What Is Margin of Error?

Margin of error is a statistical term that represents the range of uncertainty or variability around an estimate or measurement. It quantifies the degree of confidence we can have in the estimate's accuracy. When conducting surveys or collecting datasurveying the entire population is often not feasible or practical. Insteada sample is takenand the results are used to make inferences about the larger population. The margin of error helps to account for the potential discrepancy between the sample and the populationleading to more accurate findings from your data analytics.

For exampleyou may want to know if your customers would support a new product releaseso you poll a sampling of your existing customer base through an email survey. Since this sampling does not include all of your customersthe margin of error would account for the percentage of customers who may or may not agree with those surveyed.

The margin of error is typically expressed as a plus or minus valueindicating the range within which the true value is likely to fall. If a survey reports a margin of error of ±3 percentthe results are believed to be accurate within three percentage points in either direction. This means the true value could be three percent higher or three percent lower than the reported estimate.

For exampleif your poll found that 80 percent of surveyed customers approved of a new product release with a margin of error of ±3 percentyour actual value could range from 77 to 83. This range of values is known as the confidence interval and represents the degree of uncertainty or certainty in your estimate.

Data with a lower margin of error is more accurate and reliable than data with a higher margin of error. All data chosen as a random sample will have some uncertainty; the margin of error explains how much.

How to calculate margin of error

You can calculate your margin of error in two waysdepending on whether you are using population parameters or sample statistics. Depending on your sample size and whether you know the population standard deviationyou will either use a z-score or a t-score as your critical value.

For population parameters:

Margin of error = Critical value x Standard deviation of the population

For sample statistics:

Margin of error = Critical value x Standard error of the sample

What impacts the margin of error? 

Three main factors will usually impact your margin of error: sample sizestandard deviationand confidence level. If any of those changethe margin of error will change with them. 

• Sample size: Your sample size refers to the number of people or other entities you include in your survey. A larger population sample is a more realistic representation of that populationso it's more likely to be accurate. 

• Standard deviation: The population's standard deviationor variabilitymeasures how far apart data points are from one another. Larger deviations mean a larger margin of errorwhile smaller ones usually make for a smaller margin. 

• Confidence level: Confidence level is a percentage that shows how certain you are that your sample is representative of your entire population. Commonly used confidence levels are 90 percent95 percentand 99 percent. As the confidence level increasesthe margin of error becomes wider to capture a higher level of certainty. Converselyif a lower confidence level is chosenthe margin of error will be narrowerindicating a lower level of certainty.

Are margin of error and sampling error the same?

The margin of error is a summary of the sampling errorquantifying the uncertainty of your measurement. This sampling error accounts for the difference between our sample findings and the true population parameter. 

Typicallyyou represent this sampling error as the margin of errordenoted as “+/-” your margin of error. When you combine this margin of error with your sample statisticyou create a confidence interval. This intervalpresented alongside an associated level of confidenceshows how “certain” you are that the true population value is captured in this range.

Related terms 

• Data analytics

• Unstructured data

• Statistical modeling 

• Sample size

Learn how to find margin of error and explore data analytics on Coursera

The margin of error is an important component of many statistical studies. It shows how much variability you expect around your measurement. As a data analystthis is an important tool for accurately representing your findings and portraying the certainty of your measurements. 

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