The effectiveness of prayer can be discovered. Survey a large group of people who have prayed for things and compare the number of answered prayers to the non-answered in say a 5 year wait period.
That’s a terrible methodology.
At best, it would give you an answer to the question “Do people think that their prayers have been answered?”, when you are supposed to be interested in an answer to the question “Are the prayers of the people answered?”.
And you can get the answer to the question “Do people think that their prayers have been answered?” by asking that right away.
I have many friends and at least two dozen older cousins who have all prayed extensively for their parents and aunts and uncles when they were diagnosed with some bad, probably fatal illness.
And how exactly do you know that?
Did you put microphones in their rooms, or what?
Maybe they prayed that the suffering would be lessened - a prayer, which, if answered “affirmatively”, could be very compatible with death coming sooner?
Maybe they prayed generally, that things would end well? Again, things end well if one goes to heaven after death.
Exactly how do they help? If the requests are not fulfilled the prayer was a waste of time.
Why don’t you actually wait for the answer before coming to your conclusion?
Then there is always the list of God’s attributes, one of which strongly states that He is not affected by the actions of any being. Praying to him is trying to affect him into doing something that the prayer wishes. Impossible if the attribute list is to be believed.
And why would God have to be changed by anything for the prayers to work? Maybe you’re missing the part where God is also outside of time?