SPSS returns lower and upper bounds for Reliability. While calculating the Standard Error of Measurement, should we use the Lower and Upper bounds or continue using the Reliability estimate.

I am using the formula :

$$\text{SEM}\% =\left(\text{SD}\times\sqrt{1-R_1} \times 1/\text{mean}\right) × 100$$

where SD is the standard deviation, $R_1$ is the intraclass correlation for a single measure (one-way ICC).

  • You seem to be calculating the coefficient of variation of the measurement, not the standard deviation or standard error. – GaBorgulya Apr 7 '11 at 14:47
  • @GaBorgulya Usually, SEM is computed in a different way; contrary to SD or SE, it is supposed to account for scores reliability, specific to the measurement instrument. – chl Apr 8 '11 at 1:10

You should use the point estimate of the reliability, not the lower bound or whatsoever. I guess by lb/up you mean the 95% CI for the ICC (I don't have SPSS, so I cannot check myself)? It's unfortunate that we also talk of Cronbach's alpha as a "lower bound for reliability" since this might have confused you.

It should be noted that this formula is not restricted to the use of an estimate of ICC; in fact, you can plug in any "valid" measure of reliability (most of the times, it is Cronbach's alpha that is being used). Apart from the NCME tutorial that I linked to in my comment, you might be interested in this recent article:

Tighe et al. The standard error of measurement is a more appropriate measure of quality for postgraduate medical assessments than is reliability: an analysis of MRCP(UK) examinations. BMC Medical Education 2010, 10:40

Although it might seem to barely address your question at first sight, it has some additional material showing how to compute SEM (here with Cronbach's $\alpha$, but it is straightforward to adapt it with ICC); and, anyway, it's always interesting to look around to see how people use SEM.

There are 3 ways to calculate SEM. Also it is important if you want to have SEM agreement or SEM consistency. I will show you the SEM calculaton from reliability.

First you should have ICC (intra-class correlation) and the SD (standard Deviation). Then you calculate SEM as follows:
$$ SEM= SD*(\sqrt{1-ICC}) $$

  • Welcome to the site, @amin. I took the liberty of editing your post to clean it up slightly & display the formula with $\LaTeX$. Please make sure everything still says what you want. – gung Feb 17 '13 at 3:39
  • Moved the "1-" inside the square root which I believe is the correct relationship – Ming-Chih Kao Dec 13 '13 at 13:11

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