<s>
Modern	O
significance	O
testing	O
is	O
largely	O
the	O
product	O
of	O
Karl	O
Pearson	O
(	O
p-value	B-General_Concept
,	O
Pearson	B-General_Concept
's	I-General_Concept
chi-squared	I-General_Concept
test	I-General_Concept
)	O
,	O
William	O
Sealy	O
Gosset	O
(	O
Student	O
's	O
t-distribution	O
)	O
,	O
and	O
Ronald	O
Fisher	O
(	O
"	O
null	B-General_Concept
hypothesis	I-General_Concept
"	O
,	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
,	O
"	O
significance	B-General_Concept
test	I-General_Concept
"	O
)	O
,	O
while	O
hypothesis	O
testing	O
was	O
developed	O
by	O
Jerzy	O
Neyman	O
and	O
Egon	O
Pearson	O
(	O
son	O
of	O
Karl	O
)	O
.	O
</s>
<s>
Fisher	O
popularized	O
the	O
"	O
significance	B-General_Concept
test	I-General_Concept
"	O
.	O
</s>
<s>
He	O
required	O
a	O
null-hypothesis	B-General_Concept
(	O
corresponding	O
to	O
a	O
population	O
frequency	O
distribution	O
)	O
and	O
a	O
sample	O
.	O
</s>
<s>
His	O
(	O
now	O
familiar	O
)	O
calculations	O
determined	O
whether	O
to	O
reject	O
the	O
null-hypothesis	B-General_Concept
or	O
not	O
.	O
</s>
<s>
Significance	O
testing	O
did	O
not	O
utilize	O
an	O
alternative	B-General_Concept
hypothesis	I-General_Concept
so	O
there	O
was	O
no	O
concept	O
of	O
a	O
Type	O
II	O
error	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
was	O
devised	O
as	O
an	O
informal	O
,	O
but	O
objective	O
,	O
index	O
meant	O
to	O
help	O
a	O
researcher	O
determine	O
(	O
based	O
on	O
other	O
knowledge	O
)	O
whether	O
to	O
modify	O
future	O
experiments	O
or	O
strengthen	O
one	O
's	O
faith	B-Error_Name
in	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Hypothesis	O
testing	O
(	O
and	O
Type	O
I/II	O
errors	O
)	O
was	O
devised	O
by	O
Neyman	O
and	O
Pearson	O
as	O
a	O
more	O
objective	O
alternative	O
to	O
Fisher	O
's	O
p-value	B-General_Concept
,	O
also	O
meant	O
to	O
determine	O
researcher	O
behaviour	O
,	O
but	O
without	O
requiring	O
any	O
inductive	O
inference	O
by	O
the	O
researcher	O
.	O
</s>
<s>
Fisher	O
thought	O
that	O
it	O
was	O
not	O
applicable	O
to	O
scientific	O
research	O
because	O
often	O
,	O
during	O
the	O
course	O
of	O
the	O
experiment	O
,	O
it	O
is	O
discovered	O
that	O
the	O
initial	O
assumptions	O
about	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
are	O
questionable	O
due	O
to	O
unexpected	O
sources	O
of	O
error	O
.	O
</s>
<s>
Some	O
of	O
Neyman	O
's	O
later	O
publications	O
reported	O
p-values	B-General_Concept
and	O
significance	B-General_Concept
levels	I-General_Concept
.	O
</s>
<s>
Neyman	O
and	O
Pearson	O
provided	O
the	O
stronger	O
terminology	O
,	O
the	O
more	O
rigorous	O
mathematics	O
and	O
the	O
more	O
consistent	O
philosophy	O
,	O
but	O
the	O
subject	O
taught	O
today	O
in	O
introductory	O
statistics	O
has	O
more	O
similarities	O
with	O
Fisher	B-General_Concept
's	I-General_Concept
method	I-General_Concept
than	O
theirs	O
.	O
</s>
<s>
Sometime	O
around	O
1940	O
,	O
authors	O
of	O
statistical	O
text	O
books	O
began	O
combining	O
the	O
two	O
approaches	O
by	O
using	O
the	O
p-value	B-General_Concept
in	O
place	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
(	O
or	O
data	O
)	O
to	O
test	O
against	O
the	O
Neyman	O
–	O
Pearson	O
"	O
significance	B-General_Concept
level	I-General_Concept
"	O
.	O
</s>
<s>
+	O
A	O
comparison	O
between	O
Fisherian	O
,	O
frequentist	B-General_Concept
(	O
Neyman	O
–	O
Pearson	O
)	O
#	O
Fisher	O
's	O
null	B-General_Concept
hypothesis	I-General_Concept
testing	O
Neyman	O
–	O
Pearson	O
decision	O
theory	O
1	O
Set	O
up	O
a	O
statistical	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Paul	O
Meehl	O
has	O
argued	O
that	O
the	O
epistemological	O
importance	O
of	O
the	O
choice	O
of	O
null	B-General_Concept
