Backsights and default accuracy estimates

[Olly Betts]

On Thu, May 09, 2002 at 07:05:04PM +0100, M.J. Green wrote:
> Strictly with the grade 5 BCRA limits, errors should be called for greater
> than 2 degrees, for fore sight to back sight discrepancies.

That's true.  I'd not looked at it like this.

> I think that 2 s.d. equalling the BCRA grade is probably more apropriate.
> But that is just my random gut reaction, I like 2sds.
> If we assume that instruments reading follow a top hat probability
> distribution

Except that the corners aren't very square - the closer a value is to the edge,
the more likely it is to be read as the value below.  So 0.51 is nearly as
likely to be read as 0 than as 1.  0.55 a bit less so, and 0.9 is fairly
unlikely to be misread.  So you'll actually get something a lot more like a
normal distribution than a uniform one.

> then the most appropriate value to choose for 1 sd
> 3^-0.5 x the limit.  As this is the standard deviation of a top hat
> function.  This means that 1.73 s.d. = the BCRA limit.

Hmm, that would be another way to choose the "how many sds to regard the BCRA
limit as".

> I do not know how many standard deviations survex accepts before shouting.

Currently it's 3.  And at the other end, the BCRA grades are interpreted as 3
sd limits, so it cancels out in this case.  Except that the default grades are
approximately grade 4, not grade 5 as I probably intended...

> Perhaps this could be defined so that 2 degrees is when it shouts.

That's a thought.  At present, you get about 1.6 degrees, so if you read
to the half degree, it starts to shout at 2 anyway, but the test value could
be tuned to make this exactly true.

Cheers,
Olly