<s>
Named	O
after	O
the	O
Dutch	O
mathematician	O
Bartel	O
Leendert	O
van	O
der	O
Waerden	O
,	O
the	O
Van	B-General_Concept
der	I-General_Concept
Waerden	I-General_Concept
test	I-General_Concept
is	O
a	O
statistical	O
test	O
that	O
k	O
population	O
distribution	O
functions	O
are	O
equal	O
.	O
</s>
<s>
The	O
Van	B-General_Concept
der	I-General_Concept
Waerden	I-General_Concept
test	I-General_Concept
converts	O
the	O
ranks	O
from	O
a	O
standard	O
Kruskal-Wallis	B-General_Concept
one-way	I-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
to	O
quantiles	O
of	O
the	O
standard	O
normal	O
distribution	O
(	O
details	O
given	O
below	O
)	O
.	O
</s>
<s>
Analysis	B-General_Concept
of	I-General_Concept
Variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
is	O
a	O
data	B-General_Concept
analysis	I-General_Concept
technique	O
for	O
examining	O
the	O
significance	O
of	O
the	O
factors	O
(	O
independent	O
variables	O
)	O
in	O
a	O
multi-factor	O
model	O
.	O
</s>
<s>
The	O
one	O
factor	O
model	O
can	O
be	O
thought	O
of	O
as	O
a	O
generalization	O
of	O
the	O
two	B-General_Concept
sample	I-General_Concept
t-test	I-General_Concept
.	O
</s>
<s>
That	O
is	O
,	O
the	O
two	B-General_Concept
sample	I-General_Concept
t-test	I-General_Concept
is	O
a	O
test	O
of	O
the	O
hypothesis	O
that	O
two	O
population	O
means	O
are	O
equal	O
.	O
</s>
<s>
The	O
one	O
factor	O
ANOVA	B-General_Concept
tests	O
the	O
hypothesis	O
that	O
k	O
population	O
means	O
are	O
equal	O
.	O
</s>
<s>
The	O
standard	O
ANOVA	B-General_Concept
assumes	O
that	O
the	O
errors	O
(	O
i.e.	O
,	O
residuals	O
)	O
are	O
normally	O
distributed	O
.	O
</s>
<s>
If	O
this	O
normality	O
assumption	O
is	O
not	O
valid	O
,	O
an	O
alternative	O
is	O
to	O
use	O
a	O
non-parametric	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
Van	B-General_Concept
der	I-General_Concept
Waerden	I-General_Concept
test	I-General_Concept
can	O
then	O
be	O
defined	O
as	O
follows	O
:	O
</s>
<s>
If	O
the	O
hypothesis	O
of	O
identical	O
distributions	O
is	O
rejected	O
,	O
one	O
can	O
perform	O
a	O
multiple	B-General_Concept
comparisons	I-General_Concept
procedure	O
to	O
determine	O
which	O
pairs	O
of	O
populations	O
tend	O
to	O
differ	O
.	O
</s>
<s>
The	O
most	O
common	O
non-parametric	B-General_Concept
test	I-General_Concept
for	O
the	O
one-factor	O
model	O
is	O
the	O
Kruskal-Wallis	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
Kruskal-Wallis	B-General_Concept
test	I-General_Concept
is	O
based	O
on	O
the	O
ranks	O
of	O
the	O
data	O
.	O
</s>
<s>
The	O
advantage	O
of	O
the	O
Van	B-General_Concept
Der	I-General_Concept
Waerden	I-General_Concept
test	I-General_Concept
is	O
that	O
it	O
provides	O
the	O
high	O
efficiency	O
of	O
the	O
standard	O
ANOVA	B-General_Concept
analysis	O
when	O
the	O
normality	O
assumptions	O
are	O
in	O
fact	O
satisfied	O
,	O
but	O
it	O
also	O
provides	O
the	O
robustness	O
of	O
the	O
Kruskal-Wallis	B-General_Concept
test	I-General_Concept
when	O
the	O
normality	O
assumptions	O
are	O
not	O
satisfied	O
.	O
</s>
