Standard Error

Reviewed by Annapoorna | Updated on Sep 28, 2020

Catalogue

What is Meant by Standard Error?

The standard error refers to a statistical concept that tests the precision of which a sample distribution utilises standard deviation to describe a population. In statistics, a sample mean will deviate from a population's real mean—this divergence is the mean standard error.

The average standard deviation of a statistical sample population is, therefore, a standard error (SE) of a statistic.

Standard Error Explained

The term "standard error" is used to denote the standard deviation of different sample statistics, for instance, the mean or median. The "standard mean error", for example, refers to the standard deviation in the distribution of sample means taken from a population. The lower the standard error, the more representative the sample is of the population as a whole.

The relation between the standard error a well as the standard deviation is such that the standard error is equal to standard deviation divided by the square root of the sample size for a given sample size. Also, the standard error is inversely proportional to the sample size; the bigger the sample size, the lower the standard error as the figures approximate the real value.

The standard error is a part of the descriptive statistics. It reflects the mean standard deviation within a dataset. It acts as a variance measure for random variables, including a measure of the distribution. The lower the scatter, the more reliable the dataset would be.

Essentials of Standard Error

The mean, or average, is usually measured when a population is being sampled. The standard error can involve variance between the population's measured mean and one that is considered known, or recognised as accurate. It helps mitigate any possible inaccuracies related to processing the sample.

In cases where multiple samples are obtained, the mean of each sample may be slightly different from the others, creating a spread among variables. Very commonly, this distribution is calculated as the standard error, accounting for the variations in the datasets between methods.

The more data points that participate in the mean estimates, the lower the standard error appears to be. When the standard error is small, it is assumed that the data is more reflective of the true mean. The data may have some noticeable anomalies in cases where the standard error is high.

The standard deviation refers to a measure of the diffusion of each data point. The standard deviation is used to help assess the validity of the data based on the number of shown data points at each standard deviation level. Standard errors act as a way to evaluate the sample accuracy or the precision of several samples by evaluating variance within the means.