<s>
The	O
Shapiro	B-General_Concept
–	I-General_Concept
Wilk	I-General_Concept
test	I-General_Concept
is	O
a	O
test	B-General_Concept
of	I-General_Concept
normality	I-General_Concept
.	O
</s>
<s>
The	O
Shapiro	B-General_Concept
–	I-General_Concept
Wilk	I-General_Concept
test	I-General_Concept
tests	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
a	O
sample	O
x1	O
,	O
...	O
,	O
xn	O
came	O
from	O
a	O
normally	O
distributed	O
population	O
.	O
</s>
<s>
with	O
parentheses	O
enclosing	O
the	O
subscript	O
index	O
i	O
is	O
the	O
ith	O
order	B-General_Concept
statistic	I-General_Concept
,	O
i.e.	O
,	O
the	O
ith-smallest	O
number	O
in	O
the	O
sample	O
(	O
not	O
to	O
be	O
confused	O
with	O
)	O
.	O
</s>
<s>
is	O
made	O
of	O
the	O
expected	O
values	O
of	O
the	O
order	B-General_Concept
statistics	I-General_Concept
of	O
independent	O
and	O
identically	O
distributed	O
random	O
variables	O
sampled	O
from	O
the	O
standard	O
normal	O
distribution	O
;	O
finally	O
,	O
is	O
the	O
covariance	O
matrix	O
of	O
those	O
normal	O
order	B-General_Concept
statistics	I-General_Concept
.	O
</s>
<s>
The	O
cutoff	O
values	O
for	O
the	O
statistics	O
are	O
calculated	O
through	O
Monte	B-Algorithm
Carlo	I-Algorithm
simulations	I-Algorithm
.	O
</s>
<s>
The	O
null-hypothesis	B-General_Concept
of	O
this	O
test	O
is	O
that	O
the	O
population	O
is	O
normally	O
distributed	O
.	O
</s>
<s>
Thus	O
,	O
if	O
the	O
p	B-General_Concept
value	I-General_Concept
is	O
less	O
than	O
the	O
chosen	O
alpha	O
level	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
and	O
there	O
is	O
evidence	O
that	O
the	O
data	O
tested	O
are	O
not	O
normally	O
distributed	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
if	O
the	O
p	B-General_Concept
value	I-General_Concept
is	O
greater	O
than	O
the	O
chosen	O
alpha	O
level	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
that	O
the	O
data	O
came	O
from	O
a	O
normally	O
distributed	O
population	O
)	O
can	O
not	O
be	O
rejected	O
(	O
e.g.	O
,	O
for	O
an	O
alpha	O
level	O
of	O
.05	O
,	O
a	O
data	O
set	O
with	O
a	O
p	B-General_Concept
value	I-General_Concept
of	O
less	O
than	O
.05	O
rejects	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
data	O
are	O
from	O
a	O
normally	O
distributed	O
population	O
–	O
consequently	O
,	O
a	O
data	O
set	O
with	O
a	O
p	B-General_Concept
value	I-General_Concept
more	O
than	O
the	O
.05	O
alpha	O
value	O
fails	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
data	O
is	O
from	O
a	O
normally	O
distributed	O
population	O
)	O
.	O
</s>
<s>
Like	O
most	O
statistical	B-General_Concept
significance	I-General_Concept
tests	I-General_Concept
,	O
if	O
the	O
sample	O
size	O
is	O
sufficiently	O
large	O
this	O
test	O
may	O
detect	O
even	O
trivial	O
departures	O
from	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
i.e.	O
,	O
although	O
there	O
may	O
be	O
some	O
statistically	B-General_Concept
significant	I-General_Concept
effect	O
,	O
it	O
may	O
be	O
too	O
small	O
to	O
be	O
of	O
any	O
practical	O
significance	B-General_Concept
)	O
;	O
thus	O
,	O
additional	O
investigation	O
of	O
the	O
effect	O
size	O
is	O
typically	O
advisable	O
,	O
e.g.	O
,	O
a	O
Q	B-Application
–	I-Application
Q	I-Application
plot	I-Application
in	O
this	O
case	O
.	O
</s>
<s>
Monte	B-Algorithm
Carlo	I-Algorithm
simulation	I-Algorithm
has	O
found	O
that	O
Shapiro	O
–	O
Wilk	O
has	O
the	O
best	O
power	B-General_Concept
for	O
a	O
given	O
significance	B-General_Concept
,	O
followed	O
closely	O
by	O
Anderson	B-General_Concept
–	I-General_Concept
Darling	I-General_Concept
when	O
comparing	O
the	O
Shapiro	O
–	O
Wilk	O
,	O
Kolmogorov	B-General_Concept
–	I-General_Concept
Smirnov	I-General_Concept
,	O
and	O
Lilliefors	B-General_Concept
.	O
</s>
