In this video we'll take a look at how
to interpret a p-value. So what is a
p-value? P-value stands for probability
value; it indicates how likely it is that
a result occurred by chance alone.
If the p-value is small, it indicates the
result was unlikely to have occurred by chance
alone.
These results are known as being
statistically significant. A small
p-value means that it's greater than
chance alone,
something happened; the test is
significant.
Whereas a large p-value indicates that
the result is within chance or normal
sampling error, or in other words nothing
happened,
the test is not significant. And p values
range from 0 to 1.
Let's go ahead and take a look at some p-values of popular computer
output.
So here's SPSS and the p-value is given
where it says Sig. (2-tailed) and it's very
small in this example at .002. Now we'll
formalize this in a minute, but for now,
that's beyond chance, it's quite small, so
we would say that the result is
statistically significant.
Taking a look at another example, here we
see a p-value, reported as Sig. once again
in SPSS, as .268. Now that's not
really that small, so that's within
normal sampling error we would say, or
it's not beyond chance. So the result is
not statistically significant.
Now to formalize this, we want to look at
what is known as alpha.
And when we interpret whether a p-value
is significant, that is beyond chance or
not, we need to know the level of alpha
being used for the test. The two most
common levels are .05 for alpha,
or .01.
Alpha is decided beforehand by the
researcher or analyst. So if we use an
alpha of .05, the following rule
applies: If p or Sig., as you saw in our
output, is less than alpha or less than
.05 in this case, the test is
significant.
Whereas if p or Sig. is greater than
.05, the test is not significant.
So, as an example, if we had a p-value or
a Sig. of .03, using the rule
up above, with an alpha of .05, would the
test be significant or not?
Well the test would be significant, right, because
.03 is less than .05.
Let's go ahead and take a look at another
example. So if we have a p of .12
now with alpha .05, try and assess
whether or not that test would be
significant.
It would not be significant because
.12 is greater than .05, so
it's not significant, or it's not beyond
sampling error. And here's a table of
some different outcomes, so looking at
this first row, if we had a p of
.04, and we use alpha
.05 in all decisions,
this is less than .05 so we would
say it's significant. Our second value,
.075, that's greater than .05
right, so we would say that's not
significant.
.049, that's very close, but it is
less than .05, so that would be
significant. And then .523, that's
definitely greater than .05, so it's
not significant. And then finally,
.001, definitely less than .05, so
this result is significant.
Now if we look at alpha of .01
we use really the same decision rule, if
p is less than alpha, this time alpha's
.01 though, the test is significant. Whereas
if p is greater than alpha, the test
is not significant.
So if we have an example here with a p
of .04, using an alpha of .01,
we would see that the test is not
significant, because .04 is greater
than .01. If we had an example of
.003, we would see that it is
significant in this case, because
.003 is less than .01.
So let's go and take a look at some
examples as well with alpha .01.
So here we have a p of
.001, that's definitely less than alpha
of .01, so it's significant.
.02, it's close, but it's greater
than .01, so it's not
significant.
.009, once again, quite close, but
less than alpha of .01, so it's
significant. .523 is greater than
.01, so it's not significant.
And then finally, .012, close once
again, but it is greater than
.01, so it's not significant.
OK let's look at a p-value again in SPSS.
So now we have a p of
.002,
and it's very small, let's assess this
for significance using alpha .05.
So because .002 is less than
.05, the test is significant at
alpha .05. Now before we close ask
yourself would it have been significant if
alpha .01 was used.
Well since .002 is less than
.01, the test would be significant
if an alpha .01 was used as
well.
OK that's it. Thanks for watching