<s>
Misuse	B-General_Concept
of	I-General_Concept
p-values	I-General_Concept
is	O
common	O
in	O
scientific	O
research	O
and	O
scientific	O
education	O
.	O
</s>
<s>
p-values	B-General_Concept
are	O
often	O
used	O
or	O
interpreted	O
incorrectly	O
;	O
the	O
American	O
Statistical	O
Association	O
states	O
that	O
p-values	B-General_Concept
can	O
indicate	O
how	O
incompatible	O
the	O
data	O
are	O
with	O
a	O
specified	O
statistical	O
model	O
.	O
</s>
<s>
From	O
a	O
Neyman	O
–	O
Pearson	O
hypothesis	O
testing	O
approach	O
to	O
statistical	O
inferences	O
,	O
the	O
data	O
obtained	O
by	O
comparing	O
the	O
p-value	B-General_Concept
to	O
a	O
significance	B-General_Concept
level	I-General_Concept
will	O
yield	O
one	O
of	O
two	O
results	O
:	O
either	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
(	O
which	O
however	O
does	O
not	O
prove	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
false	O
)	O
,	O
or	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
cannot	O
be	O
rejected	O
at	O
that	O
significance	B-General_Concept
level	I-General_Concept
(	O
which	O
however	O
does	O
not	O
prove	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
)	O
.	O
</s>
<s>
From	O
a	O
Fisherian	O
statistical	O
testing	O
approach	O
to	O
statistical	O
inferences	O
,	O
a	O
low	O
p-value	B-General_Concept
means	O
either	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
and	O
a	O
highly	O
improbable	O
event	O
has	O
occurred	O
or	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
false	O
.	O
</s>
<s>
The	O
following	O
list	O
clarifies	O
some	O
issues	O
that	O
are	O
commonly	O
misunderstood	O
regarding	O
p-values	B-General_Concept
:	O
</s>
<s>
The	O
p-value	B-General_Concept
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
or	O
the	O
probability	O
that	O
the	O
alternative	O
hypothesis	O
is	O
false	O
.	O
</s>
<s>
A	O
p-value	B-General_Concept
can	O
indicate	O
the	O
degree	O
of	O
compatibility	O
between	O
a	O
dataset	O
and	O
a	O
particular	O
hypothetical	O
explanation	O
(	O
such	O
as	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
.	O
</s>
<s>
Specifically	O
,	O
the	O
p-value	B-General_Concept
can	O
be	O
taken	O
as	O
the	O
probability	O
of	O
obtaining	O
an	O
effect	O
that	O
is	O
at	O
least	O
as	O
extreme	O
as	O
the	O
observed	O
effect	O
,	O
given	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
This	O
should	O
not	O
be	O
confused	O
with	O
the	O
probability	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
given	O
the	O
observed	O
effect	O
(	O
see	O
prosecutor	O
's	O
fallacy	O
)	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
is	O
not	O
the	O
probability	O
that	O
the	O
observed	O
effects	O
were	O
produced	O
by	O
random	O
chance	O
alone	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
is	O
computed	O
under	O
the	O
assumption	O
that	O
a	O
certain	O
model	O
,	O
usually	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
is	O
true	O
.	O
</s>
<s>
This	O
means	O
that	O
the	O
p-value	B-General_Concept
is	O
a	O
statement	O
about	O
the	O
relation	O
of	O
the	O
data	O
to	O
that	O
hypothesis	O
.	O
</s>
<s>
The	O
0.05	O
significance	B-General_Concept
level	I-General_Concept
is	O
merely	O
a	O
convention	O
.	O
</s>
<s>
The	O
0.05	O
significance	B-General_Concept
level	I-General_Concept
(	O
alpha	O
level	O
)	O
is	O
often	O
used	O
as	O
the	O
boundary	O
