What is the difference between sem and standard deviation

In short, standard error of a statistic is nothing but the standard deviation of its sampling distribution. It has a great role to play the testing of statistical hypothesis and interval estimation. It gives an idea of the exactness and reliability of the estimate.

The smaller the standard error, the greater is the uniformity of the theoretical distribution and vice versa. The points stated below are substantial so far as the difference between standard deviation is concerned:. By and large, the standard deviation is considered as one of the best measures of dispersion, which gauges the dispersion of values from the central value.

On the other hand, the standard error is mainly used to check the reliability and accuracy of the estimate and so, the smaller the error, the greater is its reliability and accuracy. Hii there You are doing pretty well..

I went through your series of post previously and you are phenomenally informative with your words and articulation. Go on You rock pal.

Your email address will not be published. Save my name, email, and website in this browser for the next time I comment. Key Differences Between Standard Deviation and Standard Error The points stated below are substantial so far as the difference between standard deviation is concerned: Standard Deviation is the measure which assesses the amount of variation in the set of observations.

Standard Error gauges the accuracy of an estimate, i. Standard Deviation is a descriptive statistic, whereas the standard error is an inferential statistic.

Standard Deviation measures how far the individual values are from the mean value. On the contrary, how close the sample mean is to the population mean. These sample results are used to make inferences based on the premise that what is true for a randomly selected sample will be true, more or less, for the population from which the sample is chosen.

However, the precision with which sample results determine population parameters needs to be addressed. Figure 2 shows mean of 25 groups of 10 individuals each drawn from the population shown in Figure 1. Mean of all these sample means will equal the mean of original population and standard deviation of all these sample means will be called as SEM as explained below. This figure illustrates the mean of 25 groups of 10 individuals each drawn from the population of individuals shown in the Figure 1.

The means of three groups shown in Figure 1 are shown using circles filled with corresponding patterns. SEM is the standard deviation of mean of random samples drawn from the original population.

Just as the sample SD s is an estimate of variability of observations, SEM is an estimate of variability of possible values of means of samples. As mean values are considered for calculation of SEM, it is expected that there will be less variability in the values of sample mean than in the original population.

The precision increases as the sample size increases [ Figure 3 ]. Thus, SEM quantifies uncertainty in the estimate of the mean. Its main function is to help construct confidence intervals CI. This true population value usually is not known, but can be estimated from an appropriately selected sample. If samples are drawn repeatedly from population and CI is constructed for every sample, then certain percentage of CIs can include the value of true population while certain percentage will not include that value.

Wider CIs indicate lesser precision, while narrower ones indicate greater precision. In essence, a confidence interval is a range that we expect, with some level of confidence, to include the actual value of population mean. But in many articles, SEM and SD are used interchangeably and authors summarize their data with SEM as it makes data seem less variable and more representative. However, unlike SD which quantifies the variability, SEM quantifies uncertainty in estimate of the mean.

The importance of SD in clinical settings is discussed below. Thus, there is a quick summary of the population and the range against which to compare the specific findings. If one confused the SEM with the SD, one would believe that the range of the population is narrow Additionally, when two groups are compared e. Effect size is determined by calculating the difference between the means divided by the pooled or average standard deviation from two groups.

Generally, effect size of 0. More importantly, SEMs do not provide direct visual impression of the effect size, if number of subjects differs between groups. Exceptionally the SD as an index of variability may be a deceptive one in many experimental situations where biological variable differs grossly from a normal distribution e.

In these cases, because of the skewed distribution, SD will be an inflated measure of variability. In such cases, data can be presented using other measures of variability e. There are two reasons for this trend.

First, the SEM is a function of the sample size, so it can be made smaller simply by increasing the sample size n [ Figure 3 ]. In general, the use of the SEM should be limited to inferential statistics where the author explicitly wants to inform the reader about the precision of the study, and how well the sample truly represents the entire population.

Further, in every case, standard deviations should preferably be reported in parentheses [i. Proper understanding and use of fundamental statistics, such as SD and SEM and their application will allow more reliable analysis, interpretation, and communication of data to readers. Though, SEM and SD are used interchangeably to express the variability; they measure different parameters. SEM, an inferential parameter, quantifies uncertainty in the estimate of the mean; whereas SD is a descriptive parameter and quantifies the variability.

As readers are generally interested in knowing variability within the sample, descriptive data should be precisely summarized with SD. Source of Support: Nil. Conflict of Interest: Dr. Views and opinions presented in this article are solely those of the author and do not necessarily represent those of the author's present or past employers. National Center for Biotechnology Information , U. Journal List Perspect Clin Res v. Perspect Clin Res. Mohini P. Barde and Prajakt J.

But you can't predict whether the SD from a larger sample will be bigger or smaller than the SD from a small sample. This is not strictly true.

It is the variance -- the SD squared -- that doesn't change predictably, but the change in SD is trivial and much much smaller than the change in the SEM. Note that standard errors can be computed for almost any parameter you compute from data, not just the mean.

The phrase "the standard error" is a bit ambiguous.