<- file 95cv.html ->

CV Coefficient of variation

===================John ??, Sept 1995=======ssc Pearson's dimension rule tells us that the CV of x:y:z::1:2:3, if x is one-dimensional, y two-dimensional, and z three-dimensional. Experience tells us that the CV of length (=height = breadth) is around 3 to 5 %. So if the CV of the length of the forearm is 4%, the CV of the palm area can be predicted to be 8%, and the volume of the skull 12%. Taking volume to be equivalent to weight, the CV of body weight could also be predicted to be 12%. My experience is that the CV of the diameter of the skull is less than the CV of diameter of the waist. (I suppose because flab means greater variation is possible than in the case of bone.) I mean to say that the rule is approximate. If there is a major deviation, perhaps there is a sensible explanation. Yes, the CV (calculated on a sample) has a sampling distribution. See the Statistical Encylopedia for more info. However, to me the CV is a descriptive statistic and its standard error is less interesting than the s.e. of (say) the slope of a straight-line regression. A statement like: "The CV of corn yield was 12%" is very comforting, where-as ditto "30%" should make all the alarm bells go off. Finally, be sure that the thing you are measuring has a natural origin (that "0" really means "nothing", "empty", "zilch"). Otherwise the CV has an arbitrary value, depending on the arbitrary origin used in the measurement. (The standard example is temperature in Celsius and Fahrenheit. Write down some numbers and calculate the CV. Convert the numbers from C to F or vice versa. The CV will change, but the underlying variation is the same.) Hope this helps, John. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Document by Rich Ulrich. E-mail to wpilib+@pitt.edu

FAQ top.

Ulrich home page.

Ulrich FAQ. http://www.pitt.edu/~wpilib/stats99.html