Standard error is the standard deviation of the sampling distribution of a statistic. It can be abbreviated as S.E.
Standard error plays a very crucial role in the large sample theory. It also may form the basis for the testing of a hypothesis. The statistical inference involved in the construction of the confidence interval is mainly based on standard error.
The magnitude of the standard error gives an index of the precision of the estimate of the parameter. It is inversely proportional to the sample size, meaning that smaller samples tend to produce greater standard errors.
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The standard deviation of a sample is generally designated by the Greek letter sigma (σ). It can also be defined as the square root of the variance present in the sample.