Effectiveness of prayers of intercession

I understand that there are many different reasons to pray: confessing your sins, thanking God for daily provisions. However, many people pray for intercession and believe in the possibility that God will intervene on their behalf. There are also examples of this in the Bible. Is there any evidence to suggest that God intervenes on our behalf (in the modern world). There is plenty of anecdotal evidence, but are there any studies demonstrating proof of the effectiveness of intercessory prayer? If God intervenes on our behalf surely this can easily be proved, reproducible, and should be statistically greater than chance. If there is no evidence to suggest this type of prayer is effective, is there any purpose for praying for intercession?