- #1
nomadreid
Gold Member
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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.
(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.