You absolutely have a faster pace on the road. You have nothing but yourself keeping pace. Plus, the road varies in incline. That makes you work harder, both uphill and downhill.
And, treadmills lie. I read somewhere that all but the highest end treadmills continually over state the mileage you're putting in.
I find that my gait and stride are very different between treadmill and road. That translates to a different pace.
My suggestion is to get a running watch (GPS) that will monitor your pace and give you a beep when you vary from it. I use a Garmin Forerunner 405
. It's simple, has the bells and whistles I need and a heart monitor included.
It's got a virtual partner feature that allows you to set a pace and will let you know how far ahead or behind that pace you are.
I found that monitoring my heart rate is a very effective way of telling me where I am concerning my pace.
When seconds count...the police are minutes away.