<s>
In	O
statistics	O
,	O
almost	B-General_Concept
sure	I-General_Concept
hypothesis	I-General_Concept
testing	I-General_Concept
or	O
a.s.	O
hypothesis	O
testing	O
utilizes	O
almost	O
sure	O
convergence	O
in	O
order	O
to	O
determine	O
the	O
validity	O
of	O
a	O
statistical	O
hypothesis	O
with	O
probability	O
one	O
.	O
</s>
<s>
This	O
is	O
to	O
say	O
that	O
whenever	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
then	O
an	O
a.s.	O
hypothesis	O
test	O
will	O
fail	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
w.p.	O
</s>
<s>
Similarly	O
,	O
whenever	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
then	O
an	O
a.s.	O
hypothesis	O
test	O
will	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
with	O
probability	O
one	O
,	O
for	O
all	O
sufficiently	O
large	O
samples	O
.	O
</s>
<s>
The	O
posterior	O
probability	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
high	O
,	O
indicating	O
strong	O
evidence	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
in	O
better	O
agreement	O
with	O
the	O
data	O
than	O
is	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
