How to Calculate Margin of Error
If you are calculating the margin of error, you are looking for how precise your results reflect the target population. When designing a survey, you use a sample size where the participants are in your target population. A higher sample size relative to the target population will lower your margin of error, which will increase the accuracy of your results. The accepted margin of error in research is 5 percent.
Using this calculator allows calculating the margin of error to be simple and easy. You can raise or lower the sample size in order to find what margin of error you’d like to place in your study.
Choose the alpha level and corresponding confidence level
The sum between alpha and confidence interval always equals 1. So if you want your alpha to be .05, then your confidence level will be .95 or 95%. The alpha is the probability of rejecting the null hypothesis of the survey. In other words, alpha is the percent of your study that does not reflect the target population.
Generally, 0.05 is the accepted alpha level. Other common alpha levels are .1, .02 and .01. If you can’t decide which alpha level to use, set alpha to 0.05.
Estimate the standard deviation
When it comes to standard deviation, unless you have access to raw data in research prior to what you are conducting, set it to .5.
Please note if you are going to use a standard deviation value other than 0.5 you have the replace 𝜎 with the true population standard deviation.
Find the Z-score for the confidence level
Here are the most commonly used confidence levels along with their Z scores. Z score is the amount of standard deviations away from the mean. Confidence level is the probability of that Z score.
If you have a different alpha, Z score can easily be found using a Z score table which can be found in most statistics books. Assuming you’re conducting a two tail test, subtract alpha divided by 2 from 1. Then find the closest probability value in the Z score table and add your Z score row + column.
For example, when you’re trying to find Z score for a two tail test at alpha = .05. 1-(.05/2) = .975. On the 1.9 row and the .06 column you will find .9750. This means your Z = 1.96
Common confidence levels with Z scores
Margin of Error formula
z= z score, 𝜎 = population standard deviation, n = sample size
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