Suppose we would like to compare two raters using a kappa statistic but the
raters have different range of scores. This situation most often presents itself
where one of the raters did not use the same range of scores as the other rater. 

Let us consider an example where two graduate students where asked to rate 12
movies based on a scale from 1-3. One rater used all of the three scores
possible while rating the movies whereas the other student did not like any of
the movies and therefore rated all of them as either a 1 or a 2. Thus, the range
of scores is the not the same for the two raters.

To obtain the kappa statistic in SPSS we are going to use the crosstabs command with the statistics
= kappa
 option. By default,
SPSS will only compute the kappa statistics if the two
variables have exactly the same categories, which is not the case in this
particular instance. We can get around this problem by adding a fake observation
and a weight variable shown below. The weight variable takes value of 1 for all
the real observations and value of 0.00001 (something very small) for the fake
observation that we have just added. The trick is then to weight the
observations using the
weight
command.

data list list 
/rater1 rater2.
begin data.
  1         1
  1         1
  1         1
  1         1
  2         2
  2         2
  2         2
  2         2
  3         2
  3         2
  3         2
  3         2
end data.

save outfile = kappa.
data list list 
/rater1 rater2.
begin data.
  3         3
end data.

add files file = *
/file = kappa.
exe.

compute weight = 1.
if ( rater1 =3 & rater2 =3 ) weight = .00001.
exe.

weight by weight.
crosstabs
  /tables=rater1 by rater2
  /statistics=kappa.

Symmetric Measures
|---------------------|-----|---------------|----------|------------|
|                     |Value|Asymp. Std.    |Approx. T |Approx. Sig.|
|                     |     |Error(a)       |       (b)|            |
|---------------|-----|-----|---------------|----------|------------|
|Measure of     |Kappa|.500 |.156           |3.000     |.003        |
|Agreement      |     |     |               |          |            |
|---------------|-----|-----|---------------|----------|------------|
|N of Valid Cases     |12   |               |          |            |
|                     |     |               |          |            |
|---------------------|-----|---------------|----------|------------|
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.