The Comprehensive Guide to the Margin of Error in Statistical Surveys

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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. 

In simple words, it tells you if the amount 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 is a way of showing what the uncertainty in statistics is. 

With a small margin of error, there are more confidence levels in your survey results, no matter if the survey focused on market research, customer experience, or patient experience

Similarly, a higher margin of error means a lower confidence level reflected in the result of a survey.

Confidence interval reveals if the confidence level of a survey a researcher has in the result is appropriate to represent the real population or not. 

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.

When is margin of error used?

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. If they randomly select a sample of that population for a survey, they can calculate the margin of error on the percent 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

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For every statistical survey calculation of margin of error is required. The universal formula used for the calculation is Here, ‘p-hat’ is Sample Proportion

‘N’ is Sample Size  

‘Z’ is Z-Score

  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%

      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

      3. Put these parameters in the formula to calculate.

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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 is a “+ 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 the confidence level of 95% and 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. 

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

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

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
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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.

Check out Voxco’s
Margin of Error Calculator

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

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, you may want to increase 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: In this type of sample size any individual has the chance of being chosen. Researchers, in order to keep the margin of error as minimum as possible, can choose participants from their area of research.

  • Non-probability Sampling: In this sample, participants are selected based on cost-effectiveness and convenience. Some sections of the population may as well be excluded. 

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

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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. After that the difference in decreasing margin of error reduces.

Want to calculate your statistical significance?
Use our A/B testing calculator.

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

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 would you need to survey for your research project? Remember to consider as part of your sample only the respondents that 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.

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 is your survey. 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.

How Voxco can help?

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