Standard errors are easy to calculate and commonly used because: To make the uncertainty one-tenth as big, the sample size (n) needs to be one hundred times bigger. This is because the standard deviation is divided by the square root of the sample size. However, to make the uncertainty (standard error of the mean) in an average value half as big, the sample size (n) needs to be four times bigger. Then the standard error of the mean will be smaller because the standard deviation is divided by a bigger number. Usefulness Ī practical result: One can become more sure of an average value by having more measurements in a sample. In which case, the numbers in the sample are not independent, and special equations are used to try to correct for this. Sometimes, a sample may come from one place even though the whole group may be spread out, while other times, a sample may be made in a short time period when the whole group covers a longer time. There are special equations to use if a sample has less than 20 measurements. There is another equation to use if the number of measurements is for 5% or more of the whole group: Then the standard error of the mean for the sample will be within 5% of the actual standard error of the mean (that is, if the whole group were measured). As a rule of thumb, there should be at least six measurements in a sample. In general, the larger the sample, the closer the estimated standard error of the mean is to the actual standard error of the mean. S is the sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population), and n is the number of measurements in the sample. The standard error, sometimes abbreviated as S E For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value.
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