# Hypothesis Testing with Spatial Data

I have production data for several wells. I know that a subset has been treated with a product, and I'd like to determine if the difference in production is due to the product treatment, or the placement of the wells.

For each test well I've collected the $K$ nearest neighbors required to obtain $N$ control wells. This gives me $N$ control wells, and $K-N$ test wells. I then perform a two-tailed z-test, using the standard deviation of the production of the $K$ wells as the sample standard deviation.

I was wondering if this sounds like a decent approach to this problem, or if there is a more sophisticated way of incorporating spatial data for testing the hypothesis that the production for the test and control groups is the same.

• How was the treatment subset selected? – whuber May 8 '14 at 18:42
• It was the total number wells in that area that had been treated with a product. The control wells were all of the wells in the area that had not been treated. – cjohnson318 May 8 '14 at 18:44
• Then please explain how the treatment area was selected. This gets to the heart of the matter: if that selection was not independent of the subsequent performance of the wells--and such independence is practically guaranteed only by a randomization procedure--then that will limit your options and force you to make some strong modeling assumptions. – whuber May 8 '14 at 18:47
• The treatment area selection was motivated by past production reports, and limited by what plots were available. The offset wells are all within about five miles of the test wells I am studying, and target the same formations, assuming the reports are accurate. – cjohnson318 May 8 '14 at 18:56