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• # Margin of Error: An Ultimate Guide

“What is margin of error?”

You must have spotted the plus and a minus sign together with a digit, like this ±1. This value of the plus-minus sign and a number is nothing but the margin of error of the survey results.

The margin of error shows the error in the calculation of survey results. It indicates the probability of precisely two values by which the survey results can vary from the actual results. One of these values is obtained through addition, while the other is obtained through subtraction.

Wondering why an error is entirely accepted and considered while analyzing survey results?

Well, no survey is 100% accurate.

In most cases, it is impossible to garner responses from the total research population. So, to bridge the gap between actual and obtained results, a value called the margin of error is taken into account to get a better picture of the survey results.

Thus, if you’re in pursuit of obtaining the most accurate survey results and wish to learn how you can reduce the margin of error, then you have landed at the right place. In this blog, we will explore:

## What is the Margin of Error?

Margin of error is a range of values that differ from the actual survey results.

No survey can be 100% accurate. Thus, every survey comes with a range of above and below the real population value. This number, coupled with a plus and minus sign, is the degree of uncertainty your survey results hold.

A smaller margin of error reflects more confidence levels in your survey, while a higher error margin reflects a lower level.

## Why do we Use a Margin of Error?

The margin of error is used when you cannot record the reply or feedback from every person of the targeted population. However, to estimate their response, you pick out a set of people who act as the sample population, representing the total targeted population.

To gain accurate survey results from this random population sample, you calculate the margin of error that helps interpret the precise response from the population, had the total population been surveyed.

Let’s understand this through an example.

Firstly, the most commonly used Confidence Level is 90%, 95%, or 99%.

So, if we take 95% as the confidence level with a 4% margin of error, it implies that your survey result will be above or below 4% over the real population value 95% of the time.

For example, if 70% of survey respondents replied with a “yes,” this implies that 66%-74% of respondents would reply with a “yes” to your survey. This margin of error helps gauge the percentage points of uncertainty that a survey’s results denote.

## How to Calculate Margin of Error

Margin of error can be calculated using the following formula:

MOE = z*√((p*(1−p))/n)

Here’s a breakdown of each of the values:

‘z*’ is the z-score that corresponds to the desired confidence level

‘p’ is the sample proportion

‘n’ is the sample size

## Example of Margin of Error Calculation

Now let’s try and understand how you can apply this calculation to your data.

Suppose you wish to gain insight into how well your customers responded to a new upgrade in your technology product.

To start with, you determine your survey population. So from your customer database, you go ahead and select a few customers randomly to have an adequate sample size without any bias or preferences. For this example, let’s say you take your sample size as 1000.

Also, in this survey, the margin of error is ±2% at a confidence level of 95%. This means that the z-score you will take into account will be 1.96 (refer to Table below).

On conducting your research, you find out that 70% of the respondents approve of the new upgrade in the product. This implies that this percentage varies from the actual result by a margin of error of ±2%, 95 out of 100 times.

Thus, you can say that if you conduct a survey 100 times, then 68 to 72% of the respondents approve of the new upgrade, most of the time, which in this case is 95% of the time.

To calculate the margin of error of this survey, you perform the following steps:

Firstly, the number of respondents that approve of your survey is 700 (70% of the population).

So, 700 will be your sample proportion (p), and 1000 will be your sample size (n).

Thus, the number we’ll be working with here is 700(p)/1000(n), i.e., 0.7.

Step 1: 1−p → 1−0.7 = 0.3

Step 2: 0.7 ✕ 0.3 = 0.21

Step 3: 0.21/1000 = 0.00021

Step 4: √0.00021 = 0.0144913767

Step 5: 0.0144913767 ✕ 1.96 = 0.0284030983. This number can be rounded off to 2%.

Hence, it is clear that, with a confidence interval of 95%, 70% of your customers approve of the upgrade, ±2%.

Note: Ascertain your confidence level for the survey. You can never have a 100% confidence level unless, of course, you survey the entire population!

You can determine the z-score for your confidence level using the following table:

## Margin of Error in Sample Sizes

The margin of error in sample sizes can be better understood in the following manner.

If you take the case of probability sampling wherein each member of the population has an equal chance of being selected for being part of the sample population. In this, the margin of error is bound to be on the lower side of the scale.

On the other hand, if you take the case for non-probability sampling wherein there is a probability of excluding a substantial population, the margin of error is bound to be on the higher side. This exclusion can be partly due to ease of data extraction or pre-defined bias.

The most accepted confidence level is considered as 95%. Next, we will go through the table to identify the margin of error for various sample sizes.

Take a look.

Thus, it is apparent that as the sample size ‘n’ keeps on increasing, the margin of error keeps on decreasing.

## Why Does the Margin of Error Decrease as the Sample Size Increases?

Wondering how does increasing the sample size affects the margin of error?

Well, when you take a larger sample size, it undeniably decreases the margin of error. This is because a larger sample size better represents the targeted population.

To put it simply, the margin of error and the sample size share an inverse relationship. Thus, invariably, a smaller sample size will result in a higher margin of error, and larger sample size will result in a lower margin of error.

## How to Reduce Margin of Error

Surveyors strive to reduce error as a lower margin implies greater accuracy of survey results. Thus, the goal is to get a precise estimate of the margin of error to assure the actual value of responses.

A lower margin of error can be achieved by following a few best practices as below:

• Increasing the sample size – More observations, more minor will be the interval around your sample statistic. Therefore, increasing the sample size will provide a value representing the total population.
• Reducing the variability of sample population – This provides you with a homogeneous population, assuring a narrower standard deviation, and consequently, lesser variation in answers received.
• Adopting a one-sided confidence interval – A one-sided confidence interval is better than a two-sided confidence interval. But this is only possible if you are clear that an estimate will either be greater or less than the obtained value.
• Lowering the confidence level – A lower confidence level answers a more precise confidence interval.

## Margin of Error vs Standard Error?

Often, people mistake the standard error as the margin of error, using them interchangeably while surveying. However, though similar, they are different and do not imply the same error.

Let’s look at the key differences between the two terms, the margin of error and the standard error.

Here it goes!

First, let’s look at their respective definitions. The margin of error is the possible degree of error while conducting a survey. The standard error measures the accuracy of sample population representation to the mean using the standard deviation.

Second, the margin of error is calculated to determine the difference between results obtained from the sample population that may vary from results that would have been obtained from surveying the entire research population. On the other hand, the standard error is calculated to determine your research population’s variable.

Third, the margin of error is displayed using the following formula:

MOE = z*√((p*(1−p))/n)

OR

MOE = z*(S÷√n)

Where,

‘z*’ is the z-score that corresponds to the selected confidence level

‘p’ is the sample proportion

‘n’ is the sample size

‘S’ is the standard deviation

To calculate the standard deviation, we apply the following formula:

Standard error = s/√n

Where,

s is the sample standard deviation

n is the sample size

Thus, it is clear that the standard error is part of calculating the margin of error.

## Enhance Survey Results With an Accurate and Lower Margin of Error

Calculating the margin of error is crucial for enhancing the credibility of a survey result. The lower the margin of error, the greater the credibility of a survey will be. Of course, this should be coupled with a larger sample size for the perfect representative sample. This is because a more inclusive sample size will mirror the actual views of your targeted audience with better accuracy.

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