Re: st: statistical question: best summary measure for a 5-point Likert scale

[Ron�n Conroy <rconroy@rcsi.ie>]

On 14 Meith 2006, at 17:57, Christopher W. Ryan wrote:

> I may be wrong, but I have some reservations about calculating  
> means of
> scores on a 5-point Likert scale.  To me it seems like an ordinal  
> scale.
>  I keep making the claim that the proper measure of central  
> tendency in
> this case would be the median.  None of my colleagues agree; I get the
> feeling they don't see any problem with putting arbitrary consecutive
> integer values on the different levels of performance.  My point is
> that, while it is neat and tidy and perhaps intuitive, we have no
> evidence that the labeled levels on the performance scale are equally
> "spaced."

A single item 5-point scale is problematic. If you have these  
relative frequencies

A - 0%
B - 20%
C - 60%
D - 5%
E - 15%

there is no doubt as to the unequal spacing of the items, but the  
median (C) is also the 25th and 75th centiles. Indeed, the most  
important piece of information here is that almost two thirds of the  
data fall into one of the five categories, while a further category  
has no observations at all. This is not invented; I am analysing data  
from clinical assessments that looks pretty much like this, and the  
distribution of marks has led to the scrapping of the assessment.  
Amongst other things, it revealed that a problem with the marks and  
standards meant that there was almost no way a student could get a D  
grade.

With a single item, I believe that there is no way of knowing what  
the best data summary is until you have looked at the data.

A scale made up of such 5-point items, however, is a different  
matter. Here, the assumption is that the inequalities in scale  
intervals will cancel out and that the underlyings scale will  
approximate to an interval measure. In this case, I favour averaging  
the total score rather than presenting it as a sum.

We frequently see scales where the lowest response is scored as 1 and  
the highest as 5. This means that the sum can vary between k and 5k,  
where k is the number of items. Interpreting the sum entails knowing  
how many items there are and remembering that no-one can score lower  
than this. Silly.

The alternative is to take the average, which maps the final score  
back onto the original measurement scale. No argument, say I.



=========
Ron�n Conroy
Royal College of Surgeons in Ireland
rconroy@rcsi.ie
+353 (0) 1 402 2431
+353 (0) 87 799 97 95
www.flickr.com/photos/ronanconroy




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