We tested this with http://www.reedge.com for a client that integrated the facebook login on the checkout page of a Magento shop. I remember that Around 8% more finished the checkout compared to when we did not show the facebook login option.

The problem was we did not test the actual login, just having the option. The client did not give us details on revenue/turnover or hoe many people actually used login of facebook.

It was a health product on the US market.

wellll ok, the real answer is:

It depends on your execution.

In general, reducing friction will increase signups. That's hard to argue against. The only situation where reducing friction will reduce signups is where you seemingly reduce perceived value by doing it, but again, that all depends on execution.

Facebook connect sign in could be executed in a couple of ways:

1) Click a Facebook button. Click approve. Boom, you're registered in your app.

2) Click a Facebook button. Click approve. Get redirected to another signup form and have to fill in more data. Click "Send". Oops, there was an error with your form input, please enter a valid email address. Fill in data. Click "Send".

I can say with confidence that (1) will increase signups, but (2) will hardly move the needle.

It depends on your execution.