For quick calculations & reference, users may use this SE calculator to estimate or generate the complete work with steps for SE of sample mean (x̄), SE of sample proportion (p), difference between two sample means (x̄ 1 - x̄ 2) & difference between two sample proportions (p 1 - p 2). The standard error of the mean, also known as the standard deviation of the mean, helps to determine the differences between more than one sample of information. It's a statistic measure calculated from the sampling distributions where the large size samples or proportions reduces the SE of a statistic proportionally and vice versa. Setup the test of significance or hypothesis for large & small sample size (student's t & Z statistic) to measure the reliability of sample & population parameter and the estimation the confidence interval for population parameter are some of the major applications of standard error. It is one of an important & most frequently used functions in statistics & probability. In other words, it's a numerical value that represents standard deviation of the sampling distribution of a statistic for sample mean x̄ or proportion p, difference between two sample means (x̄ 1 - x̄ 2) or proportions (p 1 - p 2) (using either standard deviation or p value) in statistical surveys & experiments. It shows how effective the selected sample size n is in the statistical experiments or the reliability of experiment results with respect to the sample size.
In probability & statistics, the standard deviation of sampling distribution of a statistic is called as Standard Error often abbreviated as SE.
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