to conduct a hypothesis test we need to know two things alpha and DF or the
degrees of freedom we'll go ahead and use alpha 0.05 for our test which by far
is the most commonly used level of alpha and statistics DF stands for degrees of
freedom it is equal to N minus 2 where N is equal to the number of pairs of
scores and our data recall we have 5 people in our example or five pairs of
scores therefore the DF is equal to 5 minus 2
or 3 so once again we have DF of 3 and alpha 0.05 now what we need to do is
find the critical value for this test and here's a snapshot of a table of
critical values for Pearson's r remember alpha .05 so we're going to work
in this column the second most common level of alpha is .01 so I showed
it here as well for those who are interested but we're using .05
which is the most commonly used level of alpha and our DF is 3 so we want to find
the row DF here of 3 where it intersects or meets with alpha .05 so here
the shaded value critical value is 0.87 8 so here this is the set up for
hypothesis testing now here we have Pearson's r the Center is 0 and notice
the critical value remember how we had 0.878 so I have a positive 0.878
here a negative .878 here these are my critical values you can think of
them as lines in the sand now if I cross the critical value if my calculated
correlation is beyond this line in the sand towards the more extreme value here
or beyond this line in the sand towards the more extreme value here then I will
reject the null hypothesis okay either of these two values if I get it over to
the right in the tail or to the left in the tail so if it's bigger than .878
I reject if it's smaller or you know negative value here so if it's to the
tail here then I reject as well but if it's anywhere inside here then I
would fail to reject the null or some people refer to it as accept the null
now our values you recall was negative 0.9 so it was right about over here
somewhere in this area notice it's beyond that line in the sand
right if we have for example negative point eight eight negative point eight
nine negative point nine or in the tail here so because our value was in the
tail it was beyond the critical value we're going to go ahead and reject the
null hypothesis and when we do that we conclude that the
test is statistically significant therefore we reject the null hypothesis
and recall we stated this at the beginning of the presentation where the
null said Rho XY = 0 so we are rejecting that and if we're rejecting
that then that means we're saying that Rho XY does not equal zero and because
of that we conclude that our correlation is significantly different from zero
because we rejected this statement when our value fell in the tail beyond the
critical value or that line in the sand and we can go ahead and write the
results as follows there was a significant negative relationship
between x and y and then here we have r of three and this is the degrees of
freedom equals -.90 that's the value we calculated by hand and then
P is less than .05 and in these results as I said three is
for the degrees of freedom the P is less than .05 indicates that the
test is statistically significant using an alpha level of .05
now if the result was not significant say that we had a correlation of
-.80 and recall the critical value was -.878
so -.80 would have been
about right here it would not have crossed that line in the sand if that
was the case then we would have said P is greater than.05 and we
would have said there was not a significant negative relationship
between x and y but because it was significant we do go ahead and write it
as was shown here and we write P is less than .05 so anytime you have
a result that is statistically significant or beyond that line in the
sand and our distribution in the tail then we always write P is less than and
then you can put the alpha here when you're doing this by hand so if we used
alpha .05 you would say P is less than .05 okay that's it
thanks for watching