hypothesis	I-General_Concept
has	O
gone	O
largely	O
unacknowledged	O
.	O
</s>
<s>
When	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
predicted	O
by	O
theory	O
,	O
a	O
more	O
precise	O
experiment	O
will	O
be	O
a	O
more	O
severe	O
test	O
of	O
the	O
underlying	O
theory	O
.	O
</s>
<s>
When	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
defaults	O
to	O
"	O
no	O
difference	O
"	O
or	O
"	O
no	O
effect	O
"	O
,	O
a	O
more	O
precise	O
experiment	O
is	O
a	O
less	O
severe	O
test	O
of	O
the	O
theory	O
that	O
motivated	O
performing	O
the	O
experiment	O
.	O
</s>
<s>
Thus	O
Laplace	O
's	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
birthrates	O
of	O
boys	O
and	O
girls	O
should	O
be	O
equal	O
given	O
"	O
conventional	O
wisdom	O
"	O
.	O
</s>
<s>
1900	O
:	O
Karl	O
Pearson	O
develops	O
the	O
chi	B-General_Concept
squared	I-General_Concept
test	I-General_Concept
to	O
determine	O
"	O
whether	O
a	O
given	O
form	O
of	O
frequency	O
curve	O
will	O
effectively	O
describe	O
the	O
samples	O
drawn	O
from	O
a	O
given	O
population.	O
"	O
</s>
<s>
Thus	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
a	O
population	O
is	O
described	O
by	O
some	O
distribution	O
predicted	O
by	O
theory	O
.	O
</s>
<s>
1904	O
:	O
Karl	O
Pearson	O
develops	O
the	O
concept	O
of	O
"	O
contingency	B-Application
"	O
in	O
order	O
to	O
determine	O
whether	O
outcomes	O
are	O
independent	O
of	O
a	O
given	O
categorical	O
factor	O
.	O
</s>
<s>
Here	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
by	O
default	O
that	O
two	O
things	O
are	O
unrelated	O
(	O
e.g.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
in	O
this	O
case	O
is	O
no	O
longer	O
predicted	O
by	O
theory	O
or	O
conventional	O
wisdom	O
,	O
but	O
is	O
instead	O
the	O
principle	O
of	O
indifference	O
that	O
led	O
Fisher	O
and	O
others	O
to	O
dismiss	O
the	O
use	O
of	O
"	O
inverse	O
probabilities	O
"	O
.	O
</s>
<s>
The	O
first	O
step	O
is	O
to	O
state	O
the	O
relevant	O
null	O
and	O
alternative	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
Decide	O
which	O
test	O
is	O
appropriate	O
,	O
and	O
state	O
the	O
relevant	O
test	B-General_Concept
statistic	I-General_Concept
T	O
.	O
</s>
<s>
Derive	O
the	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
from	O
the	O
assumptions	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
test	B-General_Concept
statistic	I-General_Concept
might	O
follow	O
a	O
Student	O
's	O
t	O
distribution	O
with	O
known	O
degrees	O
of	O
freedom	O
,	O
or	O
a	O
normal	O
distribution	O
with	O
known	O
mean	O
and	O
variance	O
.	O
</s>
<s>
If	O
the	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
is	O
completely	O
fixed	O
by	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
we	O
call	O
the	O
hypothesis	O
simple	O
,	O
otherwise	O
it	O
is	O
called	O
composite	O
.	O
</s>
<s>
Select	O
a	O
significance	B-General_Concept
level	I-General_Concept
( α	O
)	O
,	O
a	O
probability	O
threshold	O
below	O
which	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
will	O
be	O
rejected	O
.	O
</s>
<s>
The	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
partitions	O
the	O
possible	O
values	O
of	O
T	O
into	O
those	O
for	O
which	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
—	O
the	O
so-called	O
critical	O
region	O
—	O
and	O
those	O
for	O
which	O
it	O
is	O
not	O
.	O
</s>
<s>
The	O
probability	O
of	O
T	O
occurring	O
in	O
the	O
critical	O
region	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
α	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
composite	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
the	O
maximum	O
of	O
that	O
probability	O
is	O
α	O
.	O
</s>
<s>
Compute	O
from	O
the	O
observations	O
