Firstly, a note about Standard Error, what is it?
S.E. (related to a mean) is simply a modified form of the standard deviation of a set of arithmetic means from n samples. It is a measure of the average dispersion of the sample means about the population mean. Imagine that we wanted to measure the weight of lobsters caught in one month. We might decide to weigh them in batches of 5 and so each 5 will give us a mean weight for that batch. Understandably, if we repeat the process on different nights we are going to get a slightly different value for the mean of each sample of 5. However, the more we repeat the sampling the nearer the overall mean is going to approach the true mean catch weight for that population of lobsters in that month. So now, instead of calculating the standard deviation for each sample, we can calculate the S.D. for all the means that we have calculated and this is the Standard Error. The higher the number of samples, the more the various sample means approximate to the true mean and so the smaller the S.E. become
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