```Date: Thu, 4 Dec 1997 18:16:24 -0700 Reply-To: "Raymond V. Liedka" Sender: "SPSSX(r) Discussion" From: "Raymond V. Liedka" Subject: Re: Questions On Scale-Construction Comments: To: John R Hills 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 ```

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