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Max-Diff: Difference between Probability Scale, Zero-Anchored Interval Scale, and Zero-Centered Raw Scores


For MXD exercises, after analyzing the data using "HB" as the analysis type you are presented with the data in the following tabs: Probability Scale, Zero-Anchored Interval Scale, and Zero-Centered Raw Scores.

I am wondering if one is superior to the others, or if/when you would choose one over the other for further data analysis?

I typically use data  from the Probability Scale tab since the results for each survey participant sums to 100. I feel that makes your results easier to understand when presenting it in tables and figures.

Thank you!
asked Nov 16 by arbest2 (160 points)

2 Answers

+1 vote
Best answer
The three "scales" are three ways of reporting the same MaxDiff scores. Zero-Centered Raw Scores are the "raw" results of the MNL calculation and can be difficult to interpret because of their interval scaling. Zero-Anchored Interval Scale are those same scores normalized so that each respondent has a utility range of 100 points. And Probability Scale (also call Rescaled or 0-100 Scale) scores are the same scores but rescaled to sum to 100 total.

Although all three scales are statements of the same data, most people tend to report the Probability Scaled scores since they're easy to interpret and have that nice ratio property.

If you ever want to set up a MaxDiff choice simulation or TURF optimizer, then the Raw scores should be used since they can plug right back in to the logit choice formula.

For a more detailed description you can refer to the tail end of this Help article: https://sawtoothsoftware.com/help/lighthouse-studio/manual/maxdiff-individual-level-score-estimation.html
answered Nov 16 by Cameron Halversen Sawtooth Software, Inc. (425 points)
selected Nov 16 by arbest2
Thank you for the explanation!
+1 vote
Probability scores are indeed easier for non-researchers to interpret.  They add to 100.  A 10 is "worth" twice as much as a 5.  However, you'll find that on the low end of the scale the worst items all seem to crush down (at least visually) toward zero.  (However, if we truly think of things as probability scaled, then a 0.02 is twice as preferred as a 0.01, etc... so even though it seems the scores are crushed on the low end, they really aren't when you consider that they truly are ratio scaled).

For showing differences across groups of people, I sometimes prefer showing the zero-centered scaling options.  That (at least visually to the eyes) seems to achieve more separation on the scores at both the high and low ends.  I often put a "heat-map" setting on the tables of numbers so that positive numbers go toward green and negative numbers go toward red.
answered Nov 16 by Bryan Orme Platinum Sawtooth Software, Inc. (201,265 points)
Thank you for your response! Your insight is appreciated.