<s>
A	O
test	B-General_Concept
statistic	I-General_Concept
is	O
a	O
statistic	O
(	O
a	O
quantity	O
derived	O
from	O
the	O
sample	O
)	O
used	O
in	O
statistical	O
hypothesis	O
testing	O
.	O
</s>
<s>
A	O
hypothesis	O
test	O
is	O
typically	O
specified	O
in	O
terms	O
of	O
a	O
test	B-General_Concept
statistic	I-General_Concept
,	O
considered	O
as	O
a	O
numerical	O
summary	O
of	O
a	O
data-set	O
that	O
reduces	O
the	O
data	O
to	O
one	O
value	O
that	O
can	O
be	O
used	O
to	O
perform	O
the	O
hypothesis	O
test	O
.	O
</s>
<s>
In	O
general	O
,	O
a	O
test	B-General_Concept
statistic	I-General_Concept
is	O
selected	O
or	O
defined	O
in	O
such	O
a	O
way	O
as	O
to	O
quantify	O
,	O
within	O
observed	O
data	O
,	O
behaviours	O
that	O
would	O
distinguish	O
the	O
null	B-General_Concept
from	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
,	O
where	O
such	O
an	O
alternative	O
is	O
prescribed	O
,	O
or	O
that	O
would	O
characterize	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
if	O
there	O
is	O
no	O
explicitly	O
stated	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
An	O
important	O
property	O
of	O
a	O
test	B-General_Concept
statistic	I-General_Concept
is	O
that	O
its	O
sampling	B-General_Concept
distribution	I-General_Concept
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
must	O
be	O
calculable	O
,	O
either	O
exactly	O
or	O
approximately	O
,	O
which	O
allows	O
p-values	B-General_Concept
to	O
be	O
calculated	O
.	O
</s>
<s>
A	O
test	B-General_Concept
statistic	I-General_Concept
shares	O
some	O
of	O
the	O
same	O
qualities	O
of	O
a	O
descriptive	B-General_Concept
statistic	I-General_Concept
,	O
and	O
many	O
statistics	O
can	O
be	O
used	O
as	O
both	O
test	B-General_Concept
statistics	I-General_Concept
and	O
descriptive	B-General_Concept
statistics	I-General_Concept
.	O
</s>
<s>
However	O
,	O
a	O
test	B-General_Concept
statistic	I-General_Concept
is	O
specifically	O
intended	O
for	O
use	O
in	O
statistical	O
testing	O
,	O
whereas	O
the	O
main	O
quality	O
of	O
a	O
descriptive	B-General_Concept
statistic	I-General_Concept
is	O
that	O
it	O
is	O
easily	O
interpretable	O
.	O
</s>
<s>
Some	O
informative	O
descriptive	B-General_Concept
statistics	I-General_Concept
,	O
such	O
as	O
the	O
sample	B-General_Concept
range	I-General_Concept
,	O
do	O
not	O
make	O
good	O
test	B-General_Concept
statistics	I-General_Concept
since	O
it	O
is	O
difficult	O
to	O
determine	O
their	O
sampling	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
Two	O
widely	O
used	O
test	B-General_Concept
statistics	I-General_Concept
are	O
the	O
t-statistic	O
and	O
the	O
F-test	B-General_Concept
.	O
</s>
<s>
But	O
T	O
can	O
also	O
be	O
used	O
as	O
a	O
test	B-General_Concept
statistic	I-General_Concept
in	O
one	O
of	O
two	O
ways	O
:	O
</s>
<s>
the	O
exact	O
sampling	B-General_Concept
distribution	I-General_Concept
of	O
T	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
the	O
binomial	O
distribution	O
with	O
parameters	O
0.5	O
and	O
100	O
.	O
</s>
<s>
the	O
value	O
of	O
T	O
can	O
be	O
compared	O
with	O
its	O
expected	O
value	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
50	O
,	O
and	O
since	O
the	O
sample	O
size	O
is	O
large	O
,	O
a	O
normal	O
distribution	O
can	O
be	O
used	O
as	O
an	O
approximation	O
to	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
