# Margin of Error

Calculator

## Margin of Error or Confidence Interval is a statistical measure of how closely the views of your sample audience resemble the entire population. Smaller the Margin of Error, the more likely is your sample being a strong representation of the larger population.

## Calculate your Margin of Error

Margin of Error

0

The acceptable values of margin of error typically lie between 4% & 8% at a confidence level of 95%.

NOTE: Please don’t confuse confidence level with the confidence interval. The latter is just an alternate name for margin of error.

### Sample Proportion:

Expressed as a decimal, it is the number in the sample with the characteristic of interest, divided by n, the sample size.

### Sample Size:

The number of people who took your survey and is under study.

### Confidence Level:

The percentage of how closely your sample represents the population. Industry accepted standard is typically 95%.

## What is Margin of Error

Margin of Error represents how confidently you can trust your sample audience to reflect the opinion and behavior of the population as a whole. Also known as Confidence Interval, it is a statistical validation of your survey experiment. Higher the value of margin of error, lesser the faith you must have on the sample.

It is not easy to survey a mass audience and get a conclusive opinion. In such a case, surveying a sample audience is carried out. With metrics like margin of error, you can estimate the chances of it echoing the preferences of the broader population. For example, when you have a**margin of error of 5%**and**70% of the sample **has given a particular response, it means that about**65% to 75%**of the**general population has the same opinion.**

## Why calculate Margin of Error

The primary intent of having a concept like margin of error is that any sample survey results can deviate from the true value. And, quantifying this deviation is the role of the said metric. Besides, the margin of error also helps you to understand if the sample size you picked is suitable for the survey experiment. In case the value of confidence interval tends to be on the higher side, it is an indication to choose a higher sample size.

## Margin of Error Formula

MOE = z * [√p * (1 - p)/ √n]

- z is the z-score associated with a confidence level
- p is the sample proportion (in decimal)
- n is the sample size

Confidence Level | z-score |
---|---|

80 | 1.28 |

85 | 1.44 |

90 | 1.65 |

95 | 1.96 |

98 | 2.33 |

99 | 2.58 |

## Margin of Error Example

Here’s an example of margin of error. A market research firm conducted a study to find out how many users spend more than 5 hours on social media. They surveyed 1000 users, and 620 people out of it spent more than 5 hours using social media.

Assuming 95% confidence level, we get a z-score=1.96

Sample size n=1000

Sample proportion p=620/1000=0.62

Margin of Error= z * [√p * (1 - p)/ √n]

= 1.96 * [√0.62 * (1 - 0.62)/ √1000]

= 3.00%

Margin of Error FAQs

1. How can you make the margin of error smaller?

- If the value shows a higher number, it's best to increase the sample size. Another way would be to ensure the consistency of your sample data. Lesser the data variation, more precise you can expect your results to be.

2. What is an acceptable value for margin of error?

- By industry standards, the acceptable value of margin of error falls between 4% and 8%. And this is at a confidence level of 95%.

3. What if my margin of error value is zero?

- You can get an infinitesimally small value for margin of error when the conditions are ideal- i.e., your sample essentially comprises of the entire population.

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