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?
The best analysis/meta-analysis I know of regarding intercessory prayer has been conducted by the Templeton Institute, with a negative result.  Thus, there is presently no statistical support for the belief that prayer will be answered in an obvious or measurable way.

However, praying for intercession need not necessarily be done because you think God will listen to your individual plea and change outcomes accordingly.  It could also be done because you have hopes for how things will turn out and want to express those hopes in a meaningful way.