How does the t-ratio do this?
The t test sets up a sampling distribution of differences with a mean of zero.

The t test calculates if your difference between the means

is far in the tails of the

sampling distribution or far away from zero.

If it is, the difference may be too big to be chance. If your groups were really the same, then the difference between the means (and your t-score) should be close to zero.

The t-score is made a relative score by dividing the difference between the means by the standard error of the difference, which is like the standard deviation in a score. See your book for the standard error formula.

That's how we know if your difference is rare by chance as we can calculate the areas in the tails (see the z-score workshop).