What it is, Why it Matters, and How to Calculate
By Julia Simkus, published Jan 25, 2022
When you take samples from a population and calculate the means of the samples, these means will be arranged into a distribution around the true population mean.
The standard deviation of this distribution of sampling means is known as the standard error. Standard error estimates how accurate the mean of any given sample represents the true mean of the population.
A larger standard error indicates that the means are more spread out, and thus it is more likely that your sample mean is an inaccurate representation of the true population mean.
On the other hand, a smaller standard error indicates that the means are closer together, and thus it is more likely that your sample mean is an accurate representation of the true population mean.
Standard error increases when standard deviation increases. Standard error decreases when sample size increases because having more data yields less variation in your results.
SE = standard error of the sample
σ = sample standard deviation
n = number of samples
Standard error is calculated by dividing the standard deviation of the sample by the square root of the sample size.
The values in your sample are 52, 60, 55, and 65.
We use standard error to indicate the uncertainty around the estimate of the mean measurement. It tells us how well our sample data represents the whole population. This is useful when we want to calculate a confidence interval.
Standard error and standard deviation are both measures of variability, but standard deviation is a descriptive statistic that can be calculated from sample data while standard error is an inferential statistic that can only be estimated.
Standard deviation tells us how concentrated the data is around the mean. It describes variability within a single sample. On the other hand, standard error tells us how the mean itself is distributed.
It estimates the variability across multiple samples of a population. The formula for standard error calculates the standard deviation divided by the square root of the sample size.
Julia Simkus is an undergraduate student at Princeton University, majoring in Psychology. She plans to pursue a PhD in Clinical Psychology upon graduation from Princeton in 2023. Julia has co-authored two journal articles, one titled “Substance Use Disorders and Behavioral Addictions During the COVID-19 Pandemic and COVID-19-Related Restrictions," which was published in Frontiers in Psychiatry in April 2021 and the other titled “Food Addiction: Latest Insights on the Clinical Implications," to be published in Handbook of Substance Misuse and Addictions: From Biology to Public Health in early 2022.
Simkus, J. (2022, Jan 25). Standard error. Simply Psychology. www.simplypsychology.org/standard-error.html
Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. Bmj, 331(7521), 903.
Zwillinger, D. (2018). CRC standard mathematical tables and formulas. chapman and hall/CRC.
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