Margin of Error: How TO Find and Reduce It?


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Do you wonder if your survey results are close to the population you’re studying? You can easily find it out by calculating the margin of error using a margin of error calculator

But, what is a margin of error and why must you calculate it? Find out in this blog. 

What is the margin of error in a survey?

In statistical terms, the Margin of Error, also known by its synonym confidence interval, is the degree of error in the result that will differ from the real population value. 

Simply put, it tells you if the number of people you’re surveying is enough for you to feel confident about the accuracy of the data you collect.

The Margin of Error is the range of values above and below the statistical data in a confidence interval. It tells you how much the survey result can vary based on the rules of probability. 

A higher margin of error means a lower confidence level reflected in the result of a survey, and vice-versa. It helps you understand how accurately the sample of respondents represents the target population. 

Example of margin of error in a survey

For example, a 95% confidence level with a 3% margin of error implies that your statistical data will be above or below 3% points over the real population value 95% of the time. 

This means that if 60% of responders reply “yes” to a survey with a margin of error of +/- 3%, then responders between 57 to 63% of the total population think “yes” as the answer.

The most commonly acceptable margin of error used by most survey researchers falls between 4% and 8% at the 95% confidence level. It is affected by sample size, population size, and percentage.

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When should you use the Margin of Error?

The margin of error is used when researchers have a random or probability sample. In other words, the survey respondents have been selected at random from the population as a whole, and every population member has a known, non-zero probability of being included.

For example, a theatre group has a complete list of everyone who has purchased tickets to their shows in the past year. Suppose they randomly select a sample of that population for a survey. In that case, they can calculate the margin of error on the percentage of people who reported being a fan of the group.

It’s not ideal to use the margin of error if the sample has been selected in a non-random way, for example, when you use an opt-in research panel.


How to Calculate Margin of Error

To ensure a successful survey, it is important to be aware of the margin of error. There are two ways you can calculate this – by using the MoE calculator or by manually calculating it. 

Let’s look at the statistical formula for identifying the MoE.

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  • ‘p-hat’ is the Sample Proportion
  • ‘N’ is the Sample Size  
  • ‘Z’ is Z-Score

Step 1: Calculate “p-hat” by dividing the number of responders who agree with the statement of your survey by the total population of the survey.

For Example, 600/1000 = 60%

Step 2: Find the z-score in correspondence to the confidence level of the survey. 

If the confidence level is 99%, the z-score is 2.58.

Step 3: Put these parameters in the formula to calculate.


You can also calculate the margin of error if the parameters from a population or statistics are available to you.

  • Margin of Error = Critical Value X Standard Deviation from the population
  • Margin of Error = Critical Value X standard Error of a sample
Margin of Error Margin of Error

The critical value is either the “t-score” or “z-score” of your statistical data. 

Also, in case you don’t know the population standard deviation, you can use a t-score, and in case it is known you can use a z-score.

Example of using MoE formula

Let’s look at how you can use the formula in a real-world example. 

For instance, if a pizza brand is thinking of working on new flavors. So, they conduct a survey on a population chosen randomly for better results. 

In this case, the survey is conducted with a margin of error of “+ or – 3%” at a 95% level of confidence. This implies that if the survey is conducted 100 times, the statistical result will be within the percentage degree of higher or lower than the percentage that is reported 95 out of 100 times. 

The brand then finds out that 50% of the participants respond by saying the new flavor is “very good.” This means that with a confidence level of 95% and a margin of error of plus or minus 3%, it is safe to assume that the participants who said the pizza flavors are “very good” will range between 47 to 53% most (95%) of time. 

Let’s gather the values to calculate the margin of error. The total population is 1000, while only 500 agreed to the new pizza flavors. So, the sample size is 500. With a confidence level of 95%, put all the values on the formula. 

You will receive the margin of error was plus/minus 3%

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What is a sample size, and how does it affect the margin of error?

The sample size is the number of people whose responses you receive. As we learned, determining the margin of error helps us understand whether the sample size of the survey is appropriate.