the	O
observed	O
value	O
tobs	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
T	O
.	O
</s>
<s>
Decide	O
to	O
either	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
in	O
favor	O
of	O
the	O
alternative	O
or	O
not	O
reject	O
it	O
.	O
</s>
<s>
The	O
decision	O
rule	O
is	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
H0	O
if	O
the	O
observed	O
value	O
tobs	O
is	O
in	O
the	O
critical	O
region	O
,	O
and	O
not	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
otherwise	O
.	O
</s>
<s>
Compute	O
from	O
the	O
observations	O
the	O
observed	O
value	O
tobs	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
T	O
.	O
</s>
<s>
Calculate	O
the	O
p-value	B-General_Concept
.	O
</s>
<s>
This	O
is	O
the	O
probability	O
,	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
of	O
sampling	O
a	O
test	B-General_Concept
statistic	I-General_Concept
at	O
least	O
as	O
extreme	O
as	O
that	O
which	O
was	O
observed	O
(	O
the	O
maximal	O
probability	O
of	O
that	O
event	O
,	O
if	O
the	O
hypothesis	O
is	O
composite	O
)	O
.	O
</s>
<s>
Reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
in	O
favor	O
of	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
,	O
if	O
and	O
only	O
if	O
the	O
p-value	B-General_Concept
is	O
less	O
than	O
(	O
or	O
equal	O
to	O
)	O
the	O
significance	B-General_Concept
level	I-General_Concept
(	O
the	O
selected	O
probability	O
)	O
threshold	O
( α	O
)	O
,	O
for	O
example	O
0.05	O
or	O
0.01	O
.	O
</s>
<s>
The	O
former	O
process	O
was	O
advantageous	O
in	O
the	O
past	O
when	O
only	O
tables	O
of	O
test	B-General_Concept
statistics	I-General_Concept
at	O
common	O
probability	O
thresholds	O
were	O
available	O
.	O
</s>
<s>
Not	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
does	O
not	O
mean	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
"	O
accepted	O
"	O
(	O
see	O
the	O
Interpretation	O
section	O
)	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
is	O
the	O
probability	O
that	O
a	O
given	O
result	O
(	O
or	O
a	O
more	O
significant	O
result	O
)	O
would	O
occur	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
At	O
a	O
significance	B-General_Concept
level	I-General_Concept
of	O
0.05	O
,	O
a	O
fair	O
coin	O
would	O
be	O
expected	O
to	O
(	O
incorrectly	O
)	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
that	O
it	O
is	O
fair	O
)	O
in	O
about	O
1	O
out	O
of	O
every	O
20	O
tests	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
does	O
not	O
provide	O
the	O
probability	O
that	O
either	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
or	O
its	O
opposite	O
is	O
correct	O
(	O
a	O
common	O
source	O
of	O
confusion	O
)	O
.	O
</s>
<s>
If	O
the	O
p-value	B-General_Concept
is	O
less	O
than	O
the	O
chosen	O
significance	O
threshold	O
(	O
equivalently	O
,	O
if	O
the	O
observed	O
test	B-General_Concept
statistic	I-General_Concept
is	O
in	O
the	O
critical	O
region	O
)	O
,	O
then	O
we	O
say	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
at	O
the	O
chosen	O
level	O
of	O
significance	O
.	O
</s>
<s>
If	O
the	O
p-value	B-General_Concept
is	O
not	O
less	O
than	O
the	O
chosen	O
significance	O
threshold	O
(	O
equivalently	O
,	O
if	O
the	O
observed	O
test	B-General_Concept
statistic	I-General_Concept
is	O
outside	O
the	O
critical	O
region	O
)	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
rejected	O
.	O
</s>
<s>
His	O
test	O
revealed	O
that	O
if	O
the	O
lady	O
was	O
effectively	O
guessing	O
at	O
random	O
(	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
,	O
there	O
was	O
a	O
1.4	O
%	O
chance	O
that	O
the	O
observed	O
results	O
(	O
perfectly	O
ordered	O
tea	O
)	O
would	O
occur	O
.	O
</s>
<s>
Rejecting	O
the	O
hypothesis	O
that	O
a	O
large	O
