> >>I don't understand. I'm following pretty exactly the calculations
> >>stated
> >>at <http://www.johndcook.com/blog/standard_deviation/>
> >>I'm not a statistician. Perhaps others who are more literate in
Maybe I'm mistaken here,
but I think, the algorithm is not that complicated.
I try to explain it further:
Comments appreciated.
Definition var_samp = Sum of squared differences /n-1
Definition stddev_samp = sqrt(var_samp)
Example N=4
1.) Sum of squared differences 1_4Sum(Xi-XM4)²
=
2.) adding nothing 1_4Sum(Xi-XM4)²+0+0+0
=
3.) nothing
changed1_4Sum(Xi-XM4)²+(-1_3Sum(Xi-XM3)²+1_3Sum(Xi-XM3)²)+(-1_2Sum(Xi-XM2)²+1_2Sum(Xi-XM3)²)+(-1_1Sum(Xi-XM2)²+1_1Sum(Xi-XM3)²)
=
4.) parts reordered
(1_4Sum(Xi-XM4)²-1_3Sum(Xi-XM3)²)+(1_3Sum(Xi-XM3)²-1_2Sum(Xi-XM2)²)+(1_2Sum(Xi-XM2)²-1_1Sum(Xi-XM2)²)+1_1Sum(X1-XM1)²
=
5.) (X4-XM4)(X4-XM3)
+ (X3-XM3)(X3-XM2)
+ (X2-XM2)(X2-XM1)
+ (X1-XM1)²
=
6.) XM1=X1 => There it is - The iteration part of Welfords Algorithm (in
reverse order) (X4-XM4)(X4-XM3)
+ (X3-XM3)(X3-XM2)
+ (X2-XM2)(X2-X1)
+ 0
The missing piece is 4.) to 5.)
it's algebra, look at e.g.:
http://jonisalonen.com/2013/deriving-welfords-method-for-computing-variance/
> Thanks. Still not quite sure what to do, though :-) I guess in the
> end we want the answer to come up with similar results to the builtin
> stddev SQL function. I'll try to set up a test program, to see if we do.
If you want to go this way:
Maybe this is one of the very few times, you have to use a small sample
;-)
VlG-Arne
> cheers
> andrew
> --
> Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org)
> To make changes to your subscription:
> http://www.postgresql.org/mailpref/pgsql-hackers
