Table of ContentsView AllTable of ContentsDefinition and UseHow to Calculate Standard ErrorExampleImportanceStandard Error vs. Standard Deviation
Table of ContentsView All
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Table of Contents
Definition and Use
How to Calculate Standard Error
Example
Importance
Standard Error vs. Standard Deviation
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The standard error formula is a calculation of the standard error of the mean. It indicates a difference between the mean of the population and the mean of a sample drawn from that population.
Calculating the standard error can provide important information about how much a sample mean would vary if you repeated a research study using samples from the same population.
The Standard Error Formula and What It’s Used For
The standard error formula for the mean is:
Standard Error FormulaSE = σ / √n
Standard Error Formula
SE = σ / √n
In this formula, “σ” represents the standard deviation of the sample, and “n” represents the sample size.
The standard error of the mean indicates the average amount of error that can be expected when estimating the population mean based on a particular sample.
What the Standard Error Formula Is Used For
The standard error is an important statistical measure because it provides a sense of how precise an estimate of the population parameter is likely to be. Psychology researchers utilize the standard error formula to better understand the precision of their sample estimate. This can be helpful when drawing conclusions about a population based on a sample.
A smaller standard error indicates that the sample mean is a more accurate estimate of the population mean, while a larger standard error suggests more uncertainty and less precision in the estimate.
Researchers often use the standard error to calculate confidence intervals, which provide a range of values within which the true population parameter is likely to fall.
For example, imagine that researchers conduct a study to see how sleep deprivation affects driving performance. If the standard error is small, it would tell researchers that their sample is a good reflection of what they would find in the general population, giving the researchers greater confidence in their findings.
In other words, calculating the standard error provides psychology researchers with an estimate of the reliability of their results. A small standard error provides greater confidence in the generalizability of the findings of a psychological study.
The standard error is also utilized inhypothesis testing, which helps determine the statistical significance of observed differences between sample means or other sample statistics.
You can use the following steps to calculate the standard error:
The result of step five is the standard error of the mean. This final value indicates the average error that can be expected when estimating the population mean based on the sample.
It’s important to note that the steps outlined above apply to calculating the standard error of the mean. If you need to calculate the standard error for a different sample statistic, the process will vary.
An Example Calculation
It can be helpful to look at an example of how the standard error would be calculated for a set of sample data.
Gather your sample data:
Imagine that you want to learn the standard error for a set of exam scores. Sample scores from a sample of four students are as follows: 85, 90, 92, 74
Calculate the sample mean:
Calculate the sample standard deviation (s):
Calculate the differences between each value and the sample mean:
85 - 85.25 = -0.25
90 - 85.25 = 4.75
92 - 85.25 = 6.75
74 - 85.25 = -11.25
Square each difference:
(-0.25)^2, (4.75)^2, (6.75)^2, (-11.25)^2
Sum up the squared differences:
(0.0625) + (22.5625) + (45.5625) + (126.5625) = 194.75
194.75 / (4 - 1) = 64.92
Take the square root: √64.92 ≈ 8.0571
The sample standard deviation (s) is approximately 8.0571.
Determine the sample size (n):
In this example, we have a sample size of 4.
8.0571 / √4 = 8.0571 / 2 ≈ 4.0285
The result last step above is the standard error of the mean. In this example, the standard error of the mean is approximately 4.0285.
What Does Standard Error Tell You?
The calculated standard error of the mean provides valuable information about the precision andreliabilityof the sample mean as an estimate of the population mean. Some information the standard error can tell you includes the:
Precision of the Estimate
Confidence in the Estimate
The standard error is used to calculate confidence intervals, which provide a range of values within which the true population mean is likely to fall.
In many cases, a 95% confidence interval is calculated as the sample mean ± 1.96 times the standard error.In this case, the range would be between 77.3542 and 93.1458. This means that we can be 95% confident that the actual population mean lies within this range.
A narrow confidence interval suggests that if you were tocollect data from a different sample, you can be pretty sure that you would get a very similar result.
Difference Between Standard Error and Standard Deviation
The standard error (SE) and standard deviation (SD) are both measures of variability, but they have distinct purposes and interpretations. They differ in terms of:
The standard error and standard deviation are both important instatistical analysis, but they serve different purposes. They can provide valuable insights, but their use depends on what researchers look at.
Helpful Hint:
How to Find the Mean, Median, and Mode
4 SourcesVerywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.Barde MP, Barde PJ.What to use to express the variability of data: Standard deviation or standard error of mean?Perspect Clin Res. 2012;3(3):113-116. doi:10.4103/2229-3485.100662Altman DG, Bland JM.Standard deviations and standard errors.BMJ. 2005;331(7521):903. doi:10.1136/bmj.331.7521.903Andrade C.Understanding the difference between standard deviation and standard error of the mean, and knowing when to use which.Indian J Psychol Med. 2020;42(4):409-410. doi:10.1177/0253717620933419Lee DK, In J, Lee S.Standard deviation and standard error of the mean.Korean J Anesthesiol. 2015;68(3):220-223. doi:10.4097/kjae.2015.68.3.220
4 Sources
Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.Barde MP, Barde PJ.What to use to express the variability of data: Standard deviation or standard error of mean?Perspect Clin Res. 2012;3(3):113-116. doi:10.4103/2229-3485.100662Altman DG, Bland JM.Standard deviations and standard errors.BMJ. 2005;331(7521):903. doi:10.1136/bmj.331.7521.903Andrade C.Understanding the difference between standard deviation and standard error of the mean, and knowing when to use which.Indian J Psychol Med. 2020;42(4):409-410. doi:10.1177/0253717620933419Lee DK, In J, Lee S.Standard deviation and standard error of the mean.Korean J Anesthesiol. 2015;68(3):220-223. doi:10.4097/kjae.2015.68.3.220
Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read oureditorial processto learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.
Barde MP, Barde PJ.What to use to express the variability of data: Standard deviation or standard error of mean?Perspect Clin Res. 2012;3(3):113-116. doi:10.4103/2229-3485.100662Altman DG, Bland JM.Standard deviations and standard errors.BMJ. 2005;331(7521):903. doi:10.1136/bmj.331.7521.903Andrade C.Understanding the difference between standard deviation and standard error of the mean, and knowing when to use which.Indian J Psychol Med. 2020;42(4):409-410. doi:10.1177/0253717620933419Lee DK, In J, Lee S.Standard deviation and standard error of the mean.Korean J Anesthesiol. 2015;68(3):220-223. doi:10.4097/kjae.2015.68.3.220
Barde MP, Barde PJ.What to use to express the variability of data: Standard deviation or standard error of mean?Perspect Clin Res. 2012;3(3):113-116. doi:10.4103/2229-3485.100662
Altman DG, Bland JM.Standard deviations and standard errors.BMJ. 2005;331(7521):903. doi:10.1136/bmj.331.7521.903
Andrade C.Understanding the difference between standard deviation and standard error of the mean, and knowing when to use which.Indian J Psychol Med. 2020;42(4):409-410. doi:10.1177/0253717620933419
Lee DK, In J, Lee S.Standard deviation and standard error of the mean.Korean J Anesthesiol. 2015;68(3):220-223. doi:10.4097/kjae.2015.68.3.220
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