Date: Thu, 4 Dec 1997 18:16:24 -0700
Reply-To: "Raymond V. Liedka" <liedka@UNM.EDU>
Sender: "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From: "Raymond V. Liedka" <liedka@UNM.EDU>
Subject: Re: Questions On Scale-Construction
In-Reply-To: <19971203.173438.3590.1.jrhills@juno.com>
Content-Type: TEXT/PLAIN; charset=US-ASCII
On Tue, 2 Dec 1997, John R Hills wrote:
> Markus:
>
> You have received excellent responses to your query from Don
> Burrill and Paul Gardner. I have only one idea I would like to add to
> theirs.
> You comment that objectivity and reliability of your scale have
> been "proved otherwise." If, indeed, you have "proved" validity
> otherwise, why are you asking about reliability? If a scale is valid, it
> has to be reliable.
[cut]
I'm sorry, but this statement -- "If a scale is valid, it has to be
reliable" -- just isn't so.
Taking a hand from classical measurement theory, let T be the true
(unobserved) score, and e be random measurement error. Then X is the
observed score and is: X = T + e where E(e)=0 insures nonbiased
measurement (mean of the measurement error is zero).
Supppose you have two measurement instruments, then the observed
measurements for each instrument is:
X1 = T + e1 (for the first instrument)
X2 = T + e2 (for the second one)
Now...suppose that var(e1) > var(e2). The reliability of the first
instrument will be LOWER than the reliability of the second instrument.
But both are valid -- nonbiased linear functions of the true score.
I almost wrote that it was difficult to come up with examples of valid
measurement instruments that have different reliabilities, but that isn't
really true either. Take two rulers. One is marked off only in
quarter-inches, and the second is marked off in 32nds of an inch. Both
are rulers and valid instruments to measure length. But which will be
more reliable?
Raymond V. Liedka
Department of Sociology
University of New Mexico
