Paired-Sample Statistics
------------------------

The functions in this section take two arguments, which must be
vectors of equal size.  The vectors are each flattened in the same way
as by the single-variable statistical functions.  Given a numeric
prefix argument of 1, these functions instead take one object from the
stack, which must be an Nx2 matrix of data values.  Once again,
variable names can be used in place of actual vectors and matrices.

The `u C' (`calc-vector-covariance') [`vcov'] command computes the
sample covariance of two vectors.  The covariance of vectors X and Y
is the sum of the products of the differences between the elements of
X and the mean of X times the differences between the corresponding
elements of Y and the mean of Y, all divided by `N-1'.  Note that the
variance of a vector is just the covariance of the vector with itself.
Once again, if the inputs are error forms the errors are used as
weight factors.  If both X and Y are composed of error forms, the
error for a given data point is taken as the square root of the sum of
the squares of the two input errors.

The `I u C' (`calc-vector-pop-covariance') [`vpcov'] command computes
the population covariance, which is the same as the sample covariance
computed by `u C' except dividing by `N' instead of `N-1'.

The `H u C' (`calc-vector-correlation') [`vcorr'] command computes the
linear correlation coefficient of two vectors.  This is defined by the
covariance of the vectors divided by the product of their standard
deviations.  (There is no difference between sample or population
statistics here.)