paw	O
print	O
originated	O
from	O
a	O
bear	O
does	O
not	O
immediately	O
prove	O
the	O
existence	O
of	O
Bigfoot	B-Device
.	O
</s>
<s>
"	O
The	O
probability	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
function	O
of	O
five	O
factors	O
:	O
whether	O
the	O
test	O
is	O
one	O
-	O
or	O
two-tailed	O
,	O
the	O
level	O
of	O
significance	O
,	O
the	O
standard	O
deviation	O
,	O
the	O
amount	O
of	O
deviation	O
from	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
and	O
the	O
number	O
of	O
observations.	O
"	O
</s>
<s>
effect	B-Application
size	I-Application
)	O
.	O
</s>
<s>
When	O
theory	O
is	O
only	O
capable	O
of	O
predicting	O
the	O
sign	O
of	O
a	O
relationship	O
,	O
a	O
directional	O
(	O
one-sided	O
)	O
hypothesis	O
test	O
can	O
be	O
configured	O
so	O
that	O
only	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
supports	O
theory	O
.	O
</s>
<s>
Multiple	O
testing	O
:	O
When	O
multiple	O
true	O
null	B-General_Concept
hypothesis	I-General_Concept
tests	O
are	O
conducted	O
at	O
once	O
without	O
adjustment	O
,	O
the	O
overall	O
probability	O
of	O
Type	O
I	O
error	O
is	O
higher	O
than	O
the	O
nominal	O
alpha	O
level	O
.	O
</s>
<s>
Test	B-General_Concept
statistic	I-General_Concept
:	O
A	O
value	O
calculated	O
from	O
a	O
sample	O
without	O
any	O
unknown	O
parameters	O
,	O
often	O
to	O
summarize	O
the	O
sample	O
for	O
comparison	O
purposes	O
.	O
</s>
<s>
Positive	O
data	O
:	O
Data	O
that	O
enable	O
the	O
investigator	O
to	O
reject	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Region	O
of	O
rejection	O
/	O
Critical	O
region	O
:	O
The	O
set	O
of	O
values	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
for	O
which	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
.	O
</s>
<s>
Size	O
:	O
For	O
simple	O
hypotheses	O
,	O
this	O
is	O
the	O
test	O
's	O
probability	O
of	O
incorrectly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
For	O
composite	O
hypotheses	O
this	O
is	O
the	O
supremum	O
of	O
the	O
probability	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
over	O
all	O
cases	O
covered	O
by	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
test	O
:	O
A	O
predecessor	O
to	O
the	O
statistical	O
hypothesis	O
test	O
(	O
see	O
the	O
Origins	O
section	O
)	O
.	O
</s>
<s>
An	O
experimental	O
result	O
was	O
said	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
if	O
a	O
sample	O
was	O
sufficiently	O
inconsistent	O
with	O
the	O
(	O
null	O
)	O
hypothesis	O
.	O
</s>
<s>
The	O
statistical	O
hypothesis	O
test	O
added	O
mathematical	O
rigor	O
and	O
philosophical	O
consistency	O
to	O
the	O
concept	O
by	O
making	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
explicit	O
.	O
</s>
<s>
Conservative	O
test	O
:	O
A	O
test	O
is	O
conservative	O
if	O
,	O
when	O
constructed	O
for	O
a	O
given	O
nominal	O
significance	B-General_Concept
level	I-General_Concept
,	O
the	O
true	O
probability	O
of	O
incorrectly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
never	O
greater	O
than	O
the	O
nominal	O
level	O
.	O
</s>
<s>
A	O
statistical	O
hypothesis	O
test	O
compares	O
a	O
test	B-General_Concept
statistic	I-General_Concept
(	O
z	O
or	O
t	O
for	O
examples	O
)	O
to	O
a	O
threshold	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
(	O
the	O
formula	O
found	O
in	O
the	O
table	O
below	O
)	O
is	O
based	O
on	O
optimality	O
.	O
</s>
<s>
For	O
a	O
fixed	O
level	O
of	O
Type	O
I	O
error	O
rate	O
,	O
use	O
of	O
these	O
statistics	O
minimizes	O
Type	O
II	O
error	O
rates	O
(	O
equivalent	O
to	O
maximizing	O
power	B-General_Concept
)	O
.	O
</s>
<s>
Most	O
powerful	O
test	O
:	O
For	O
a	O
given	O
size	O
or	O
significance	B-General_Concept
level	I-General_Concept
,	O
the	O
test	O
with	O
