<s>
The	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
test	I-General_Concept
is	O
a	O
statistical	O
test	O
of	O
whether	O
a	O
given	O
sample	O
of	O
data	O
is	O
drawn	O
from	O
a	O
given	O
probability	O
distribution	O
.	O
</s>
<s>
K-sample	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
tests	I-General_Concept
are	O
available	O
for	O
testing	O
whether	O
several	O
collections	O
of	O
observations	O
can	O
be	O
modelled	O
as	O
coming	O
from	O
a	O
single	O
population	O
,	O
where	O
the	O
distribution	O
function	O
does	O
not	O
have	O
to	O
be	O
specified	O
.	O
</s>
<s>
quadratic	O
EDF	B-General_Concept
statistics	O
(	O
tests	O
based	O
on	O
the	O
empirical	B-General_Concept
distribution	I-General_Concept
function	I-General_Concept
)	O
.	O
</s>
<s>
is	O
the	O
Cramér	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
statistic	I-General_Concept
.	O
</s>
<s>
Thus	O
,	O
compared	O
with	O
the	O
Cramér	B-General_Concept
–	I-General_Concept
von	I-General_Concept
Mises	I-General_Concept
distance	I-General_Concept
,	O
the	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
distance	O
places	O
more	O
weight	O
on	O
observations	O
in	O
the	O
tails	O
of	O
the	O
distribution	O
.	O
</s>
<s>
The	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
test	I-General_Concept
assesses	O
whether	O
a	O
sample	O
comes	O
from	O
a	O
specified	O
distribution	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
can	O
then	O
be	O
compared	O
against	O
the	O
critical	O
values	O
of	O
the	O
theoretical	O
distribution	O
.	O
</s>
<s>
Essentially	O
the	O
same	O
test	B-General_Concept
statistic	I-General_Concept
can	O
be	O
used	O
in	O
the	O
test	O
of	O
fit	O
of	O
a	O
family	O
of	O
distributions	O
,	O
but	O
then	O
it	O
must	O
be	O
compared	O
against	O
the	O
critical	O
values	O
appropriate	O
to	O
that	O
family	O
of	O
theoretical	O
distributions	O
and	O
dependent	O
also	O
on	O
the	O
method	O
used	O
for	O
parameter	O
estimation	O
.	O
</s>
<s>
Empirical	O
testing	O
has	O
found	O
that	O
the	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
test	I-General_Concept
is	O
not	O
quite	O
as	O
good	O
as	O
the	O
Shapiro	B-General_Concept
–	I-General_Concept
Wilk	I-General_Concept
test	I-General_Concept
,	O
but	O
is	O
better	O
than	O
other	O
tests	O
.	O
</s>
<s>
Stephens	O
found	O
to	O
be	O
one	O
of	O
the	O
best	O
empirical	B-General_Concept
distribution	I-General_Concept
function	I-General_Concept
statistics	O
for	O
detecting	O
most	O
departures	O
from	O
normality	O
.	O
</s>
<s>
The	O
formulas	O
for	O
computing	O
the	O
p-values	B-General_Concept
for	O
other	O
values	O
of	O
are	O
given	O
in	O
Table	O
4.9	O
on	O
p.127	O
in	O
the	O
same	O
book	O
.	O
</s>
<s>
Any	O
other	O
family	O
of	O
distributions	O
can	O
be	O
tested	O
but	O
the	O
test	O
for	O
each	O
family	O
is	O
implemented	O
by	O
using	O
a	O
different	O
modification	O
of	O
the	O
basic	O
test	B-General_Concept
statistic	I-General_Concept
and	O
this	O
is	O
referred	O
to	O
critical	O
values	O
specific	O
to	O
that	O
family	O
of	O
distributions	O
.	O
</s>
<s>
Details	O
for	O
the	O
required	O
modifications	O
to	O
the	O
test	B-General_Concept
statistic	I-General_Concept
and	O
for	O
the	O
critical	O
values	O
for	O
the	O
normal	O
distribution	O
and	O
the	O
exponential	O
distribution	O
have	O
been	O
published	O
by	O
Pearson	O
&	O
Hartley	O
(	O
1972	O
,	O
Table	O
54	O
)	O
.	O
</s>
<s>
Fritz	O
Scholz	O
and	O
Michael	O
A	O
.	O
Stephens	O
(	O
1987	O
)	O
discuss	O
a	O
test	O
,	O
based	O
on	O
the	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
measure	O
of	O
agreement	O
between	O
distributions	O
,	O
for	O
whether	O
a	O
number	O
of	O
random	O
samples	O
with	O
possibly	O
different	O
sample	O
sizes	O
may	O
have	O
arisen	O
from	O
the	O
same	O
distribution	O
,	O
where	O
this	O
distribution	O
is	O
unspecified	O
.	O
</s>
<s>
The	O
R	B-Language
package	I-Language
kSamples	O
and	O
the	O
Python	B-Language
package	O
Scipy	B-Application
implements	O
this	O
rank	O
test	O
for	O
comparing	O
k	O
samples	O
among	O
several	O
other	O
such	O
rank	O
tests	O
.	O
</s>
