Dependent Samples T-test - different formulas?

[stattercat]

I have a question regarding hypothesis testing when the samples are not independent.

The formula I know for the test statistic for a paired samples t test is where you divide the mean difference by the standard error.

I've come across another formula that instead subtracts the mean 'after' by mean 'before' and then divides that by the combined variance (which includes the covariance).

Both methods give quite different results and I was just wondering if you would use one of another in certain situations? Or maybe I'm missing something completely

 

[CB]

Can you show the two formulae you mean?

 

[stattercat]

Yeah sure:

 

[CB]

Are you sure they give different results? Maybe show your working....

 

[stattercat]

Thanks for that. I checked the formula my lecturer had given and it was presented as plus the covariance rather than subtract for the pooled variance term. Get the same results now