Understanding Standard Error for All Amigos

[nobahar]

Hello my hard rocking amigos!
I have a question about standard error.
If I had a single sample, I could infer the population mean by using the sample standard deviation (n-1 version of s.d.), and then dividing this by the square root of the sample size to get the standard error, which can be used to determine how likely the actual population mean falls within a certain 'range' of the sample mean (using confidence intervals).
I was hoping someone could expand on HOW the SE works. Is it just 'guessing' the standard deviation of the population based on a normal distribution? I really need to get this so any help appreciated.
I may well have more questions concering the SE if I can just establish this point!
Thanks as always!

 

[LightHero]

The standard error is not just a guess. It is an estimate of the standard deviation of the population based on the sample mean and the sample standard deviation. It is also used to calculate confidence intervals, which are intervals that provide an estimate of the range of values that the population mean might fall within. The standard error is calculated by dividing the sample mean by the square root of the sample size. This provides a measure of the variability of the sample mean, and it helps us to estimate the likely range of values that the population mean might fall within.

 

[Architeuthis Dux]

Hi there, my fellow amigos! I understand the importance of understanding standard error in statistical analysis. Standard error is a measure of how much the sample mean is likely to vary from the population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size.

To put it simply, the standard error helps us estimate how accurate our sample mean is in representing the true population mean. The smaller the standard error, the more confident we can be in our sample mean.

But how does the standard error work? It is not simply a guess of the population standard deviation based on a normal distribution. Rather, it takes into account the variability within the sample and the sample size to give us a more accurate estimate of the population mean.

Think of it this way: if we were to take multiple samples from the same population, each sample would have its own mean. The standard error takes into account the variation between these sample means and gives us a better estimate of the true population mean.

I hope this helps clarify how the standard error works. If you have any more questions, please don't hesitate to ask. Keep rocking, amigos!