Difference Between Standard Deviation and Standard Error (With Table)

The term “statistics” means the practice of analyzing and collecting numerical data which is provided in large quantities. There are several statistical studies some of them are biology, finance, psychology, engineering, and many more. Statistical studies are helpful to collects and analyze any data which is in its numerical form. 

Standard Deviation and Standard Error are two of the most common measures which are used in the field of statistics. The main motive of Standard Deviation and Standard Error is to show results of statistical analysis and characteristics of sample data. Standard Deviation and Standard Error are a bit confusing but they vary from each other in many terms. 

Standard Deviation vs Standard Error 

The main difference between Standard Deviation and Standard Error is that they both vary in their statistical interferences. Standard Deviation helps individual data values to disperse. It shows the accuracy of the mean which, represents sample data. While Standard Error is based on statistical interferences of sampling data.  

In statistics, Standard Deviation expresses the number of members of a certain group which differs from the value of the mean of the same group. Karl Pearson was the first to use Standard Deviation in writing for his lectures. This term was first used in 1894. Standard Deviation was the term used for replacing alternative names used earlier for the same ideas. 

In statistics, the Standard Error is referred to as approximate Standard Deviation which is included in the statistical sample population. The variation included in the Standard Error is between the mean which is calculated based on population and the other is accurate which is accepted. If the calculation of the mean includes more data points, then the standard error will be smaller. 

Comparison Table Between Standard Deviation and Standard Error 

Parameters of ComparisonStandard DeviationStandard Error
MeaningA measure of the dispersion from the mean through a set of data.A measure of an estimate through its statistical exactness.
Denotes variabilityWithin the sample.In population, among multiple samples.
TypeDescriptive statistics.Inferential statistics.
DistributionThe observation is concerned with the normal curve.An estimate is concerned with the normal curve.
CalculationBy square rooting the variance.Dividing Standard Deviation by square roots of sample size.

What is Standard Deviation? 

Variation indicated the deviation of values that are at the average. As a result, the degree of variation is designated by measures of variation. In terms of measures of variation, Standard Deviation is one of the most common measures used. For convenient mathematical analysis, people prefer Standard Deviation as it is completely based on all the values whether it is the highest one or lowest. 

Standard Deviation is referred to as the measure of the dispersion from the mean through a set of data. Its main motive is to measure the absolute variability of any distribution. If the dispersion or variability is higher than the Standard Deviation is too greater. As a result, the magnitude of the deviation will also be greater. Standard Deviation is denoted by σ (sigma). 

When it comes to financial terms, the Standard Deviation is used in deals such as mutual funds, stocks, and others. Standard Deviation is used to measure risks that are related to an investment instrument. It is helpful for the investors because it provides them the mathematical basis to make decisions in the financial market for their investment. 

The Standard Deviation can be calculated by software that is used for statistical analysis as well as by hand. For the final result, you have to go through few steps such as find the mean than from it find each score’s deviation. Further square deviation and find the sum of squares. Then go for variance and find it, later, find the square root of it. 

What is Standard Error? 

In mathematics, Standard Error is used to measure variability in statistics. SE is its abbreviated form. It helps to make an approximation of Standard Error in a given sample. It estimates the accuracy, consistency, and efficiency of a sample or it can be said that it measures how to present a sampling distribution that represents a population in a precise way. 

Mean, or average is calculated when there is a sampled population. Standard Error helps to make up for any incidental inaccuracies linked to the gathering of the samples. When multiple samples are collected, it creates a difference among the variables as the mean of each sample slightly varies from each other. The difference is calculated as the Standard Error. 

Standard Error is useful in terms of statistics as well as in economics. When it comes to financial terms, it is helpful in the field related to econometrics. In this researcher use Standard Error to perform hypothesis testing and regression analysis. Whereas in inferential statistics Standard Error is the basis for the creation of confidence inter. 

Standard Error is calculated by dividing Standard Deviation by square root of sample size. If there are more data points in the mean calculation the Standard Error will be smaller. As a result, the data will be more representative of the true mean. In case, notable irregularities are found in data it means that Standard Error is large. 

Main Differences Between Standard Deviation and Standard Error 

  1. Standard Deviation does not rely on random sampling because from the average, it is the typical deviation. But Standard Error depends on random sampling because from the expected value, it is the typical deviation. 
  2. In terms of increase in sample size, Stanard Deviation gives the specific measure of it. On the other hand, in Standard Error, it decreases. 
  3. Standard Deviation is mentioned as sample statistics because its statistics include values that are derived from the sample. While Standard Error is mentioned as a population parameter in which parameter is a value and describes the entire population. 
  4. Standard Deviation measures the number of observations that vary from each other whereas Standard Error measures the accuracy of the sample mean to the population mean.  
  5. When it comes to the calculation of the confidence interval related to the population, Standard Deviation does not calculate through it. On the flip side, Standard Error does. 

Conclusion 

So, it can be concluded that statistical studies play an important role in the contemporary world. Standard Deviation and Standard Error are two of the most common measures used in the field of statistics. They both are used to show characteristics of sample data and analysis statistics. While they vary in terms of statistical interferences. 

Standard Deviation and Standard Error have no competition between them because they both have their use. Standard Deviation helps to conclude the variability and spread of the data. On the other hand, Standard Error shows how precise is the sample mean. 

References

  1. https://www.sciencedirect.com/science/article/pii/S0022103113000668
  2. https://www.jstor.org/stable/2729411
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