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Thread: An Example to Distinguish Standard Deviation and Standard Error of the Mean

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    Exclamation An Example to Distinguish Standard Deviation and Standard Error of the Mean

    The standard deviation and standard error of the mean measure two very different things and are often confused. Most medical investigators summarise their data with the standard error of the mean because it is always smaller than the standard deviation. It makes their data look better. However, unlike the standard deviation, which quantifies the variability in the population, the standard error of the mean quantifies uncertainty in the estimate of the mean. Since readers are generally interested in knowing about the population, data should generally not be summarised with the standard error of the mean.

    To understand the difference between the standard deviation and standard error of the mean and why one ought to summarise data using the standard deviation, suppose that in a sample of 20 patients an investigator reports that the mean cardiac output was 5.0 L/min with a standard deviation of 1 L/min. Since about 95% of all population members fall within about 2 standard deviations of the mean, this report would tell you that, assuming that the population of interest followed a normal distribution, it would be unusual to observe a cardiac output below about 3 or above 7 L/min. Thus, you have a quick summary of the population described in the paper and a range against which to compare specific patients you examine.

    Unfortunately, it is unlikely that these numbers would be reported, the investigator being more likely to say that the cardiac output was 5.0 +/- 0.22 (SEM) L/min. If you confuse the standard error of the mean with the standard deviation, you would believe that the range of most of the population was narrow indeed - 4.56 to 5.44 L//min. These values describe the range which, with about 95% confidence, contains the mean cardiac output of the entire population from which the sample of 20 patients was drawn.

    In practice, one generally wants to compare a specific patient's cardiac output not only with the population mean but with the spread in the population taken as a whole.
    Last edited by CheneyHsiung; Sun 26th April '15 at 1:05am.
    Clinical Pharmacy Specialist - Hematology

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