either	O
for	O
T	O
or	O
for	O
the	O
revised	O
test	B-General_Concept
statistic	I-General_Concept
T50	O
.	O
</s>
<s>
Using	O
one	O
of	O
these	O
sampling	B-General_Concept
distributions	I-General_Concept
,	O
it	O
is	O
possible	O
to	O
compute	O
either	O
a	O
one-tailed	B-General_Concept
or	I-General_Concept
two-tailed	I-General_Concept
p-value	B-General_Concept
for	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
coin	O
is	O
fair	O
.	O
</s>
<s>
Note	O
that	O
the	O
test	B-General_Concept
statistic	I-General_Concept
in	O
this	O
case	O
reduces	O
a	O
set	O
of	O
100	O
numbers	O
to	O
a	O
single	O
numerical	O
summary	O
that	O
can	O
be	O
used	O
for	O
testing	O
.	O
</s>
<s>
Paired	B-General_Concept
tests	I-General_Concept
are	O
appropriate	O
for	O
comparing	O
two	O
samples	O
where	O
it	O
is	O
impossible	O
to	O
control	O
important	O
variables	O
.	O
</s>
<s>
The	O
common	O
example	O
scenario	O
for	O
when	O
a	O
paired	B-General_Concept
difference	I-General_Concept
test	I-General_Concept
is	O
appropriate	O
is	O
when	O
a	O
single	O
set	O
of	O
test	O
subjects	O
has	O
something	O
applied	O
to	O
them	O
and	O
the	O
test	O
is	O
intended	O
to	O
check	O
for	O
an	O
effect	O
.	O
</s>
<s>
Z-tests	B-General_Concept
are	O
appropriate	O
for	O
comparing	O
means	O
under	O
stringent	O
conditions	O
regarding	O
normality	O
and	O
a	O
known	O
standard	O
deviation	O
.	O
</s>
<s>
A	O
t-test	B-General_Concept
is	O
appropriate	O
for	O
comparing	O
means	O
under	O
relaxed	O
conditions	O
(	O
less	O
is	O
assumed	O
)	O
.	O
</s>
<s>
Chi-squared	B-General_Concept
tests	I-General_Concept
use	O
the	O
same	O
calculations	O
and	O
the	O
same	O
probability	O
distribution	O
for	O
different	O
applications	O
:	O
</s>
<s>
Chi-squared	B-General_Concept
tests	I-General_Concept
for	O
variance	O
are	O
used	O
to	O
determine	O
whether	O
a	O
normal	O
population	O
has	O
a	O
specified	O
variance	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
it	O
does	O
.	O
</s>
<s>
Chi-squared	B-General_Concept
tests	I-General_Concept
of	O
independence	O
are	O
used	O
for	O
deciding	O
whether	O
two	O
variables	O
are	O
associated	O
or	O
are	O
independent	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
variables	O
are	O
independent	O
.	O
</s>
<s>
The	O
numbers	O
used	O
in	O
the	O
calculation	O
are	O
the	O
observed	O
and	O
expected	O
frequencies	O
of	O
occurrence	O
(	O
from	O
contingency	B-Application
tables	I-Application
)	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
curve	O
fit	O
is	O
adequate	O
.	O
</s>
<s>
F-tests	B-General_Concept
(	O
analysis	O
of	O
variance	O
,	O
ANOVA	O
)	O
are	O
commonly	O
used	O
when	O
deciding	O
whether	O
groupings	O
of	O
data	O
by	O
category	O
are	O
meaningful	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
two	O
variances	O
are	O
the	O
same	O
–	O
so	O
the	O
proposed	O
grouping	O
is	O
not	O
meaningful	O
.	O
</s>
<s>
Proofs	O
exist	O
that	O
the	O
test	B-General_Concept
statistics	I-General_Concept
are	O
appropriate	O
.	O
</s>
<s>
Name	O
Formula	O
Assumptions	O
or	O
notesOne-sample	O
z-test(Normal population or n large )	O
and	O
σ	O
known	O
.	O
</s>
<s>
(	O
z	O
is	O
the	O
distance	O
from	O
the	O
mean	O
in	O
relation	O
to	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	I-General_Concept
the	I-General_Concept
mean	I-General_Concept
)	O
.	O
</s>