the	O
greatest	O
power	B-General_Concept
(	O
probability	O
of	O
rejection	O
)	O
for	O
a	O
given	O
value	O
of	O
the	O
parameter(s )	O
being	O
tested	O
,	O
contained	O
in	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
earliest	O
use	O
of	O
statistical	O
hypothesis	O
testing	O
is	O
generally	O
credited	O
to	O
the	O
question	O
of	O
whether	O
male	O
and	O
female	O
births	O
are	O
equally	O
likely	O
(	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
,	O
which	O
was	O
addressed	O
in	O
the	O
1700s	O
by	O
John	O
Arbuthnot	O
(	O
1710	O
)	O
,	O
and	O
later	O
by	O
Pierre-Simon	O
Laplace	O
(	O
1770s	O
)	O
.	O
</s>
<s>
Arbuthnot	O
examined	O
birth	O
records	O
in	O
London	O
for	O
each	O
of	O
the	O
82	O
years	O
from	O
1629	O
to	O
1710	O
,	O
and	O
applied	O
the	O
sign	B-General_Concept
test	I-General_Concept
,	O
a	O
simple	O
non-parametric	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Considering	O
more	O
male	O
or	O
more	O
female	O
births	O
as	O
equally	O
likely	O
,	O
the	O
probability	O
of	O
the	O
observed	O
outcome	O
is	O
0.582	O
,	O
or	O
about	O
1	O
in	O
4,836,000,000,000,000,000,000,000	O
;	O
in	O
modern	O
terms	O
,	O
this	O
is	O
the	O
p-value	B-General_Concept
.	O
</s>
<s>
In	O
modern	O
terms	O
,	O
he	O
rejected	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
equally	O
likely	O
male	O
and	O
female	O
births	O
at	O
the	O
p	O
=	O
1/282	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
He	O
concluded	O
by	O
calculation	O
of	O
a	O
p-value	B-General_Concept
that	O
the	O
excess	O
was	O
a	O
real	O
,	O
but	O
unexplained	O
,	O
effect	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
was	O
that	O
the	O
Lady	O
had	O
no	O
such	O
ability	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
was	O
a	O
simple	O
count	O
of	O
the	O
number	O
of	O
successes	O
in	O
selecting	O
the	O
4	O
cups	O
.	O
</s>
<s>
Fisher	O
asserted	O
that	O
no	O
alternative	B-General_Concept
hypothesis	I-General_Concept
was	O
(	O
ever	O
)	O
required	O
.	O
</s>
<s>
The	O
lady	O
correctly	O
identified	O
every	O
cup	O
,	O
which	O
would	O
be	O
considered	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
.	O
</s>
<s>
The	O
first	O
one	O
,	O
,	O
is	O
called	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
second	O
one	O
,	O
,	O
is	O
called	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
It	O
is	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
that	O
one	O
hopes	O
to	O
support	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
sample	O
originated	O
from	O
the	O
population	O
.	O
</s>
<s>
The	O
criterion	O
for	O
rejecting	O
the	O
null-hypothesis	B-General_Concept
is	O
the	O
"	O
obvious	O
"	O
difference	O
in	O
appearance	O
(	O
an	O
informal	O
difference	O
in	O
the	O
mean	O
)	O
.	O
</s>
<s>
As	O
we	O
try	O
to	O
find	O
evidence	O
of	O
their	O
clairvoyance	O
,	O
for	O
the	O
time	O
being	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
person	O
is	O
not	O
clairvoyant	O
.	O
</s>
<s>
If	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
valid	O
,	O
the	O
only	O
thing	O
the	O
test	O
person	O
can	O
do	O
is	O
guess	O
.	O
</s>
<s>
alternative	B-General_Concept
hypothesis	I-General_Concept
(	O
true	O
clairvoyant	O
)	O
.	O
</s>
<s>
When	O
the	O
test	O
subject	O
correctly	O
predicts	O
all	O
25	O
cards	O
,	O
we	O
will	O
consider	O
them	O
clairvoyant	O
,	O
and	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
no	O
radioactive	O
material	O
is	O
in	O
the	O
suitcase	O
and	O
that	O
all	O
measured	O
counts	O
are	O
due	O
to	O
ambient	O
radioactivity	O
typical	O
of	O
the	O
surrounding	O
air	O
and	O
harmless	O
objects	O
.	O
</s>
<s>
We	O
can	O
then	O
calculate	O
how	O
likely	O
it	O
is	O
that	O
we	O
