What Justifies Using a Single SD for All Measurements in a Dataset?

[Niles]

Hi

Ok, we all know that if a quantity T is measured N times, then all measurements have the same standard deviation (SD). Now, with this assumption one can derive the width of the average to get SD/sqrt(N).

I have often encountered a dataset D, where each measurement has been assigned no SD. Then one finds the SD for the whole dataset, and then the author uses SD/sqrt(N) to find the width of the average of D.

My question is: In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements, such that one can use SD/sqrt(N)?

I hope you understand.


Niles.

 

[statdad]

"In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements"

The assumption that all the values in the data set come from the same population - one having a constant standard deviation.

 

[Niles]

Thanks, that makes sense.

Best wishes,
Niles.