In article <4F1F6C7CD038D111BC7F00805F19987A0591966C@LMIG-MSG-03>,
[EMAIL PROTECTED] (Chen, Peter) wrote:
> Is the sum still a better measure of the "trait" than any individual
item?
That is very often the case.
> It is not clear what inferences can be drawn from the sum of the four
items.
Two answers:
1. Consider that with LISREL modeling it would be considered better to
use two "multiple indicators" of a trait than one for an analysis. And
four items which are "multiple indicators" are only that much better.
So, within the field of social science research, there is a double
standard: one the one hand, with a summed scale we expect a reliability
of say, .7. But in LISREL analysis, we accept as few as two multiple
indicators and don't worry about the reliability of the items. Yes,
there are computational differences between a LISREL model and using a
summed scale. But the logical issues are mainly the same.
2. Consider the measurement model for item i:
y(i) = x + e(i)
where y(i) is the response on item i,
x is true trait level,
e(i) is measurement error.
As we add the scores for several items, the correlation of y(1) + y(2) +
... with x increases, because the error terms tend to cancel out. This
is most clearly the case when the error terms are uncorrelated. But it
will generally occur to a lesser extent as long as all items are
correlated with x and error terms are not perfectly correlated.
> Reliability is the prerequisite of validity.
Yes, but the question, "How much reliability/validity is necessary?" is
not one with an exact answer. The level needed for a given application
depends on (1) the magnitude of the effect one is trying to detect, and
(2) the sample size. If the hypothesized effect is large enough, and
one has a large enough sample size, then a scale with relatively low
reliability (e.g., .3) and relatively low validity (e.g., .3^.5) may be
enough. One way to tell: if you get significant results with a scale
that has low reliability/validity, then your scale was reliable/valid
enough for that study.
John Uebersax
[EMAIL PROTECTED]
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