How to Test a Correlation for Significance - YouTube

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

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