How do I test for a trend between group means representing different subjects?
Let us suppose we wish to test for a linear trend between between subjects group means. This can be done using polynomial coefficients
ONEWAY OUTCOME BY GROUP /POLYNOMIAL= 1 /MISSING ANALYSIS .
In the case of unequal group sizes SPSS produces two outputs called weighted and unweighted sums of squares. The weighted sums of squares assumes group sizes are important for example to reflect relative sizes of each group in the general population. Unweighted sums of squares ignore differences in group sizes and compares group means using the same average group size for each group so each group contributes equally to the trend analysis.
For further discussion on the differences between weighted and unweighted analyses see the first half of Amy Shelton's excellent on-line tutorial given in a pdf file located [http://www.psy.jhu.edu/~ashelton/courses/stats315/week9.pdf here.] If the link is broken the file containing the tutorial can be accessed from [attachment:weights.pdf here.]