The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean.
The Standard Error ("Std Err" or "SE"), is an indication of the reliability of the mean. A small SE is an indication that the sample mean is a more accurate reflection of the actual population mean. A larger sample size will normally result in a smaller SE (while SD is not directly affected by sample size).
Standard error measures the amount of discrepancy that can be expected in a sample estimate compared to the true value in the population. Therefore, the smaller the standard error the better. In fact, a standard error of zero (or close to it) would indicate that the estimated value is exactly the true value.
The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.
The standard error of estimate, denoted Se here (but often denoted S in computer printouts), tells you approximately how large the prediction errors (residuals) are for your data set in the same units as Y.
SEm is directly related to the reliability of a test; that is, the larger the SEm, the lower the reliability of the test and the less precision there is in the measures taken and scores obtained.
Standard Error of Measurement is directly related to a test's reliability: The larger the SEm, the lower the test's reliability. If test reliability = 0, the SEM will equal the standard deviation of the observed test scores. If test reliability = 1.00, the SEM is zero.
Uncertainty is measured with a variance or its square root, which is a standard deviation. The standard deviation of a statistic is also (and more commonly) called a standard error. Uncertainty emerges because of variability.
The standard error of the regression (S), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable.
The standard error is the average error that would be expected in using a sample mean as an estimate of the real population mean. It turns out to also be the basis for many of the most frequently performed statistical tests.
Every inferential statistic has an associated standard error. Although not always reported, the standard error is an important statistic because it provides information on the accuracy of the statistic (4). As discussed previously, the larger the standard error, the wider the confidence interval about the statistic.
Standard error and standard deviation are both measures of variability. The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population.
If we want to indicate the uncertainty around the estimate of the mean measurement, we quote the standard error of the mean. The standard error is most useful as a means of calculating a confidence interval. For a large sample, a 95% confidence interval is obtained as the values 1.96×SE either side of the mean.
The standard error of the coefficient is always positive. Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. The smaller the standard error, the more precise the estimate. Dividing the coefficient by its standard error calculates a t-value.
Statisticians have determined that values no greater than plus or minus 2 SD represent measurements that are are closer to the true value than those that fall in the area greater than ± 2SD. Thus, most QC programs require that corrective action be initiated for data points routinely outside of the ±2SD range.
A high standard error (relative to the coefficient) means either that 1) The coefficient is close to 0 or 2) The coefficient is not well estimated or some combination.
A low standard error of regression means that your data adheres more tightly to your regression line, and you can more accurately predict the results at a particular dependent variable level.
The standard error of the regression (S) is often more useful to know than the R-squared of the model because it provides us with actual units. If we're interested in using a regression model to produce predictions, S can tell us very easily if a model is precise enough to use for prediction.
Standard deviation measures the dispersion of data in relation to the mean, while standard error indicates the precision of the estimate of the sample mean.
The standard error of a coefficient estimate is the estimated standard deviation of the error in measuring it. Also, the estimated height of the regression line for a given value of X has its own standard error, which is called the standard error of the mean at X.
The standard error (abbreviated SE) is one way to indicate how precise your estimate or measurement of something is. Confidence intervals provide another way to indicate the precision of an estimate or measurement of something. But there is not written anything how to indicate accuracy of the measurement.
There exists a simple relationship between the reliability coefficient of a test and the standard error of measurement: The higher the reliability coefficient, the lower the standard error of measurement. The lower the reliability coefficient, the higher the standard error of measurement.
The sample mean plus or minus 1.96 times its standard error gives the following two figures: This is called the 95% confidence interval , and we can say that there is only a 5% chance that the range 86.96 to 89.04 mmHg excludes the mean of the population.
It is good practice to report some measure of variability with any result. It does not really matter whether you report the standard deviation, the standard error, a confidence interval as the reader can convert between them as long as s/he knows the sample size.