I am confused about the counting of degrees of freedom. Yes, I know that it is the number of vectors which are free to vary. But that definition gives way to different interpretations: (1) the number of data points minus the number of independent variables. This seems to be the basis of the standard "n-1" or "n-2" in many applications. (2) just the number of independent variables. This seems to be the basis in applications with 1 degree of freedom (example below), or when one says that the movement of a robot arm has 6 degrees of freedom, being +x,+y,+z,-x,-y,-z. [In this latter example, I am puzzled why, say (2,0,0) is considered the same as (1,0,0) for the purposes of counting, but they are considered distinct from (-1, 0, 0). Both (2,0,0) and (-1,0,0) are just λ(1,0,0).] So, for example reading a psychology paper with statistics that appear to me dubious, I came across the following set of data in which the author is making a correlation between female first names and places of residence, Milwaukee: Women named Mildred= 865, expected value = 806 Virginia Beach: Women named Mildred= 230, expected value = 289 Milwaukee: Women named Virginia= 544, expected value = 603 Virginia Beach: Women named Virginia = 275, expected value = 216 [I am not making this up. Ignobel Prizes, take note: "Why Susie Sells Seashells by the Seashore: Implicit Egotism and Major Life Decisions" by Pelham, B., Mirenberg, M., and Jones, J.; Journal of Personality and Social Psychology 2002, Vol. 82, No. 4, 469-487] The authors then state (p. 471) that the "association between name and place of residence for women was highly significant, [itex]\chi[/itex]2(1) = 38.25, p<.001." Apart from other questions of validity of this study, my question is whether the df= 1 here is justified. This would seem to be the number of independent variables interpretation, ignoring the number of data points. So, three questions: is (1) or (2) above correct (and so why the other interpretation exists), why North and South are considered separately in a robot arm, and whether the psychology paper is fudging with the df count. Thanks in advance.