Indeed sounds like a difficult mission to complete nevertheless it is possible. The business owners you trying to prove to are probably old school hence they would believe in that you would be wasting money on digital analytics and digital marketing. To lure them in, you would have to win over their confidence. before they can buy your product they need to know they need it. How do you make them need it, well you need to relate it to something that appeals to them. and that differs between person to person. one possible way would be explaining to the person that as the world is evolving so is business and if you do not keep up with trends eventually you will become obsolete. its better for the companies name that they are using newer technologies. Use the fact that competitors are doing this as well and it is in fact is profitable.

The business owners need to understand what it is they are going to do. Via digital analytics you get to know the customer better, and that is of importance to know your customer. With data from analytics you know what to show and feed specific customers.
In this way you showing the right things to the right customers and thus making more sales.

I believe its difficult to sell digital analytics. but this is because people merely do not know.