What is the difference between STANDARD DEVIATION and STANDARD ERROR In the statistical analysis ?
The standard error of mean (SEM) is calculated by dividing the standard deviation (SD) by the square root of N. This relationship is worth remembering, as it can help you interpret published data. If the SEM is presented, but you want to know the SD, multiply the SEM by the square root of N. If you are comparing means using t test or ANOVA, make 95% confidence interval of the mean your error bar. if you plot mean of replicate samples with an error bar, use standard deviation but if you want to let people see how well you know your mean, use standard error whose bars are characteristically shorter than the rest.
Qaswaa -
Please keep in mind that the standard deviation of a population is a constant. A larger sample size will estimate it better, but not change it. Standard errors are reduced by increasing sample size.
We use standard deviations and the desired standards errors as the basis for every estimation of sample size needs. Methodology also enters into it.
Best wishes - Jim
PS - You can use other levels of confidence besides 95%, by the way. It depends on application.
PSS - By the way, I think some might call a standard error the standard deviation of an estimated mean, or estimated total, or other such statistic.
Depending on the context, key distinctions between standard deviation and standard error are as follow:
- Standard Deviation is the measure that assesses the amount of variation in the set of observations. Standard Error gauges the accuracy of an estimate, i.e. it is the measure of the variability of the theoretical distribution of a statistic.
- Standard Deviation is a descriptive statistic while the standard error is an inferential statistic.
- Standard Deviation measures how far the individual values are from the mean value while standard error measures how close the sample mean is to the population mean.
- Standard Deviation is the distribution of observations with reference to the normal curve while the standard error is the distribution of an estimate with reference to the normal curve.
- Standard Deviation is defined as the square root of the variance while the standard error is described as the standard deviation divided by the square root of sample size.
- An increase in the sample size provides a more particular measure of standard deviation while an increase in the sample size decreases the standard error.
- In summary, the standard deviation is one of the best measures of dispersion, that gauges the dispersion of values from the central value while the standard error is mainly used to check the reliability and accuracy of the estimate. Hence, the smaller the error, the greater is its reliability and accuracy.
The standard deviation (SD) measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean (SEM) measures how far the sample mean (average) of the data is likely to be from the true population mean
In biomedical journals, Standard Error of Mean (SEM) and Standard Deviation (SD) are used interchangeably to express the variability. However, they measure different parameters. SEM quantifies uncertainty in estimate of the mean whereas SD indicates dispersion of the data from mean.
In other words, SD characterizes typical distance of an observation from distribution center or middle value. If observations are more disperse, then there will be more variability. Thus, a low SD signifies less variability while high SD indicates more spread out of data.
On the other hand, SEM by itself does not convey much useful information. Its main function is to help construct confidence intervals (CI). CI is the range of values that is believed to encompass the actual (“true”) population value. This true population value usually is not known, but can be estimated from an appropriately selected sample. Wider CIs indicate lesser precision, while narrower ones indicate greater precision.
In conclusion, SD quantifies the variability, whereas SEM quantifies uncertainty in estimate of the mean. As readers are generally interested in knowing the variability within sample and not proximity of mean to the population mean, data should be precisely summarized with SD and not with SEM.
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.
Kindly refer to these citations for additional information:
1. What to use to express the variability of data: Standard deviation or standard error of mean? https://doi.org/10.4103/2229-3485.100662
2. Empowering statistical methods for cellular and molecular biologists. https://doi.org/10.1091/mbc.E15-02-0076
3. Error bars in experimental biology. https://doi.org/10.1083/jcb.200611141
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