To  interpret  the X^2 value, first determine the value of the degrees
   of  freedom  (df),  which  is  equal  to n 1, where n is the number of
   different categories into which each datum point may fall. The greater
   the  number  of categories, the more deviation is expected as a result
   of chance.

   For  the  3:1  ratio, n = 2, so df = 1. For the 9:3:3:1 ratio, df = 3.
   X^2  can then be determined by looking up the probability value (p) in
   a table.