# [QUANTITY] Why quantities always have errors

Ed Shaya Edward.J.Shaya.1 at gsfc.nasa.gov
Tue Nov 18 07:12:51 PST 2003

```Mark,
Interesting model.  Does anyone have a UML diagram of a frame?
Also, don't we automatically get a tuple if we just say quantity
aggregates Value and Error?  As a humorous aside, I prefer to reserve
the word vector for the physics/math term of an amplitude plus direction
and use tuple for a tightly coupled set of numbers.   Perhaps we need to
start using UCD2-like terms phys:vector and cs:vector?

I would like to know first what things are going to be in the Error
before I can know what sort of beast it is.  We should create a wish
list of things that COULD go into an Error object.  Then we can go over
it and strike things that are either too rare to bother with or just too
complicated.  Here is my wish list:

positiveError:  error bar to the plus side
negativeError:  error bar to the minus side
Error:  for symmetric error bars
sigma:  number of standard deviations that the  Error represents
confidence:  percentage confidence level that the Error represents
distributionFunction:  gaussian, laurentzian, hat-function, etc

PgtV: Sometimes error is presented as the probability of exceeding  the
given value
PltV:  or not reaching the given value

And, one may have the entire probability function as the quantity in the
Error.

All of the above for each of
randomError: Error resulting from finite precision of the measurement
systematicError:  inaccuracy intoduced by faulty equipment, calibration,
or technique.
significantFigures: number of significant digits in the number

We also need to deal with the issue of an upperLimit or lowerLimit,
[which, by the way, usually does not have an error because it is either
the error or a measured value plus an error.  But, it can have an error
which is actually the error-on-the-error.]

Ed

Mark Cresitello-Dittmar wrote:

> Hi,
>
> Brian.. in your model, is ERROR required to have the same
> dimensionality,units,Frames as the Value it is associated with?
>
> If it does, I don't think I like it.
> If it doesn't then it is in itself a QUANTITY cuz it has
>  dimensionality, units, frames, etc..
> If error it is a quantity, then it would have an error? (ExactNoError?)
>
> My current thinking for our model is to define a thing which has:
>   + Axis Frames (with Mappings between)  <- defines data axes
>   + Value Frames (with Mappings between) <- defines Units etc.
>
> This would be my 'Quantity', if I want to associate an error with this
> thing I could:
>   A) Make a quantity which is a vector of 2 quantities  1=value 2=error
>   B) Define a 'measurement' which has two quantities, a value and
>        associated error, and probably some other stuff...
>
> Two non-exclusive means of obtaining the same goal without requiring
> every 'value' to have an error, and allowing a lot of flexibility in
> defining the error since it doesn't need to have the same structure as
> the 'value' it is associated with.  One could have an error which is
> a vector of several 'flavors' of error (systematic, efficiency,...)
>
> Mark
>
>
>

```