Theists' typical response to these failures (i. e., of prayer to affect rates of healing) is to say either God won't let himself be tested or That's not what prayer is about: it's simply a way to converse with God. But you can bet that had these studies shown a large positive effect, the religious would be noisily flaunting this as evidence for God. The confirmation bias shown by accepting positive results but explaining away negative ones is an important difference between science and religion.

p. 116 - Faith vs. Fact (2015)