An interesting read - mathematical approach to estimate of errors

[IconicPCB]

Stumbled into this article; thought it an interesting light read.

https://www.edn.com/a-mathematical-approach-to-estimate-probable-errors-in-a-measurement-task/?utm_source=newsletter&utm_campaign=link&utm_medium=EDNTestMeasure-20201116

[guenthert]

I don't know.

"Probable error of direct measurements

The probable error, r, of a single measurement of a series, is a quantity in which one half of the errors of the series are greater than it and the other half less than it. For a direct measurement, the probable error can be computed using the formula:

r = 0.6745 √ ((v1 2 + v2 2 +⋅⋅⋅ ….vn 2) / n-1)"

Sorry, I have difficulties with texts using magic numbers like that.  How did they arrive at that formula and where does 0.6745 come from?

[Mechatrommer]

long story... http://www.spcpress.com/books.php
short story...

That is the value that defines where 50% of the values lie for a normal distribution.  Within +- 0.675 standard deviation of the mean.  See figure 5.

if that rings any bells...
https://www.spcforexcel.com/knowledge/measurement-systems-analysis/probable-error-and-your-measurement-system
https://en.wikipedia.org/wiki/Probable_error

ps: we can believe whatever we want, thats why some people hate school, because they cant believe whatever they want... statistics is an science to represent art into numbers, only if i say it correctly, imho... (not directly relating to anything in this thread) cheers.