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 if 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. After the end of the presentation, each and every one would get to know how extremely simple this topic is. Difference between standard deviation and standard error of the mean will not be tricky again. Let’s get into it.
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.. That is a big problem which needs to be addressed. 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 spend 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. Just to remind you of a basic math formula, SD = √(variance). When SD is calculated wholly, the sigma symbol ‘σ’ stands for SD. Previous knowledge of this fact is necessary when visualizing what is the difference between standard deviation and standard error?
Definition of Standard Error (SE)
It makes a lot of sense to say that SE can be determined from the SD. 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 and become virtually the same. Let’s take a look at a statistical scenario: Assuming you are undertaking a research project to find HIV infections in a community. You may not be able to individual test all the community members. But you 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.Having followed the above discussion, what’s the difference between standard error and standard deviation? Surprisingly, when you have good mathematical eyes or good statistical eyes, you would be able to see vast the 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 the sample size (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 equivalent of standard error. It’s so easy for anybody to understand that SD focuses on showing how data values are scattered (dispersed) about the mean value. SE doesn’t concern itself with the degree of spreading of data. Rather, it’s a more accurate method 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 σx̅while 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 can’t run away from, especially if you are into math or statistics.
The difference between standard deviation and standard error isn’t far-fetched. 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 has something to do with standards. Hell No! There is no relation of that sort. When mention is made of these terms, start tuning your mind to symmetrical values. Still confused about difference standard error and standard deviation?