<s>
In	O
statistics	O
,	O
Grubbs	B-General_Concept
's	I-General_Concept
test	I-General_Concept
or	O
the	O
Grubbs	O
test	O
(	O
named	O
after	O
Frank	O
E	O
.	O
Grubbs	O
,	O
who	O
published	O
the	O
test	O
in	O
1950	O
)	O
,	O
also	O
known	O
as	O
the	O
maximum	O
normalized	O
residual	O
test	O
or	O
extreme	O
studentized	O
deviate	O
test	O
,	O
is	O
a	O
test	O
used	O
to	O
detect	O
outliers	O
in	O
a	O
univariate	B-General_Concept
data	O
set	O
assumed	O
to	O
come	O
from	O
a	O
normally	O
distributed	O
population	O
.	O
</s>
<s>
Grubbs	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
based	O
on	O
the	O
assumption	O
of	O
normality	O
.	O
</s>
<s>
Grubbs	B-General_Concept
's	I-General_Concept
test	I-General_Concept
detects	O
one	O
outlier	O
at	O
a	O
time	O
.	O
</s>
<s>
Grubbs	B-General_Concept
's	I-General_Concept
test	I-General_Concept
is	O
defined	O
for	O
the	O
hypothesis	O
:	O
</s>
<s>
with	O
and	O
denoting	O
the	O
sample	O
mean	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
,	O
respectively	O
.	O
</s>
<s>
The	O
Grubbs	O
test	O
statistic	O
is	O
the	O
largest	O
absolute	O
deviation	O
from	O
the	O
sample	O
mean	O
in	O
units	O
of	O
the	O
sample	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
with	O
tα/	O
( 2N	O
)	O
,	O
N−2	O
denoting	O
the	O
upper	O
critical	O
value	O
of	O
the	O
t-distribution	O
with	O
N−2	O
degrees	O
of	O
freedom	O
and	O
a	O
significance	B-General_Concept
level	I-General_Concept
of	O
α/	O
( 2N	O
)	O
.	O
</s>
<s>
The	O
Grubbs	O
test	O
can	O
also	O
be	O
defined	O
as	O
a	O
one-sided	B-General_Concept
test	I-General_Concept
,	O
replacing	O
α/	O
( 2N	O
)	O
with	O
α/N	O
.	O
</s>
<s>
Several	O
graphical	B-Application
techniques	I-Application
can	O
be	O
used	O
to	O
detect	O
outliers	O
.	O
</s>
<s>
A	O
simple	O
run	O
sequence	O
plot	O
,	O
a	O
box	B-Application
plot	I-Application
,	O
or	O
a	O
histogram	B-Algorithm
should	O
show	O
any	O
obviously	O
outlying	O
points	O
.	O
</s>
<s>
A	O
normal	B-Application
probability	I-Application
plot	I-Application
may	O
also	O
be	O
useful	O
.	O
</s>
