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I would like to convert the mean score of a sample that was administered a questionnaire using a six point likert scale into a mean that is comparable to the same questionnaire using a four point likert scale.

The questionnaire in question is the Rosenberg Self-Esteem Scale (RSES) which is most commonly administered using a four point likert scale (0-3). I want to convert a mean from a six point likert scale ranging from 1-6 into the standard 0-3 so that I can compare sample means across different studies.

What is the conversion formula for this operation? What are some theoretical concerns in doing this conversion, and is this kind of conversion described in any scientific literature that can be referred to?

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  • $\begingroup$ Whatever formula you use, make sure it is reversible. Convert from six point to four point, and then use the equivalent formula to convert from six point to four point; if it doesn't produce the original values you'll know it's an inappropriate formula. $\endgroup$ Aug 25, 2023 at 12:25

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A major issue here is that answers on such scales are usually seen as ordinal, meaning that the value difference between subsequent levels doesn't carry any meaning. People who hold this view may say that means can't be meaningfully compared in the first place. Even though some are more liberal on that (including myself), they might still get a headache from comparing means computed from two different scales like 4-point vs. 6-point, whatever standardisation to achieve comparability is actually done (whatever you can do will treat the data at interval level, which they are actually not). Different scales may have different verbal descriptors (no way can we know how these "translate" into each other), and there is really no way to justify a statement that, say, 2 in the 6-point scale corresponds to 0.7 in the 4-point scale.

So it would be rather irresponsible to tell you that this is a valid thing to do. But in any case, as I can understand that you may just want to play around with something anyway, here's a "quick and dirty" idea (it's really dirty, see above):

A possible conversion would be to transform all scales into the $[0,1]$-interval, i.e., dividing the 0-3 scale by 3 and subtracting 1 from the 1-6 scale to reach 0-5, then dividing by 5.

Note however that other alternatives are conceivable. Particularly one may want to take the actual data into account so that if a variable only ever scores 2 and 3 out of 0-3, it is still spread out over the whole interval. Also some might object that the conversion about will map the lowest and highest values of both scales on 0 and 1, respectively, but in fact the 6-point scale has a larger range and 1 and 6 should maybe be more extreme than 0 and 3 of the 4-point scale. Many arguments could be made, and there is no objective reason to prefer one over another.

I don't think that this is recommended in any literature, as it really shouldn't be recommended. ;-)

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