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Margin of Error Calculator


How does Margin of Error calculator work?

The working principle of the margin of error calculator is very easy;
  • Enter the sample size
  • Enter the population size
  • Enter the sample proportion (max = 1)
  • Select the confidence level
  • Hit the "calculate" button to get the step-by-step solution.
  • You can erase all the values by clicking on the "reset" button.





Margin of error calculator


The margin of error calculates the MOE using sample size (n), population size (P), sample proportion (p), and confidence level. It gives a step-by-step solution to the problem.


What is the margin of error?


The margin of error (MOE) for a survey tells you ways close you'll be able to expect the survey results to be to the proper population price. E.g., In a random survey, we came to know that 55% of the population favored Brand X over Brand Y with 2% MOE.

According to this survey, the actual population percentage that voted for Brand X falls within the range of 55% ± 2%. MOE refers to the degree of error in the results that we get from surveys of random sampling.


The formula for the margin of error:


There are two different cases to calculate the margin of error of a raw sample.

Margin of error with FPC:

The formula to calculate the MOE with FPC is as follows:

MOE with finite population correction :

Margin of error with FPC

Now let’s have a look at the FPC, in the sample survey statistics, this concept plays a vital role. It is a factor that is used to balance the estimated variance for a hypothetical total or mean.

In the above formula,

  • “P hat” is the sample proportion
  • “P” is the population size
  • “z” is the z-score
  • “n” is the sample size

Simple margin of error:

The simple MOE can be calculated using the following formula:

Simple Margin of error

  • “P hat” is the sample proportion
  • “z” is the z-score
  • “n” is the sample size

Procedure to calculate the margin of error:


In this section, with the assistance of examples, the procedure is explained briefly.

Example 1:

Calculate the MOE with FPC if the sample proportion is 0.2, the population size is 1029, the sample size is 112, and the confidence interval is 95%.

Solution:

Step 1: Extract the data

Sample proportion =  = 0.2

Population size = p = 1029 

The confidence interval of z at 95% = 1.960

Sample size = n = 112

Step 2: enter the values in the following formula

MOE with FPC = 

MOE with FPC = 1.960 {{0.2 (1 - 0.2)}/ {112(1029 – 1)/ (1029 – 112)}

MOE with FPC = 1.960 {0.2 (0.8) / {(112) * (1028) / (917)}}}

MOE with FPC = 1.960 { 0.2(0.8)/ {112(1.121)}

MOE with FPC = 1.960 {0.16/ {125.55}}

MOE with FPC = 1.960 * 0.03569761

MOE with FPC = 0.06996

MOE with FPC = 6.997%


References:


Margin of error | Statistics How To.

Your guide to margin of error | Qualtrics