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I understanding that if Z1, Z2, …, Zk, are independent standard normal variables, then Z12 + Z22 + … + Zk2 has a χ² distribution with k degrees of freedom.

However, say we have a 2 rows and 3 columns, then we're taking (observed - expected)2 divided by expected for 6 cells. Why then is the degrees of freedom not 6?

user1205901 - Reinstate Monica
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  • Very general answers, covering a range of points of view and degrees of sophistication, can be found at http://stats.stackexchange.com/questions/16921. – whuber Mar 17 '15 at 21:32

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