MaxDiff - Probability vs. Zero-Centered Ranking Discrepancy

Question

I'm working on a Maxdiff project and realized once findings have been delivered to the client that the Total sample rankings have been reported from "Probability" scaling, but rankings from two segments also reported on were ranked and reported using the "Zero-centered Raw" Scaling.

I am trying to send along the scores for all items tested, so I went to change those scores that were zero-centered to probability, but this causes the overall rankings have now changed.

I guess I was under the assumption that regardless of scaling method, the order of preference for items would remain the same, but that doesn't seem to be the case given this discrepancy. Can anyone provide further insight on why this might be (highly likely due to relative ignorance about the nuances of different scaling methods) - thanks in advance!

Answer 1

Sure, this is a common misunderstanding.  The "Probability" rescaling method is a non-linear transformation (exponential) that takes items on the lower part of the scale and squishes them closer together and items at the upper end of the scale and stretches them somewhat.  The zero-centered Raw scaling transformation, however, is a linear transformation that doesn't involve a non-linear stretching.

Within a single respondent's scores, whether you do one transformation or the other, the ranking of the items cannot change.  But, take multiple respondents with differences in preference and perform the two transformations on those individual respondents...but then average those results across respondents...and the rank order of the average summary preferences (across respondents) can indeed change between linear and non-linear transformation methods.

Usually the changes in rank order from the average results (due to a linear transformation vs. a non-linear transformation) across respondents aren't very noteworthy in terms of changing managerial implications.