would	O
observe	O
10	O
counts	O
per	O
minute	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
true	O
.	O
</s>
<s>
If	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
predicts	O
(	O
say	O
)	O
on	O
average	O
9	O
counts	O
per	O
minute	O
,	O
then	O
according	O
to	O
the	O
Poisson	O
distribution	O
typical	O
for	O
radioactive	O
decay	O
there	O
is	O
about	O
41%	O
chance	O
of	O
recording	O
10	O
or	O
more	O
counts	O
.	O
</s>
<s>
Thus	O
we	O
can	O
say	O
that	O
the	O
suitcase	O
is	O
compatible	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
this	O
does	O
not	O
guarantee	O
that	O
there	O
is	O
no	O
radioactive	O
material	O
,	O
just	O
that	O
we	O
do	O
n't	O
have	O
enough	O
evidence	O
to	O
suggest	O
there	O
is	O
)	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
predicts	O
3	O
counts	O
per	O
minute	O
(	O
for	O
which	O
the	O
Poisson	O
distribution	O
predicts	O
only	O
0.1	O
%	O
chance	O
of	O
recording	O
10	O
or	O
more	O
counts	O
)	O
then	O
the	O
suitcase	O
is	O
not	O
compatible	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
and	O
there	O
are	O
likely	O
other	O
factors	O
responsible	O
to	O
produce	O
the	O
measurements	O
.	O
</s>
<s>
The	O
double	O
negative	O
(	O
disproving	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
of	O
the	O
method	O
is	O
confusing	O
,	O
but	O
using	O
a	O
counter-example	O
to	O
disprove	O
is	O
standard	O
mathematical	O
practice	O
.	O
</s>
<s>
The	O
test	O
described	O
here	O
is	O
more	O
fully	O
the	O
null-hypothesis	B-General_Concept
statistical	B-General_Concept
significance	I-General_Concept
test	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
represents	O
what	O
we	O
would	O
believe	O
by	O
default	O
,	O
before	O
seeing	O
any	O
evidence	O
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
is	O
a	O
possible	O
finding	O
of	O
the	O
test	O
,	O
declared	O
when	O
the	O
observed	O
sample	O
is	O
unlikely	O
to	O
have	O
occurred	O
by	O
chance	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
true	O
.	O
</s>
<s>
One	O
characteristic	O
of	O
the	O
test	O
is	O
its	O
crisp	O
decision	O
:	O
to	O
reject	O
or	O
not	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Statistical	O
hypothesis	O
testing	O
is	O
a	O
key	O
technique	O
of	O
both	O
frequentist	B-General_Concept
inference	I-General_Concept
and	O
Bayesian	O
inference	O
,	O
although	O
the	O
two	O
types	O
of	O
inference	O
have	O
notable	O
differences	O
.	O
</s>
<s>
Statistical	O
hypothesis	O
tests	O
define	O
a	O
procedure	O
that	O
controls	O
(	O
fixes	O
)	O
the	O
probability	O
of	O
incorrectly	O
deciding	O
that	O
a	O
default	O
position	O
(	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
is	O
incorrect	O
.	O
</s>
<s>
The	O
procedure	O
is	O
based	O
on	O
how	O
likely	O
it	O
would	O
be	O
for	O
a	O
set	O
of	O
observations	O
to	O
occur	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
true	O
.	O
</s>
<s>
This	O
probability	O
of	O
making	O
an	O
incorrect	O
decision	O
is	O
not	O
the	O
probability	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
nor	O
whether	O
any	O
specific	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
This	O
contrasts	O
with	O
other	O
possible	O
techniques	O
of	O
decision	O
theory	O
in	O
which	O
the	O
null	O
and	O
alternative	B-General_Concept
hypothesis	I-General_Concept
are	O
treated	O
on	O
a	O
more	O
equal	O
basis	O
.	O
</s>
<s>
Other	O
approaches	O
to	O
decision	O
making	O
,	O
such	O
as	O
Bayesian	B-General_Concept
decision	I-General_Concept
theory	I-General_Concept
,	O
attempt	O
to	O
balance	O
the	O
consequences	O
of	O
incorrect	O
decisions	O
across	O
all	O
possibilities	O
,	O
rather	O
than	O
concentrating	O
on	O
a	O
