It's no contraction if you believe in a clever god that doesn't want that the effect gets scientifically measured.

But then the believer can't claim God can do things that could be scientifically measured - for instance, curing people who pray more often than people who don't, at least while a scientist is watching. Believers who want to pray for their health should use timeless decision theory to figure out what conditions to meet so that God is allowed to cure them without making that observable to later scientists. Cult startup, anyone?