If the margin of error appears too big, consider increasing the size of the sample so that the attitudes of the population surveyed match those of the total population more closely. This is why it is important to send surveys to a large population because not everyone will respond. Probably 15% of the randomly chosen people will respond. 

So, it is better to keep the margin of error and confidence level in balance with a large population.

Here are the types of sampling methods you can consider: 

  • Probability Sampling: Any individual can be chosen in this type of sample size. To keep the margin of error as minimal as possible, researchers can choose participants from their area of research.
  • Non-probability Sampling: Participants in this sample are selected based on cost-effectiveness and convenience. Some sections of the population may be excluded. 

If the margin of error is bigger, the researcher needs to increase the size of the sample. As seen in the table, it decreases with the increase in sample size.

Margin of Error Margin of Error

A sample size of 50 has a margin of error of +/- 14%. The difference in the decreasing margin of error is quite significant from sample sizes 50 to 1500.  

Now that you know how it is calculated and how it affects your results, let’s learn how to reduce it to improve the reliability of your data.

Also read: Accelerate Survey Research with Voxco Audience

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How to reduce the margin of error in your survey results?

Reducing your margin of error is a sure way of increasing the reliability of your surveys and ensuring more accurate results.

Here are the steps that you need to take to reduce the margin error in your surveys:

Step 1: Define your population

Identify the sample for your total population so you’re able to know whether your margin of error is the right one.

Step 2: Decide the level of accuracy you want in your survey

Establish the accuracy percentage you would like to achieve with your survey by measuring both the margin of error and the confidence level of your sample.  

Step 3: Define the sample size

Decide how many people you would need to survey for your research project. Remember to consider as part of your sample only the respondents who completed the survey.

Step 4: Define the response rate

Response rate is the percentage of actual respondents among those who received your survey. Make an educated guess. If you’re sampling a random population, a conservative guess is about 10% to 15% will complete the survey. Look at your past surveys to check what your usual rate is.

Step 5: Now you know the number of people to survey!

After you’ve followed these steps, you’ll arrive at the total number of people to survey.

From the percentage derived in step-4, you’ll know how many people you need to send the survey to so as to get enough completed responses. 

The margin of error calculator is a way of measuring how effective your survey is. The narrower the margin of error, the more confidence you can have in the results. The broader the margin of error, the further the opinions from the total population.

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How to ensure a representative sample with Voxco Audience?

Sampling or selection bias and underrepresentation of the population can lead to inaccurate or misleading results. As it is often impractical to study the entire population due to many constraints, leveraging a market research panel like Voxco Audience can help overcome factors resulting in an inaccurate sample of high MoE. 

One of the key solutions to reducing the margin of error is by increasing the sample size. And this is one of the benefits that brings us to the use of market research panels. 

1. Diverse panel: 

A market research panel maintains a diverse panel of respondents, including various geographic locations, demographics, and backgrounds. This ensures that you can access a wide range of perspectives and experiences by creating a sample using a panel. 

Voxco Audience offers access to 10M respondents and empowers you to create a representative sample using 90+ data and profiling points. Create a large sample to reduce the margin of error. 

2. Targeted sampling: 

Market research panel helps you overcome underrepresentation. Target specific characteristics when selecting a sample to ensure that your sample not only represents the total population but also reduces the probability of non-response bias. 

Voxco Audience offers you a wide marketplace to select respondents who qualify for your survey needs.

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3.  Data quality assurance: 

By gaining access to a diverse and representative panel, you can gather insights into a wide range of perspectives, experiences, expectations, and needs. A market research panel also ensures that you gather error-free data and remove potential fraud. 

Voxco Audience gives you access to respondents who are vetted and verified and consented to participate in the survey. Leverage our bot detection, screening, IP detection, dedupe, encrypted survey links, and more to identify suspicious behavior and maintain research integrity. Voxco Audience Data Quality Promises. 

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Understanding and minimizing the margin of error is essential for conducting accurate research. A 

representative sample is crucial for reducing the MoE and ensuring that you can generalize your survey results to the larger population. Using tools like Voxco Audience can help you achieve a more representative sample, enable targeted sampling, and streamline your research. 

This post is also available in French.