why does my outside ac unit run even when the ac is turned off?

Question

I noticed when we moved into this home in mid-winter, the outside AC unit was constantly running.  When I turned the heat off, it still ran.  Now, when I use the AC, it cools the house, but when the thermostat is off, the outside AC unit still runs.  Could this be a mis-wired thermostat?  What should I do to test this, I don't have the $$$$ to call a repair technician.