This tool determines your sample’s error based on sample size, proportion, and/or standard deviation. Check out our calculators for the sampling distribution of the sample proportion and the normal probability for sampling distributions if you’re interested in the opposite issue: the likelihood of finding a range of sample means or proportions.
- Sampling error = confidence level × [standard deviation of population / (square root of sample size)]
- Sampling error = confidence level × [standard deviation of population / (square root of sample size)]
How to calculate sampling error
The following six steps can be used to determine sampling error:
1. Record the sample size
The sampling error formula’s easiest number to find is this one. Review your study to find the sample size. For instance, if your sample consisted of 60 individuals, enter 60 into the formula.
2. Find the standard deviation of the population
The standard deviation calculates the deviation of each data point from the mean. To determine the standard deviation, use the population’s characteristics and the data’s average value. If you’re not familiar with the formula for sample standard deviation, you can look it up.
3. Determine your confidence level
Use the confidence interval for your sample size to calculate the confidence level. The range of values in a sample that are likely to contain the correct population mean is specified by confidence intervals. Take the sample size’s square root and multiply it by half the confidence interval. To determine your confidence level, divide this by the sample standard deviation. Finally, determine your equivalent score using a confidence level table.
4. Calculate the square root of the sample size
Find the square root of your sample size. If the square root of your sample size is a whole number, it might be a perfect square. For instance, the square root of two makes the number four a perfect square, while the square root of three makes the number ten not a perfect square. 16.
5. Divide the standard deviation value by the square root value
the square root of your population’s standard deviation divided by the sample size Using a calculator rather than doing it manually is frequently simpler. Record the result to use in the next step.
6. Multiply the result by the confidence level
In the final step, multiply the figure from the previous step by the confidence level score you discovered earlier. Continue using a calculator to work with these complex decimals. The product represents the sampling error for your study.
What is a sampling error?
When a tester uses a sample that doesn’t accurately represent the population under consideration, a calculation called the sampling error is used to measure statistical error. The results from studies with skewed samples may be incorrect. An analysis called sampling calls for choosing a number of observations, typically from larger populations. For instance, one study’s hypothesis states that individuals between the ages of 30 and 45 consume fruit at least once per week. To represent the target population, they can choose 100 people in this age range from their neighborhood, and they can observe their eating habits. Sampling error decreases as the sample size increases.
Heres the formula for calculating sampling error:
Sampling error is calculated as confidence level [population standard deviation / (square root of sample size)]
The percentage of samples that researchers can anticipate reflecting the characteristics of the entire population is known as the confidence level. How far the researcher’s data are from the mean is indicated by the population’s standard deviation. The amount that, when multiplied by itself, equals the sample size value is known as the square root of the sample size. Researchers can find the level of confidence in their sample and the corresponding number using charts for confidence levels that are available online.
Why is calculating sampling error important?
Sampling error is a crucial metric for determining how uncertain a sample size is. Typically, statisticians will use random samples to draw conclusions about a population as a whole. It is uncommon for the sample to match the true population exactly. Testers frequently deal with some degree of accuracy inaccuracy in their findings because it’s frequently difficult for an entire population to participate in a study. Researchers can determine whether the sample size is inadequate or not representative of the larger population by computing sampling error. After that, they might carry out additional research or include the sampling error in their report.
Types of sampling errors
Here are a few typical sampling mistakes you might discover in a study:
How can you correct sampling errors?
There are several steps researchers can take to lessen the level of uncertainty in their research. They might rely on probability sampling, which gives every member of a population a chance to take part in a study. As a result, researchers may be able to more accurately generalize their findings and the sample size may become more representative of the entire population.
Here are some additional pointers for reducing and managing a sampling error:
Example sampling error calculations
You can use the following calculations as examples to help you identify a sampling error:
Sampling with a higher confidence level
The research firm Mind Laboratories wants to determine the sampling error for one of its studies. Mind Laboratories study had a sample size of 100 people. The standard deviation of the population is 0. 50. For a 99% confidence level, the score is 2. 58. The following values were used by Mind Laboratories to calculate sampling error:
Sampling error = 2.58 x (.50 / √100)
Sampling error = 2.58 x (.50 / 10)
**Sampling error = 2.58 x 0.05**
**Sampling error = 0.12**
Sampling with a lower confidence level
The research company Tech Flurry is attempting to determine the sampling error for one of its studies that has a lower confidence level. There were 324 participants in the study, and the standard deviation was 0. 30. For an 80% confidence level, the score is 1. 28. These figures are used by Tech Flurry in their calculation of sampling error:
Sampling error = 1.28 x (.30 / √324)
**Sampling error = 1.28 x (.30 / 18)**
Sampling error = 1.28 x 0.016
*Sampling error = 0.02*
02 Finding Sampling Error
FAQ
What is sampling error in statistics?
The difference between a population parameter and the sample statistic used to estimate it is known as sampling error. For instance, sampling error accounts for the variance between a population mean and a sample mean.
How do you find the sampling error of the sample mean?
First, determine the mean by dividing the total number of samples by the total number of samples. Step 2: Subtract each measurement’s individual value from the mean to determine its deviation from the mean. Step 3: Square each deviation from mean. Squared negatives become positive.
How do you calculate sampling?
- Sampling Error = 1. 96 * %E2%88%9A[70% * (1 %E2%80%93 70%) / 500] * [1 %E2%80%93 %E2%88%9A(500 / 100000000)]
- Sampling Error = 4.01%
