Difference Between Standard Deviation and Standard Error

Difference Between Standard Deviation and Standard Error

Even if you aren’t a math genius, at least you should still know difference between standard deviation and standard error. Due to their thinly – separated meanings, the terms often confuse a lot of people. In fact, majority of men on the streets actually can’t tell the exact distinctions that part the terms. Well, ignorance isn’t an excuse. Just like how the earth rotates around the sun, good statisticians rotate around these terms, as their lives depend on them.

This topic may involve a little bit of math, but don’t be scared. Since most students are curious about this topic, we are going to discuss and touch on salient points, but not to bore you with complex numbers and formulae. At the end of the presentation, each and every one would get to know the simplicity of this topic.  Difference between standard deviation and standard error of the mean will not be tricky again.

If you want to fully understand a statistic, you can’t do that by relying on only the mean. It doesn’t give more information about the actual characteristics of the individual values which contribute to the mean. This is where SD and SE come in. When applied, SD will dig into the details of the general data scatter. This will help you to know the proximity of data with regard to mean. More importantly, the SD will assist you to picture how the distribution is shaped like.

Finally, when SE comes into play, interpretations become more interesting. It will accurately predict the closeness of sample mean to the actual mean – in this case, it captures the total population. Factually speaking, SE communicates to us about the mean’s reliability.  A smaller SE implies that population mean has been accurately reflected by the sample mean.

Definition of Standard Deviation

To give you a clearer picture and narrow down the scope, SD is a statiscal terminology. It’s a numerical figure which measures degree of scatter. Thus, it absolutely measures dispersion.  Owing to its close association with other key terms such as means, SD is frequently misinterpreted. This misunderstanding must be addressed as soon as possible. It’s true that the terms are like twins, but they aren’t identical twins – big differences separate them.

Standard error of the mean and standard deviation difference is about to be captured by your fingertips. But let’s expend more effort in trying to decipher the definition. In the end, this knowledge will prove very beneficial in future math research works. The temptation to introduce a math formula here is really high, but we can still do it without writing long formulae.

When the variance is taken and raised to the power of a half (1/2), SD is obtained. Thus, SD = √ (variance). When SD is calculated wholly, the sigma symbol “σ” stands for SD. What is the difference between standard deviation and standard error? Knowledge of this area becomes necessary when interpreting numerical results.

Definition of Standard Error

In order for you to grasp standard deviation and standard error difference, you have got to understand that, sometimes SD and SE get stuck to each other and become virtually the same.

Examples, assuming you are undertaking a research project to find HIV infections in a community. You may not be able to individually test all the community members. But you can collect samples of a fraction of the community.

When you do this for different number of times, you end up getting different mean (average) infection rates. Carefully distribute these means and you end up realizing that the SD obtained will be equivalent to SE.  Mathematically, SE = σ/√n

Standard Deviation vs Standard Error Comparison Table

So far, a lot of important points have already been discussed about this. But what is the difference between standard error and standard deviation? The answers can be found in the following table.

Basis of Comparison Standard Deviation Standard Error
Definition Measures dispersionEstimates the sample mean’s precision
Formula SD = √variance SE = σ/√n
Uses It is used to predicts how measurements are spread with respect to the average value Making an inference  from statistics
Symbols SD, σ SE, σx̅
Accuracy Less accurate More accurate

Conclusion of the Main Difference Between Standard Deviation vs Standard Error

Having followed the above discussion, what’s the difference between standard error and standard deviation? Surprisingly, when you look with good mathematical eyes, you would be able to see the vast differences here. SD and SE may have a lot (in common) to do with the mean, but they aren’t exactly equals. The latter is a more accurate way of estimating samples. When you carefully examine their mathematical formulae, one will quickly understand that SE = σ/√n.

This means that, SE varies proportionally (directly) with SD. This direct proportion relationship doesn’t necessarily make them to be equals. Putting that aside (keeping SD constant), SE varies inversely with (n). There you go! Never bow down to the complexities of the topic. When you take your time to revisit your basic math, you will realize that the difference between standard error and standard deviation is as easy as taking breakfast.

To further cast all doubts away, be reminded that the “mangrove may dwell in the river, but that doesn’t make it a crocodile”. Similarly, SD may hide its face by dwelling in the mean, but that doesn’t make it to be an SE equivalent. It’s so easy for anybody to understand that SD focuses on showing data dispersion. SE doesn’t concern itself with the degree of spreading of data. Rather, it’s a proper way of drawing inferences. Further differences can be found by looking at their mathematical symbols. By their symbols, you can differentiate them. SE has the symbol σx̅ while SD takes σ .

As outlined above, standard error and standard deviation difference isn’t as complex as most people see them to be. It’s said that chances favor the prepared mind. Never allow the information presented here to slip away because you may regret one day. This topic is one that you can’t run away from, especially if you are into math or statistics.

All it takes is patience and good will. One thing you shouldn’t forget is that, in most distributions, more than 90% of the values do not fall outside of 2 SDs. It will be a very bad idea for one to assume that SD or maybe SE is standardized. Hell No! There is no relation of that sort. When mention is made of these terms, start tuning your mind to symmetrical values. One big question is about when to apply SD or SE? For a statistical data that’s characteristic of a normal distribution, it’s wise to apply SD. But for a distorted data,   you can’t successfully apply SD.

The discussion on this topic will not be complete if we don’t attempt to grasp meanings that can be read into the magnitude of SD and SE values. Since they are numbers, sometimes their calculated values can really be high. In other times, they are very low. Higher magnitudes of SD values imply that the amount of scatter is less. Thus, the data values are very much dispersed. Similarly, for low magnitude SD, the data values near the average.

Just a simple question: Would you struggle if you are asked to state the unit of SD for a given data? That’s tricky but the answer is buried within the question itself – here is the statistical beauty of SD; its unit doesn’t differ from the expressed units of the data. SD is not a monopoly of statisticians; scientists also use it to report on research works.

Majority of scientists like to calculate the SD of experiments that involve numerical data. In this way, they concern themselves with effects that go above 2 deviations from expected result. This helps them to work out random errors from other effects. With this information presented here, you can’t raise your eyebrows at the mention of difference standard error and standard deviation

The usage of SD goes beyond the boundaries of science or statistics, and extends its arms to finance. In this field, the SD on the rate of ROI (return on investment) directly measures how volatile that investment is. Knowledge of this volatility can either motivate investors to invest their resources on a particular business or not. High volatility usually scares investors as it means that their investment can suddenly crash.

Many investors don’t take this big risk. For example, Warren Buffet and other wise investors prefer buying shares to cryptocurrencies; because their volatility is too high

SE also has practical applications, especially in uncertainty calculations.  The idea is that, if the SE of many quantities is determined, then it’s easier to calculate the SE of some quantities. In the same vein, when the probability of certain values are known, then the confidence interval becomes easier to determine.

Even in cases where probability isn’t known, it’s still possible to calculate the interval by using inequalities. In science and literature, data emerging from experiments are summarized by employing the mean and SE or SD. The common usage of these statistical couples is the reason behind their often confused interchangeability. But they are very different.

Admittedly, this topic has been treated extensively to give your brain the best possible preparation it needs to be able to iron out the difference between standard deviation and standard error. Now that you have won the battle of confusion surrounding the terms, you can walk away as a champion who is ready to take any exam on the subject.