The ‘Standard Error’ is another of those confusing statistical terms marketers need to understand. It is often confused with, and is as misunderstood as ‘Standard Deviation’. While they are related, and the Standard Deviation calculation is used in the calculation of the Standard Error, they tell entirely different stories.
The standard error calculates how accurate the mean of any sample from a population is likely to be, compared to the true mean of the total population.
An increase in the standard error means that the means of varying samples of data are spread out, so it becomes more unlikely that any mean of a sample will be an accurate reflection of the true population mean. The higher the standard error, the more spread out will be the population around the mean. Conversely, a low standard error indicates a closely distributed data set, and so is more likely to be representative of the population.
To continue the example in the earlier post explaining Standard Deviation. If you were planning to improve Sydney’s terrible road congestion, it would be valuable to know how representative of the total commuting population of Sydney the mean of your trips from Artarmon to the CBD of 30 minutes was.
To do that, you would do a wider study of the whole population, and calculate the mean, and standard deviation. You would then apply the Standard Error formula to calculate the standard error of the Artarmon sample, compared to the mean of the whole Sydney population.
The standard error is the standard deviation divided by the square root of the sample size. It therefore tells you the accuracy of a sample mean by measuring its variability from the known mean of the total sample.
Header illustration courtesy Wikipedia.
PS. I guess the government could have done such a exercise in parking lots, swimming pools, women’s change rooms, and all the rest. Perhaps they do not understand real statistics when disconnected from political statistics?
