# Standard Error

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 forms 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. The reciprocal is generally taken as the measure of the reliability or the precision of the statistic. In other words, it is inversely proportional to the sample size. This means that the greater the standard error, the smaller the size of the sample. Thus, in order to double the precision, it should be reduced to one half, and for this, the sample size should be increased to four times the original size.

The standard error 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.