Attempting to test God as a way of dispelling doubts is ruled out by a number of Bible passages. Both these things you mention seem to involve doing that. (I think there are often questions about the theological underpinnings of prayer studies, amongst other things.)

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Due_Kindheartedness wrote:

@FZM the former is testing God but the latter isn't. The latter is observation.

​The studies I have come across are like consciously organised experiments with targeted recipients, control groups and so on and experimenters wanting to collect the results. They look like tests.

Intercessory prayer in 'natural' none experimental contexts is going on continuously. I don't know how you would observe whether it is 'effective' or not. (Besides the effectiveness of all of the prayer that isn't for healing illnesses).
 

I pray, not to persuade God to take away my burden, but to give me the strength to endure it. At the end of it, I always feel like a better person, heart and soul.