This is expressed in the standard deviation. We do not know the variation in the population so we use the variation in the sample as an estimate of it. The variation depends on the variation of the population and the size of the sample. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population.Īs noted above, if random samples are drawn from a population, their means will vary from one to another.
How do you calculate standard error series#
The series of means, like the series of observations in each sample, has a standard deviation. This can be proven mathematically and is known as the "Central Limit Theorem". These means generally follow a normal distribution, and they often do so even if the observations from which they were obtained do not. If we draw a series of samples and calculate the mean of the observations in each, we have a series of means. Thus the variation between samples depends partly also on the size of the sample. A consequence of this is that if two or more samples are drawn from a population, then the larger they are, the more likely they are to resemble each other - again, provided that the random sampling technique is followed. In other words, the more people that are included in a sample, the greater chance that the sample will accurately represent the population, provided that a random process is used to construct the sample. Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample. Thus the variation between samples depends partly on the amount of variation in the population from which they are drawn. For example, a series of samples of the body temperature of healthy people would show very little variation from one to another, but the variation between samples of the systolic blood pressure would be considerable. They will show chance variations from one to another, and the variation may be slight or considerable. Resource text Standard error of the meanĪ series of samples drawn from one population will not be identical. This section considers how precise these estimates may be. The earlier sections covered estimation of statistics. Learning objectives: You will learn about standard error of a mean, standard error of a proportion, reference ranges, and confidence intervals.
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