Standard Error
Candlefocus EditorThe standard error is a measure of the standard deviation of the sample mean estimate of a population mean. It indicates the extent to which a sample mean deviates from the population mean and provides a measure of the accuracy of a statistic. It is also used to assign confidence intervals which indicate the degree of confidence one has in the interval.
The standard error is calculated as the square root of the sample variance divided by the sample size. It is a measure of the accuracy and can be calculated, as indicated above.
A small standard error indicates that the sample mean is closer to the population mean and vice versa. The standard error helps to quantify the deviation of a sample statistic, and this can be used to make inferences about a population.
A large standard error indicates that the sample mean is farther away from the population mean. The standard error is most commonly used to calculate the confidence interval of a standard mean. The confidence interval is a range around the sample mean that defines the range of values that are expected to contain the population mean.
The standard error is also used to compare the precision of different estimates. For example, if two different samples give a high standard error, that implies that the estimates of the samples may not be very precise.
In summary, the standard error is an important concept in statistics that is used to measure the accuracy of a statistic. By calculating the standard error, one can estimate the standard deviation of the sample population, compare different estimates to each other, and create confidence intervals to gain information about a population.