The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.
A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. It measures the variability or the level of uncertainty or a sampling data or a survey. It also gives an idea about the range within which the value will fall. Since it shows the deviation from the actual values, the calculation gives a confidence level about the accuracy.
Margin of error refers to the method of measuring the level of uncertainty while making a survey from a sample of data. While conducting a survey from a set of sample data, it is often not possible to gather the relevant information from each and every sample due to the large volume. In such cases a small number of representative samples is taken which is used to draw the conclusion of the study.
Thus, the method explains the quantity or the extent of deviation of the sample from the actual value. It is expressed in a positive or a negative form has a confidence level in the calculation. The confidence level explains the level of probability that the true value of the population falls within the margin of error.
The confidence levels that are commonly used in the calculation include 90%, 95%, and 99%. It is important to note that a small margin of error is possible is the sample size is larger because many samples tend to provide estimates that have a higher level of accuracy. However, it also depends on the sample variability.
The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.
Mathematically, it is represented as,
Margin of Error = Z * ơ / √n
Follow the below steps:
Let us understand the concept with the help of an example.
Let us take the example of 900 students who were part of a survey, and it was found that the average GPA of the population was 2.7, with a population standard deviation of 0.4. Calculate the margin of error for
We are going to use the following data for the calculation.
For a 90% Confidence Level
For a 90% confidence level, the critical factor or z-value is 1.645 i.e. z = 1.645
Therefore, the error at a 90% confidence level can be made using above the formula as,
Margin Error at 90% confidence level will be-
For a 95% Confidence Level
For a 95% confidence level, the critical factor or z-value is 1.96 i.e. z = 1.96
Therefore, the calculation of margin of error at a 95% confidence level can be done using the above the formula as,
Margin Error at 95% confidence level will be-
For a 98% confidence level
For a 98% confidence level, the critical factor or z-value is 2.33 i.e. z = 2.33
Therefore, the calculation of margin of error at a 98% confidence level can be done using the above the formula as,
Margin Error at 98% confidence level will be-
Therefore, the error for the sample at 98% confidence level is 0.0311.
For a 99% confidence level
For a 99% confidence level, the critical factor or z-value is 2.58 i.e. z = 2.58
Therefore, the calculation of margin at a 99% confidence level can be done using the above the formula as,
Margin Error at 99% confidence level will be-
Consequently, it can be seen that the error of a sample increases with the increase in confidence level.
You can use the following calculator.
Like any other statistical concept, this concept also has some benefits and limitations. Let us understand the benefits.
The margin of error equation can be seen as a way of measuring the effectiveness of the survey. It is essential to understand this concept because it indicates how much one can expect that survey results reflect the true view of the overall population. It should be kept in mind that a survey uses a smaller group of people (also known as survey respondents) to represent a much larger population (also known as the target market.
A higher margin indicates that the survey results may stray from the actual views of the total population. On the other hand, a smaller margin indicates that the results are close to the true reflection of the total population, which builds more confidence in the survey.
Apart from the benefits, the concept has some limitations, which are as follows:
Both the above statistical concepts identify the uncertainty of a situation in a sample data set. However, the difference between them are as follows.
The margin of error in a confidence interval is the amount added and taken off. If we could collect numerous samples of the same size, the standard error would be the standard deviation of the sample statistics.
What reduces the margin of error?The margin of error diminishes as the sample size grows. The margin of error grows as population variability increases. As the degree of confidence rises, so does the margin of error.
What happens if the margin of error is too high?A statistical measure known as the margin of error describes how much random sampling error there is in survey results. One should be less confident that a poll's findings correctly mirror those of a population census the higher the margin of error.
This has been a guide to the Margin of Error and its definition. Here we learn how to calculate the Margin of Error using its formula along with practical examples and a downloadable excel template. You can learn more about financial analysis from the following articles –
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