The COMPARE procedure judges
numeric values unequal if the magnitude of their difference, as measured
according to the METHOD= option, is greater than the value of the
CRITERION= option. PROC COMPARE provides four methods for applying
CRITERION=:
-
The EXACT method tests for exact
equality.
-
The ABSOLUTE method compares the
absolute difference to the value specified by CRITERION=.
-
The RELATIVE method compares the
absolute relative difference to the value specified by CRITERION=.
-
The PERCENT method compares the
absolute percent difference to the value specified by CRITERION=.
For a numeric variable
compared, let
x be its value
in the base data set and let
y
be its value in the comparison data set. If both
x and
y are
nonmissing, then the values are judged unequal according to the value
of METHOD= and the value of CRITERION= (γ) as follows:
-
If METHOD=EXACT, then the values
are unequal if
y does not equal
x.
-
If METHOD=ABSOLUTE, then the values
are unequal if
-
If METHOD=RELATIVE, then the values
are unequal if
The values are equal
if
x=
y=0.
-
If METHOD=PERCENT, then the values
are unequal if
If
x or
y is
missing, then the comparison depends on the NOMISSING option. If the
NOMISSING option is in effect, then a missing value will always be
judged equal to anything. Otherwise, a missing value is judged equal
only to a missing value of the same type (that is, .=., .^=.A, .A=.A,
.A^=.B, and so on).
If the value that is
specified for CRITERION= is negative, then the actual criterion that
is used, γ, is equal to the absolute value of the specified
criterion multiplied by a very small number, ε (epsilon), that
depends on the numerical precision of the computer. This number ε
is defined as the smallest positive floating-point value such that,
using machine arithmetic, 1−ε<1<1+ε. Round-off
or truncation error in floating-point computations is typically a
few orders of magnitude larger than ε. CRITERION=−1000
often provides a reasonable test of the equality of computed results
at the machine level of precision.
The value δ added
to the denominator in the RELATIVE method is specified in parentheses
after the method name: METHOD=RELATIVE(δ). If not specified
in METHOD=, then δ defaults to 0. The value of δ can
be used to control the behavior of the error measure when both
x and
y are
very close to 0. If δ is not given and
x and
y are
very close to 0, then any error produces a large relative error (in
the limit, 2).
Specifying a value for
δ avoids this extreme sensitivity of the RELATIVE method for
small values. If you specify METHOD=RELATIVE(δ) CRITERION=γ
when both
x and
y are
much smaller than δ in absolute value, then the comparison is
as if you had specified METHOD=ABSOLUTE CRITERION=δγ.
However, when either
x or
y is
much larger than δ in absolute value, the comparison is like
METHOD=RELATIVE CRITERION=γ. For moderate values of
x and
y,
METHOD=RELATIVE(δ) CRITERION=γ is, in effect, a compromise
between METHOD=ABSOLUTE CRITERION=δ γ and METHOD=RELATIVE
CRITERION=γ.
For character variables,
if one value is longer than the other, then the shorter value is padded
with blanks for the comparison. Nonblank character values are judged
equal only if they agree at each character. If the NOMISSING option
is in effect, then blank character values are judged equal to anything.