Standard error is a measurement which describes the deviation between a sample mean and the population mean, by calculating the standard deviation of the sampling distribution. Standard error is a measure which takes into account the sample size of a data set and in fact, by looking at the formula for this statistic, it is noticeable that sample size is actually considered twice^{1}

Formula: standard error = √variance/ (n)

In this formula:

√ = square root

n = sample size

Recall that when calculating the variance, the sample size is required as one of the variables in the formula. Thus, by analyzing the above equation for standard error, it is clear that sample size is considered twice in this calculation, once from the variance measure and once on its own as denoted by “n”.

Therefore, when calculating the standard error for data sets with the same variance, you will always get rather different standard error values, as long as the sample sizes differ. Essentially, standard error can be considered as a measure which accounts for one set of data, but acts as if you repeated the same experiment many times obtaining a range of means^{1}. By computing the standard error calculation, you can avoid repeating your experiment numerous times.

Overall, the objective of using the standard error calculation is to analyze the accuracy with which the sample mean actually represents the population mean. Smaller standard error values indicate that the difference between the means is lower, whereas larger standard error values signify that the difference between the means is greater.

References:

1. Davidson College. (2002). *A Beginner's Guide For Descriptive Statistics*. Retrieved from: http://www.bio.davidson.edu/courses/bio111/bio111labman/lab%207.html

Image Credit: Home Academia Politics Archives. (January 11, 2011). *Understanding polls: Margins of error. *Retrieved from: http://davidmallard.id.au/2011/01/understanding-polls-margins-of-error/