<s>
In	O
statistics	O
,	O
the	O
reduced	B-General_Concept
chi-square	I-General_Concept
statistic	O
is	O
used	O
extensively	O
in	O
goodness	O
of	O
fit	O
testing	O
.	O
</s>
<s>
It	O
is	O
also	O
known	O
as	O
mean	O
squared	O
weighted	O
deviation	B-General_Concept
(	O
MSWD	O
)	O
in	O
isotopic	O
dating	O
and	O
variance	B-General_Concept
of	I-General_Concept
unit	I-General_Concept
weight	I-General_Concept
in	O
the	O
context	O
of	O
weighted	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
.	O
</s>
<s>
where	O
the	O
chi-squared	O
is	O
a	O
weighted	O
sum	O
of	O
squared	O
deviations	B-General_Concept
:	O
</s>
<s>
In	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
,	O
the	O
definition	O
simplifies	O
to	O
:	O
</s>
<s>
where	O
the	O
numerator	O
is	O
the	O
residual	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
squares	I-Algorithm
(	O
RSS	O
)	O
.	O
</s>
<s>
When	O
the	O
fit	O
is	O
just	O
an	O
ordinary	O
mean	O
,	O
then	O
equals	O
the	O
sample	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
When	O
the	O
variance	O
of	O
the	O
measurement	O
error	O
is	O
only	O
partially	O
known	O
,	O
the	O
reduced	B-General_Concept
chi-squared	I-General_Concept
may	O
serve	O
as	O
a	O
correction	O
estimated	O
a	O
posteriori	O
.	O
</s>
<s>
The	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
the	O
square	O
root	O
of	O
the	O
variance	O
.	O
</s>
<s>
Again	O
,	O
the	O
corresponding	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
the	O
square	O
root	O
of	O
the	O
variance	O
.	O
</s>
<s>
The	O
unweighted	O
mean	O
square	O
of	O
the	O
weighted	O
deviations	B-General_Concept
(	O
unweighted	O
MSWD	O
)	O
can	O
then	O
be	O
computed	O
,	O
as	O
follows	O
:	O
</s>
<s>
By	O
analogy	O
,	O
the	O
weighted	O
mean	O
square	O
of	O
the	O
weighted	O
deviations	B-General_Concept
(	O
weighted	O
MSWD	O
)	O
can	O
be	O
computed	O
as	O
follows	O
:	O
</s>
<s>
In	O
data	O
analysis	O
based	O
on	O
the	O
Rasch	O
Model	O
,	O
the	O
reduced	B-General_Concept
chi-squared	I-General_Concept
statistic	I-General_Concept
is	O
called	O
the	O
outfit	O
mean-square	O
statistic	O
,	O
and	O
the	O
information-weighted	O
reduced	B-General_Concept
chi-squared	I-General_Concept
statistic	I-General_Concept
is	O
called	O
the	O
infit	O
mean-square	O
statistic	O
.	O
</s>
