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Is there a concern using a 4-point likert-type scale (i.e., agreement) when attempting a cluster analysis using k-means clustering? Most of the data for the items in my data set are favorable (e.g., Strongly Agree and/or Agree). Would I get better results with a 5-point scale?

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K-means is for interval data. So, using it means that you assume Likert rating scale is interval. OK, you have your right for this, albeit puristic people will frown and mutter "likerts are ordinal, likerts are ordinal...".

Next, K-means is expected to be "better", more discriminating, for finely grained scale (a one closer to be continuous). This is as in everywhere in analysis: thin scales are usually better than rude scales. So, generally, 5-point scale would be better than 4-point scale.

Still, you should think twice, because psychometrically 4-point and 5-point rating scales behave not identically. 4-point scale is visually opinion-disruptive, having no central point; it is perceived as forcing to take a stand. That might be bad in one contexts and good in other contexts, in the end, the decision is yours. 5-point scale suffers from having number 5 at the edge - which is culturally prominant in many societies, and it has another similarly "magic" number 3 (right in the middle!). Both can produce "focal effects" which result in prevalence of these two scores and hence the bimodal distribution (which will show up in clustering). It might be better not to display numbers with 5-point scale: letters or just bare notches instead.

Some questions/answers related to your question: this, this, this, this.

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