick out a set of people representative of that group and then base your survey results on them.

Calculating the margin of error will help you find out the likelihood that the result of the survey is close to the result had the entire population been surveyed. So its value goes a long way in determining how accurate your survey is.

How does margin of error work?

Let's assume your task is to conduct a survey of college students at four-year institutions, and ask them whether they prefer physical textbooks or ebooks.

According to the Department of Education, there are 13,494,131 students at four-year institutions. Due to lack of time and resources, we gather a random sample, for example, 2,500 that should be enough to represent the whole population.

If the survey results show that 1,875 (75%) out of 2,500 prefer ebooks, a statistician would say that your margin of error, at a 95% confidence level, would be ±2%. In other words, the statistician is 95% confident that 73-77% of students would prefer ebooks if we surveyed all 13,494,131 students.

The acceptable margin of error usually falls between 4% and 8% at the 95% confidence level. While getting a narrow margin of error is quite important, the real trick of the trade is getting that perfectly representative sample.

Picking out this group is difficult for survey researchers—the number of units in your sample should comprise the characteristics of the whole population and include the extremities as well.

Here's a handy trick to get the most out of your sample size—the Three S's:

How is the margin of error calculated?

Margin of error is mathematically calculated using the formula-

Margin of error =

• First calculate the σ ("mu sigma" or standard deviation) for your population and get a sample size.

• Take the standard deviation and divide it by the square root of your sample size.

• Multiple it with a z-score that is consistent with the confidence level, as per this table:

Climbing the confidence ladder

We can't avoid the margin of error entirely, and the key to cracking this is to keep tracking your confidence level.

Confidence level is a measure of how confident you are with the results of your study. You can never have a 100% confidence level in a study, unless you survey the whole population. Most journals won't consider studies with a confidence level of less than 80%, and more rigorous ones demand over 90%.

A 95% confidence level means that 5% of the surveys will be off the charts—that is to say that if 100 surveys are conducted using the same questions, 5 of them will have nonsensical results. For example, customers are asked the same question about customer service every week over a period of months, and “very good” is selected consistently by 50±5% of people. If 30% comes up in a period and a 49% follows in the next period, it's safe to assume the 30% is part of the "nonsensical" 5 percent, assuming proper methodology is followed.

What if I want to get closer to a higher confidence level?

There are two ways to increase your confidence level:

1. Increase your margin of error.

By increasing your margin of error from 5% to 10%, you can be more confident that your answers are accurate. For example, consider the following scenarios:

• Statistican 1 claims that 50-70% of students at a school like chocolate. The margin of error is 10%.

• Statistican 2 claims that 55-65% of students at a school like chocolate. The margin of error is 5%.

• Statistician 1 is more likely to be correct, since the range of values 50-70% is larger than 55-65%. Statistician 1 can be more "confident" of the result, but the cost is that the margin of error is higher.

2. Increase your sample size.

A higher sample size can also improve confidence levels. A statistician who's surveyed 8,000 out 10,000 people will naturally be more confident than one who has just surveyed 5,000 out of 10,000 people. The only problem here is that it's more expensive to survey 8,000 people than 5,000.