The best way to persuade someone of your new approach is to begin with three agreements:
We agree on the goals. We both want the same outcomes, we're just trying different ways to get there.
We agree on reality. The world is not flat. Facts are actually in evidence. Statistics, repeatable experiments and clear evidence of causation are worth using as tools.
We agree on measurement. Because we've agreed on goals and reality, we agree on what success looks like as well.
All three allow us to enroll on the same journey, and to hold each other accountable for our work. Any other approach disrespects your partners and leaves you in a corner, without allies.