single	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Extensions	O
to	O
the	O
theory	O
of	O
hypothesis	O
testing	O
include	O
the	O
study	O
of	O
the	O
power	B-General_Concept
of	O
tests	O
,	O
i.e.	O
</s>
<s>
the	O
probability	O
of	O
correctly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
given	O
that	O
it	O
is	O
false	O
.	O
</s>
<s>
An	O
example	O
of	O
Neyman	O
–	O
Pearson	O
hypothesis	O
testing	O
(	O
or	O
null	B-General_Concept
hypothesis	I-General_Concept
statistical	B-General_Concept
significance	I-General_Concept
testing	O
)	O
can	O
be	O
made	O
by	O
a	O
change	O
to	O
the	O
radioactive	O
suitcase	O
example	O
.	O
</s>
<s>
The	O
Neyman	O
–	O
Pearson	O
lemma	O
of	O
hypothesis	O
testing	O
says	O
that	O
a	O
good	O
criterion	O
for	O
the	O
selection	O
of	O
hypotheses	O
is	O
the	O
ratio	O
of	O
their	O
probabilities	O
(	O
a	O
likelihood	B-General_Concept
ratio	I-General_Concept
)	O
.	O
</s>
<s>
Null	B-General_Concept
hypotheses	I-General_Concept
should	O
be	O
at	O
least	O
falsifiable	O
.	O
</s>
<s>
A	O
likelihood	B-General_Concept
ratio	I-General_Concept
remains	O
a	O
good	O
criterion	O
for	O
selecting	O
among	O
hypotheses	O
.	O
</s>
<s>
The	O
original	O
test	O
is	O
analogous	O
to	O
a	O
true/false	O
question	O
;	O
the	O
Neyman	O
–	O
Pearson	B-General_Concept
test	I-General_Concept
is	O
more	O
like	O
multiple	O
choice	O
.	O
</s>
<s>
An	O
example	O
proved	O
the	O
optimality	O
of	O
the	O
(	O
Student	O
's	O
)	O
t-test	B-General_Concept
,	O
"	O
there	O
can	O
be	O
no	O
better	O
test	O
for	O
the	O
hypothesis	O
under	O
consideration	O
"	O
(	O
p	O
321	O
)	O
.	O
</s>
<s>
Hypothesis	O
testing	O
provides	O
a	O
means	O
of	O
finding	O
test	B-General_Concept
statistics	I-General_Concept
used	O
in	O
significance	O
testing	O
.	O
</s>
<s>
The	O
concept	O
of	O
power	B-General_Concept
is	O
useful	O
in	O
explaining	O
the	O
consequences	O
of	O
adjusting	O
the	O
significance	B-General_Concept
level	I-General_Concept
and	O
is	O
heavily	O
used	O
in	O
sample	O
size	O
determination	O
.	O
</s>
<s>
The	O
interpretation	O
of	O
a	O
p-value	B-General_Concept
is	O
dependent	O
upon	O
stopping	O
rule	O
and	O
definition	O
of	O
multiple	O
comparison	O
.	O
</s>
<s>
"	O
p	B-General_Concept
values	I-General_Concept
depend	O
on	O
both	O
the	O
(	O
data	O
)	O
observed	O
and	O
on	O
the	O
other	O
possible	O
(	O
data	O
)	O
that	O
might	O
have	O
been	O
observed	O
but	O
were	O
n't	O
"	O
)	O
.	O
</s>
<s>
Emphasis	O
on	O
statistical	B-General_Concept
significance	I-General_Concept
to	O
the	O
exclusion	O
of	O
estimation	O
and	O
confirmation	O
by	O
repeated	O
experiments	O
.	O
</s>
<s>
Rigidly	O
requiring	O
statistical	B-General_Concept
significance	I-General_Concept
as	O
a	O
criterion	O
for	O
publication	O
,	O
resulting	O
in	O
publication	O
bias	O
.	O
</s>
<s>
Unless	O
one	O
accepts	O
the	O
absurd	O
assumption	O
that	O
all	O
sources	O
of	O
noise	O
in	O
the	O
data	O
cancel	O
out	O
completely	O
,	O
the	O
chance	O
of	O
finding	O
statistical	B-General_Concept
significance	I-General_Concept
in	O
either	O
direction	O
approaches	O
100%	O
.	O
</s>
<s>
The	O
probability	O
of	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
a	O
function	O
of	O
decisions	O
made	O
by	O
experimenters/analysts	O
.	O
</s>
<s>
In	O
psychology	O
practically	O
all	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
claimed	O
to	O
be	O
false	O
for	O
sufficiently	O
large	O
samples	O
so	O
"	O
it	O
...	O
is	O
usually	O
nonsensical	O
to	O
perform	O
an	O
experiment	O
with	O
the	O
sole	O
aim	O
of	O
rejecting	O
the	O
null	O
hypothesis.	O
"	O
</s>
<s>
"	O
Statistically	B-General_Concept
significant	I-General_Concept
findings	O
are	O
often	O
misleading	O
"	O
in	O
psychology	O
