calc: Paired-Sample Statistics
10.7.2 Paired-Sample Statistics
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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.)
Info Catalog
calc: Single-Variable Statistics
calc: Statistical Operations