between	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
and	O
a	O
statistically	O
non-significant	O
p-value	B-General_Concept
.	O
</s>
<s>
The	O
p-value	B-General_Concept
does	O
not	O
indicate	O
the	O
size	O
or	O
importance	O
of	O
the	O
observed	O
effect	O
.	O
</s>
<s>
A	O
small	O
p-value	B-General_Concept
can	O
be	O
observed	O
for	O
an	O
effect	O
that	O
is	O
not	O
meaningful	O
or	O
important	O
.	O
</s>
<s>
In	O
fact	O
,	O
the	O
larger	O
the	O
sample	O
size	O
,	O
the	O
smaller	O
the	O
minimum	O
effect	O
needed	O
to	O
produce	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
p-value	B-General_Concept
(	O
see	O
effect	B-Application
size	I-Application
)	O
.	O
</s>
<s>
Visualizing	O
effect	B-Application
sizes	I-Application
is	O
a	O
critical	O
component	O
of	O
a	O
data-analysis	O
method	O
called	O
estimation	O
statistics	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
does	O
not	O
in	O
itself	O
allow	O
reasoning	O
about	O
the	O
probabilities	O
of	O
hypotheses	O
,	O
which	O
requires	O
multiple	O
hypotheses	O
or	O
a	O
range	O
of	O
hypotheses	O
,	O
with	O
a	O
prior	O
distribution	O
of	O
likelihoods	O
between	O
them	O
,	O
in	O
which	O
case	O
Bayesian	O
statistics	O
could	O
be	O
used	O
.	O
</s>
<s>
There	O
,	O
one	O
uses	O
a	O
likelihood	O
function	O
for	O
all	O
possible	O
values	O
of	O
the	O
prior	O
instead	O
of	O
the	O
p-value	B-General_Concept
for	O
a	O
single	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
p-value	B-General_Concept
describes	O
a	O
property	O
of	O
data	O
when	O
compared	O
to	O
a	O
specific	O
null	B-General_Concept
hypothesis	I-General_Concept
;	O
it	O
is	O
not	O
a	O
property	O
of	O
the	O
hypothesis	O
itself	O
.	O
</s>
<s>
For	O
the	O
same	O
reason	O
,	O
p-values	B-General_Concept
do	O
not	O
give	O
the	O
probability	O
that	O
the	O
data	O
were	O
produced	O
by	O
random	O
chance	O
alone	O
.	O
</s>
<s>
Errors	O
in	O
inference	O
,	O
including	O
confidence	O
intervals	O
that	O
fail	O
to	O
include	O
their	O
corresponding	O
population	O
parameters	O
or	O
hypothesis	O
tests	O
that	O
incorrectly	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
are	O
more	O
likely	O
to	O
occur	O
when	O
one	O
considers	O
the	O
set	O
as	O
a	O
whole	O
.	O
</s>
<s>
Several	O
statistical	O
techniques	O
have	O
been	O
developed	O
to	O
prevent	O
this	O
from	O
happening	O
,	O
allowing	O
significance	B-General_Concept
levels	I-General_Concept
for	O
single	O
and	O
multiple	O
comparisons	O
to	O
be	O
directly	O
compared	O
.	O
</s>
<s>
The	O
webcomic	O
xkcd	O
satirized	O
misunderstandings	B-General_Concept
of	I-General_Concept
p-values	I-General_Concept
by	O
portraying	O
scientists	O
investigating	O
the	O
claim	O
that	O
eating	O
jellybeans	O
caused	O
acne	O
.	O
</s>
<s>
In	O
fact	O
,	O
if	O
20	O
independent	O
tests	O
are	O
conducted	O
at	O
the	O
0.05	O
significance	B-General_Concept
level	I-General_Concept
and	O
all	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
true	O
,	O
there	O
is	O
a	O
64.2	O
%	O
chance	O
of	O
obtaining	O
at	O
least	O
one	O
false	O
positive	O
and	O
the	O
expected	O
number	O
of	O
false	O
positives	O
is	O
1	O
(	O
i.e.	O
</s>
<s>
The	O
FWER	O
when	O
all	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
true	O
for	O
m	O
independent	O
tests	O
,	O
each	O
conducted	O
at	O
significance	B-General_Concept
level	I-General_Concept
,	O
is	O
:	O
</s>
