On Tue, 10 Feb 2009 16:04:44 -0800 (PST), Ryan
[snip, previous. Keeping what is relevant to new question.]
It won't make any difference to your ANOVA tests, if
that is a worry to anyone, but I have a definite preference
for using the means over the sums. I'm thinking especially
of ad-hoc scales that are used in clinical trials. (Given someone's
"standard scale" that has often been reported, we are pretty-
much stuck with it. Even though the BPRS or the Hamilton
might be easier to teach if they used averages.) Here are
the main reasons.
- The sums each have an arbitrary Maximum, different for
scales with different numbers of items, so the only way to
know the 'meaning' of a total is to know the scale intimately.
That is an unnecessary burden on the reader, who is not the
PI who loves his scale. Or it is a burden on the statistician
who is dealing with dozens of scales, and wants to deal
intelligently with this scale without spending his life on it.
- The items have verbal labels which can be used to
interpret the average. On the one hand, it gives labels like
"never". Also, it is the easiest way to show any reader,
that a difference of 0.1 points is trivial, while a difference
of 1.0 points is large. The scoring reflects the units of
the "effect size" in the terms of the measurement.
- When there are occasion items that were blank, the
question of "What did you do with the missing?" is readily
answered. The score is the "average of those answered,
requiring (say) at least 3/4ths of the items to be present"
or it will be scored missing.
The other alternative that I have used frequently for
composite scores - not often for a Likert scale, but usually for
factors that are formed across different domains - is the T-score.
Scales are standardized with a mean of 50 and a standard deviation
of 10 - usually using the mean and SD for the whole sample at Pre.
That makes it relatively easy to look at group differences and
changes across time. (The standard deviation of 10 means
that you can report interesting differences without the clutter
of decimal points. The mean of 50 means that you don't
have the clutter of negative values for group means.)