t-tests and p-values

CFA Level II
#1

Quantitative is driving me insane :angry:

I think there are two concepts that I am confused between;

  1. The t-test for testing the significance of a certain hypotheses or rejecting a null hypothesis. In that case the T-test should be > the critical test
  2. In order to test a coefficient is statistically different from zero, p-value should be < the level of significance let’s say 0.05.

Totally confused between the two, can I have help on that!

#2

Both quantities are related.

A p-value of 0.05 tells you that given the null hypothesis is true you would expect to find data this far away from the null hypothesis in no more than 5%. This is equivalent to saying that given the null hypothesis is true you would expect 95% of your data to fall closer to the null than your given sample data.

If you are given a p-value of 0.05 this is equivalent to saying your t test statistic is equal to the critical t value for a 5% level of significance. If you are given a p-value of 0.10 this is equivalent to saying your t test statistic is equal to the critical t value for a 10% level of significance (and so on).

The p value contains more information then the t test statistic in that it basically tells you what is the lowest level of significance for which you can reject the null. If you are given p = 0.0723 you can reject the null hypothesis at the 7.23% level of significance. (equivalently your t test statistic would equal the critical t value for a 7.23% level of significance)

#3

Needs a bit of work…

A t-critical value conveys the identical information.