Widmann, A. & Schröger E. (1999).
Bootstrapping the distribution of the city-block distance between two repeated measures [Online].
Bootstrapping the Distribution of the City-Block Distance between Two Repeated Measures
Andreas Widmann, & Erich Schröger
The city-block distance
n C=SUM(|Y(1)i-Y(2)i|) i=1
is a special case of the «Minkowski-distances» representing the distances between two vectors in an n-dimensional space spanned by n orthogonal axes. It can be used as a measure of the similarity of the distributions/means of two repeated measures. An example is given in Schröger (1998) were it has been used to determine the replicability of a particular component of the event-related brain potential. Since in the case of small sample sizes or unknown distribution functions of Y(1) and Y(2) by which the probability function of C could be developed, the distribution function of C, required to interpret a particular value of C, is not known, a randomization test can be used (e.g. Edgington, 1980).
It is suggested to
Steps (1) to (3) are done by the provided perl script minkowski.pl. To keep the script short and to save computing time the probability for a city-block distance equal or smaller than the empirically measured one is computed rather than the cumulative distribution function.
|04.10.2001, Andreas Widmann, widmann at uni-leipzig dot de|