http://www.buildinganempire.com/poisson2.html
(towards bottom of page)
It should be a function of your normal signup ratio.
All other things being equal (that's important), if you send 3x as many visitors as your normal conversion ratio with no signups, there is only a 5% chance that would happen by chance alone if the new program is as good as the last one.
So if you normally convert 1/1500, send 4500.
If you don't have a signup, it is quite unlikely that you are going to recover and do better than 1/1500.
Sending 3x your normal conversion rate doesn't sound like much but it only makes sense if you have 0 signups at that point. If you get one, keep chugging. You'll be right 19 out of 20 times to switch back at that time.
Also, consider that I said "all other things being equal". Daily fluctuation and other factors can make comparing across days difficult.