 # Level of Significance

I’ve seen quite a few questions in the CFAI EOCs and mocks that dont specify a level of significance for which we need to test the statisitical significance of a coefficient/corelation. In this case, what do we do?

Is it ok to just see if the T values are large enough… say above 5 and reject the null. This has me soo confused!!! Can anyone help out?

Hwlp?

I haven’t reviewed this section for a couple months now, but I believe the general rule is to reject if greater than 2. I think the actual number is like 1.96.

If fail to reject at 5%, test at 1%.

If pass 5%, test at 10%.

However, I believe exam question will not be ambigious.

The given T value should be based on the level of significance. So if you’re given one T-value at which we reject if our calculated T value is greater, then the T value given came from the T table at n-1 degrees of freedom, and significance level = alpha. http://www.sussex.ac.uk/Users/grahamh/RM1web/t-testcriticalvalues.pdf thats an example of a T table.

So if they give the significant value of T to compare against your calculated T value, they’ve already given you a significance level, even though it may not have been explicitly stated.

and how do you decide if a One tail or Two tail test is needed?? any easy way to conclude this?

If your null hypothesis is just something = something, then you have a two tailed test.

But if your null hypothesis is something is less than or equal too, or greater than or equal too then you have a two tailed test.

Basically if we want to know if our correlation coefficient is not zero, our null hypothesis will be corr(x,y) = 0 and we care if it is bigger than zero or if it is less than zero, so we need a two tailed test. But if we just care if corr(x,y) is > 0 then our null hypothesis will be corr(x,y) <= 0 and we only care about proving that corr(x,y) isn’t on the left side of the distribution, so we only need a one sided test.