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
does	O
not	O
imply	O
practical	O
significance	O
,	O
and	O
correlation	O
does	O
not	O
imply	O
causation	O
.	O
</s>
<s>
Casting	O
doubt	O
on	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
thus	O
far	O
from	O
directly	O
supporting	O
the	O
research	O
hypothesis	O
.	O
</s>
<s>
Critics	O
and	O
supporters	O
are	O
largely	O
in	O
factual	O
agreement	O
regarding	O
the	O
characteristics	O
of	O
null	B-General_Concept
hypothesis	I-General_Concept
significance	O
testing	O
(	O
NHST	O
)	O
:	O
While	O
it	O
can	O
provide	O
critical	O
information	O
,	O
it	O
is	O
inadequate	O
as	O
the	O
sole	O
tool	O
for	O
statistical	O
analysis	O
.	O
</s>
<s>
Successfully	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
may	O
offer	O
no	O
support	O
for	O
the	O
research	O
hypothesis	O
.	O
</s>
<s>
The	O
American	O
Psychological	O
Association	O
has	O
strengthened	O
its	O
statistical	O
reporting	O
requirements	O
after	O
review	O
,	O
medical	O
journal	O
publishers	O
have	O
recognized	O
the	O
obligation	O
to	O
publish	O
some	O
results	O
that	O
are	O
not	O
statistically	B-General_Concept
significant	I-General_Concept
to	O
combat	O
publication	O
bias	O
and	O
a	O
journal	O
(	O
Journal	O
of	O
Articles	O
in	O
Support	O
of	O
the	O
Null	B-General_Concept
Hypothesis	I-General_Concept
)	O
has	O
been	O
created	O
to	O
publish	O
such	O
results	O
exclusively	O
.	O
</s>
<s>
Estimation	O
statistics	O
can	O
be	O
accomplished	O
with	O
either	O
frequentist	B-General_Concept
or	O
Bayesian	O
methods	O
.	O
</s>
<s>
One	O
strong	O
critic	O
of	O
significance	O
testing	O
suggested	O
a	O
list	O
of	O
reporting	O
alternatives	O
:	O
effect	B-Application
sizes	I-Application
for	O
importance	O
,	O
prediction	O
intervals	O
for	O
confidence	O
,	O
replications	O
and	O
extensions	O
for	O
replicability	O
,	O
meta-analyses	O
for	O
generality	O
.	O
</s>
<s>
On	O
one	O
"	O
alternative	O
"	O
there	O
is	O
no	O
disagreement	O
:	O
Fisher	O
himself	O
said	O
,	O
"	O
In	O
relation	O
to	O
the	O
test	O
of	O
significance	O
,	O
we	O
may	O
say	O
that	O
a	O
phenomenon	O
is	O
experimentally	O
demonstrable	O
when	O
we	O
know	O
how	O
to	O
conduct	O
an	O
experiment	O
which	O
will	O
rarely	O
fail	O
to	O
give	O
us	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result.	O
"	O
</s>
<s>
Cohen	O
,	O
an	O
influential	O
critic	O
of	O
significance	O
testing	O
,	O
concurred	O
,	O
"	O
...	O
do	O
n't	O
look	O
for	O
a	O
magic	O
alternative	O
to	O
NHST	O
[	O
null	B-General_Concept
hypothesis	I-General_Concept
significance	O
testing ]	O
...	O
</s>
<s>
Psychologist	O
John	O
K	O
.	O
Kruschke	O
has	O
suggested	O
Bayesian	B-General_Concept
estimation	I-General_Concept
as	O
an	O
alternative	O
for	O
the	O
t-test	B-General_Concept
and	O
has	O
also	O
contrasted	O
Bayesian	B-General_Concept
estimation	I-General_Concept
for	O
assessing	O
null	O
values	O
with	O
Bayesian	B-General_Concept
model	I-General_Concept
comparison	I-General_Concept
for	O
hypothesis	O
testing	O
.	O
</s>
<s>
Two	O
competing	O
models/hypotheses	O
can	O
be	O
compared	O
using	O
Bayes	B-General_Concept
factors	I-General_Concept
.	O
</s>
<s>
Neither	O
the	O
prior	O
probabilities	O
nor	O
the	O
probability	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
under	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
are	O
often	O
available	O
in	O
the	O
social	O
sciences	O
.	O
</s>
<s>
Fisher	O
's	O
strategy	O
is	O
to	O
sidestep	O
this	O
with	O
the	O
p-value	B-General_Concept
(	O
an	O
objective	O
index	O
based	O
on	O
the	O
data	O
alone	O
)	O
followed	O
by	O
inductive	O
inference	O
,	O
while	O
Neyman	O
–	O
Pearson	O
devised	O
their	O
approach	O
of	O
inductive	O
behaviour	O
.	O
</s>
