{"id":42668,"date":"2022-05-04T07:18:28","date_gmt":"2022-05-04T07:18:28","guid":{"rendered":"https:\/\/www.proprofssurvey.com\/blog\/?p=42668"},"modified":"2024-12-23T09:26:56","modified_gmt":"2024-12-23T09:26:56","slug":"margin-of-error","status":"publish","type":"post","link":"https:\/\/www.proprofssurvey.com\/blog\/margin-of-error\/","title":{"rendered":"What is Margin of Error? An Ultimate Guide, Calculation and Examples"},"content":{"rendered":"\r\n
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\"Margin<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

You must have spotted the plus and a minus sign together with a digit, like this \u00b11. This value of the plus-minus sign and a number is nothing but the margin of error of the survey results.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

Wondering why an error is entirely accepted and considered while analyzing survey results<\/a>?<\/p>\r\n\r\n\r\n\r\n

Well, no survey is 100% accurate.\u00a0<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

Thus, if you\u2019re 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:<\/p>\r\n\r\n\r\n\r\n

<\/span>What is Margin of Error?<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

Margin of error is a range of values that differ from the actual survey results.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

A smaller margin of error reflects more confidence levels in your survey, while a higher error margin reflects a lower level.<\/p>\r\n\r\n\r\n\r\n

<\/span>Why do we Use a Margin of Error?<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

Let\u2019s understand this through an example.<\/p>\r\n\r\n\r\n\r\n

Firstly, the most commonly used Confidence Level is 90%, 95%, or 99%.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

For example, if 70% of survey respondents<\/a> replied with a \u201cyes,\u201d this implies that 66%-74% of respondents would reply with a \u201cyes\u201d to your survey. This margin of error helps gauge the percentage points of uncertainty that a survey\u2019s results denote.<\/p>\r\n\r\n\r\n\r\n

<\/span>How to Calculate Margin of Error<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

Margin of error can be calculated using the following formula:<\/p>\r\n\r\n\r\n\r\n

MOE = z*\u221a((p*(1\u2212p))\/n<\/strong>)<\/p>\r\n\r\n\r\n\r\n

Here\u2019s a breakdown of each of the values:<\/p>\r\n\r\n\r\n\r\n

\u2018z*\u2019 is the z-score that corresponds to the desired confidence level<\/p>\r\n\r\n\r\n\r\n

\u2018p\u2019 is the sample proportion<\/p>\r\n\r\n\r\n\r\n

\u2018n\u2019 is the sample size<\/p>\r\n\r\n\r\n\r\n

<\/span>Example of Margin of Error Calculation<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

Now let\u2019s try and understand how you can apply this calculation to your data.<\/p>\r\n\r\n\r\n\r\n

Suppose you wish to gain insight into how well your customers responded to a new upgrade in your technology product.<\/p>\r\n\r\n\r\n\r\n

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\u2019s say you take your sample size as 1000.<\/p>\r\n\r\n\r\n\r\n

Also, in this survey, the margin of error is \u00b12% 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).<\/p>\r\n\r\n\r\n\r\n

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 \u00b12%, 95 out of 100 times.<\/p>\r\n\r\n\r\n\r\n

Thus, you can say that if you conduct a survey<\/a> 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.<\/p>\r\n\r\n\r\n\r\n

To calculate the margin of error of this survey, you perform the following steps:<\/p>\r\n\r\n\r\n\r\n

Firstly, the number of respondents that approve of your survey is 700 (70% of the population).<\/p>\r\n\r\n\r\n\r\n

So, 700 will be your sample proportion (p), and 1000 will be your sample size (n).<\/p>\r\n\r\n\r\n\r\n

Thus, the number we\u2019ll be working with here is 700(p)\/1000(n), i.e., 0.7.<\/p>\r\n\r\n\r\n\r\n

Step 1: 1\u2212p \u2192 1\u22120.7 = 0.3<\/p>\r\n\r\n\r\n\r\n

Step 2: 0.7 \u2715 0.3 = 0.21<\/p>\r\n\r\n\r\n\r\n

Step 3: 0.21\/1000 = 0.00021<\/p>\r\n\r\n\r\n\r\n

Step 4: \u221a0.00021 = 0.0144913767\u00a0<\/p>\r\n\r\n\r\n\r\n

Step 5: 0.0144913767 \u2715 1.96 = 0.0284030983. This number can be rounded off to 2%.<\/p>\r\n\r\n\r\n\r\n

Hence, it is clear that, with a confidence interval of 95%, 70% of your customers approve of the upgrade, \u00b12%.<\/p>\r\n\r\n\r\n\r\n

Note:<\/strong> Ascertain your confidence level for the survey. You can never have a 100% confidence level unless, of course, you survey the entire population!<\/p>\r\n\r\n\r\n\r\n

You can determine the z-score for your confidence level using the following table:<\/p>\r\n\r\n\r\n\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Confidence Level<\/strong><\/td>\r\nz-score<\/strong><\/td>\r\n<\/tr>\r\n
80%<\/td>\r\n1.28<\/td>\r\n<\/tr>\r\n
85%<\/td>\r\n1.44<\/td>\r\n<\/tr>\r\n
90%<\/td>\r\n1.65<\/td>\r\n<\/tr>\r\n
95%<\/td>\r\n1.96<\/td>\r\n<\/tr>\r\n
99%<\/td>\r\n2.58<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/figure>\r\n\r\n\r\n\r\n

<\/span>Margin of Error in Sample Sizes<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

The margin of error in sample sizes can be better understood in the following manner.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

Take a look.<\/p>\r\n\r\n\r\n\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Sample Size<\/strong><\/td>\r\nMargin of Error<\/strong><\/td>\r\n<\/tr>\r\n
2000<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
1500<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
1000<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
900<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
800<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
700<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
600<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
500<\/td>\r\n4<\/td>\r\n<\/tr>\r\n
400<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
300<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
200<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
100<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
50<\/td>\r\n14<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/figure>\r\n\r\n\r\n\r\n

Thus, it is apparent that as the sample size \u2018n\u2019 keeps on increasing, the margin of error keeps on decreasing.<\/p>\r\n\r\n\r\n\r\n

<\/span>Why Does the Margin of Error Decrease as the Sample Size Increases?<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

Wondering how does increasing the sample size affects the margin of error?<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

<\/span>How to Reduce Margin of Error<\/strong><\/span><\/h2>\r\n\r\n\r\n\r\n

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.<\/p>\r\n\r\n\r\n\r\n

A lower margin of error can be achieved by following a few best practices as below:<\/p>\r\n\r\n\r\n\r\n