When analyze data from multiple runs of simulations, which error makes more sense ? Standard error of the mean (SEM) or standard deviation (SD)?
Hello Kolattukudy,
What is the parameter you wish to estimate from the set of simulations?
Good luck with your work.
When analyzing data from multiple runs of simulations, the standard error of the mean (SEM) is typically more appropriate than the standard deviation (SD).
The standard deviation is a measure of the spread of the data around the mean, whereas the standard error of the mean is a measure of the precision of the estimate of the mean. The SEM takes into account the sample size and gives an indication of how well the sample mean approximates the true population mean.
Using the SEM is particularly useful when comparing means between different groups, as it allows for a more meaningful interpretation of the differences. In contrast, using the SD would not account for the fact that the sample means may vary due to chance, and could lead to incorrect conclusions about the significance of observed differences.
Therefore, it is generally recommended to report the SEM when analyzing data from multiple runs of simulations, as it provides a more accurate estimate of the precision of the sample mean.
David Morse : I calculate something like ligand-protein adsorption strength and need to give an estimate of the error over the multiple runs
Thank you very much.
Samuel Mores Geddam : Thank you for the answer. This is what I expected. Could you also mention some papers that use SEM , if you are aware?
Lai, X., Zhao, Z., Zhang, Y., Wang, X., Jiang, Y., Liu, Y., & Huang, B. (2019). Effects of Nitrogen and Phosphorus Fertilizer Application Rates on Maize Yields and Soil Nitrogen and Phosphorus Dynamics in a Long-Term Experiment in Northeast China. Agronomy, 9(11), 747.
Samuel Mores Geddam : Although I agree with you in the sense that error estimate on the mean is what we need, I also think that SD is more appropriate to report as far as molecular simulations are concerned. SD is something that is obtained from the simulations, while SEM is an estimate that you make which can be inaccurate due to insufficient number of runs ( typically 4-5).
It depends on what you want. SD is the standard deviation of your sample. That's it. If you want to infer the mean of the population from the mean of your sample, then the SEM becomes relevant. So if you use the sample mean as an estimator for the population mean, you usually want to know how good, how accurate the estimator is. For this, SEM is a measure. SEM is the dispersion of your estimator, i.e., the sample mean; the smaller the dispersion, the more precise the estimate.
Claudia Paladini. Thank you for your answer. But how accurate is SEM when I have limited number of sample means?
The SEM depends on the sample size, the formula is standard deviation of the sample divided by the square root of the sample size n.
As a rule of thumb, your estimator is considered sufficiently accurate if the SEM is one-tenth smaller than your calculated sample mean. Remember, you use the SEM when you want to use your sample mean as an estimator for the population mean.