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Revert "Updated error propagation page. re #9690"
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This reverts commit ae47f9f.
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Anders-Markvardsen committed Jul 21, 2014
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2 changes: 0 additions & 2 deletions Code/Mantid/docs/source/algorithms/BinaryOperation.txt
Expand Up @@ -10,8 +10,6 @@ Workspaces are compatible if:
* the units of the axes match
* the distribution status/counts units match

For information about how errors are handled and propagated see :ref:`Error Propagation`.

Compatible Sizes
################

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38 changes: 20 additions & 18 deletions Code/Mantid/docs/source/concepts/Error_Propagation.rst
Expand Up @@ -9,43 +9,45 @@ Propogation and how it is used in its algorithms.
Theory
------

In order to deal with error propagation, Mantid treats errors as guassian
probabilities (also known as a bell curve or normal probabilities) and each
observation as independent. Meaning that if X = 100 +- 1 then it is still
possible for a value of 102 to occur, but less likely than 101 or 99, and a
value of 105 is far less likely still than any of these values.
In order to deal with error propagation, Mantid treats errors as a
guassian curve (also known as a bell curve or normal curve). Meaning
that if X = 100 +- 1 then it is still possible for a value of 102 to
occur, but far less likely than 101 or 99, then a value of 105 is far
less likely still than 102, and then 110 is simply unheard of.

This allows Mantid to work with the errors quite simply.

Plus and Minus Algorithm
------------------------

The plus algorithm adds a selection of datasets together, including their
margin of errors. Mantid has to therefore adapt the margin of error so it
continues to work with just one margin of error. The way it does this is by
simply adding together the certain values. Consider the example where:
X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2. Then for the Plus algorithm
The plus algorithm adds a selection of datasets together, including
their margin of errors. Mantid has to therefore adapt the margin of
error so it continues to work with just one margin of error. The way it
does this is by simply adding together the certain values, for this
example we will use X\ :sub:`1` and X\ :sub:`2`. X\ :sub:`1` = 101 ± 2
and X\ :sub:`2` = 99 ± 2, Just to make it easier. Mantid takes the
average of the two definite values, 101 and 99.

X = 200 = (101 + 99).

The propagated error is calculated by taking the root of the sum of the
squares of the two error margins:
The average of the error is calculated by taking the root of the sum of
the squares of the two error margins:

(√2:sup:`2` + 2\ :sup:`2`) = √8

Hence the result of the Plus algorithm can be summarised as:

X = 200 ± √8

Mantid deals with the Minus algorithm similarly.
Mantid deals with the minus algorithm similarly, doing the inverse
function of Plus.

Multiply and Divide Algorithm
-----------------------------

The Multiply and Divide Algorithm work slightly different from the Plus
and Minus Algorithms, in the sense that they have to be more complex,
see also `here <http://en.wikipedia.org/wiki/Propagation_of_uncertainty>`_.
and Minus Algorithms, in the sense that they have to be more complex.

To calculate error propagation, of say X\ :sub:`1` and X\ :sub:`2`.
X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 ,Mantid would
X\ :sub:`1` = 101 ± 2 and X\ :sub:`2` = 99 ± 2 again, Mantid would
undertake the following calculation for divide:

Q = X\ :sub:`1`/X:sub:`2` = 101/99
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