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

 From Ronán Conroy To statalist@hsphsun2.harvard.edu Subject Re: st: statistical question: best summary measure for a 5-point Likert scale Date Mon, 19 Jun 2006 10:03:07 +0100

```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.

=========
Ronán 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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