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t-testing the Case-Shiller

The Case-Shiller index rose 1.2% in May compared with April. I asked myself today - Is the 1.2% rise due to chance, or are house prices actually rising?

I downloaded the Case-Shiller excel file and ran paired t-tests comparing the results of 20 cities from February, March, April, and May of 2010.
Here's the results (mean value):

February (133.2) v. March (133.1); p > 0.05
March (133.1) v. April (134.0); p < 0.001
April (134.0) v. May (134.5); p = 0.011

In conclusion, the Case-Shiller index has been rising since March and it is very unlikely that this is due to chance... Average house prices in these 20 cities are significantly rising. 

Disclosure: No positions in US housing