The MaxDiff is a long-established academic mathematical theory with very specific assumptions about how people make choices: it assumes that respondents evaluate all possible pairs of items within the displayed set and choose the pair that reflects the maximum difference in preference or importance. it may be thought of as a variation of the method of Paired Comparisons. Consider a set in which a respondent evaluates four items: A, B, C and D. If the respondent says that A is best and D is worst, these two responses inform us on five of six possible implied paired comparisons:
- A > B, A > C, A > D, B > D, C > D
The only paired comparison that cannot be inferred is B vs. C. In a choice among five items, MaxDiff questioning informs on seven of ten implied paired comparisons.
Relationship to Best-Worst Scaling
Maxdiff and Best-Worst Scaling (BWS) have erroneously been considered synonyms. Respondents can produce best-worst data in any of a number of ways, with a maxdiff process being but one. Instead of evaluating all possible pairs (the maxdiff model), they might choose the best from n items, the worst from the remaining n-1, or vice versa (sequential models). Or indeed they may use another method entirely. Thus it should be clear that maxdiff is a subset of BWS; maxdiff is BWS, but BWS is not necessarily maxdiff. Indeed maxdiff might not be considered an attractive model on psychological and intuitive grounds: as the number of items increases, the number of possible pairs increases in a multiplicative fashion: n items produces n(n-1) pairs (where best-worst order matters). Assuming respondents do evaluate all possible pairs is a strong assumption. Early work did use the term maxdiff to refer to BWS, but with Marley's return to the field, correct academic terminology has been disseminated throughout Europe and Asia-Pacific.
Commercial software named maxdiff
In North America the term maxdiff continues to be used for studies that are in fact BWS studies. This probably reflects the fact that Sawtooth Software in the USA implements a procedure it has named maxdiff. Indeed it is unclear whether this procedure implements maxdiff procedures in estimating parameters of their models, or whether the simpler, sequential BWS model is used.
Conduct and analysis of a maxdiff survey
A maxdiff survey may be designed and analysed in two ways:
- Through manual design and researcher-led analysis using standard statistical software procedures (see BWS) or
- By utilising a commercial survey company which supports this type of discrete choice model.
- Marley, Anthony AJ; Louviere, Jordan J. (2005-01-01). "Some probabilistic models of best, worst, and best–worst choices". Journal of Mathematical Psychology 49 (6): 464–480. doi:10.1016/j.jmp.2005.05.003.
- Louviere, Jordan J; Flynn, Terry N; Marley, A A J (September 2015). Best-Worst Scaling: Theory, Methods and Applications. Cambridge University Press. ISBN 9781107043152. Retrieved 2 October 2015.
- Marley, A. A. J.; Louviere, J. J. (2005-12-01). "Some probabilistic models of best, worst, and best–worst choices". Journal of Mathematical Psychology. Special Issue Honoring Jean-Claude Falmagne: Part 1 49 (6): 464–480. doi:10.1016/j.jmp.2005.05.003.
- Flynn, Terry N.; Louviere, Jordan J.; Peters, Tim J.; Coast, Joanna (2008-11-18). "Estimating preferences for a dermatology consultation using Best-Worst Scaling: Comparison of various methods of analysis". BMC Medical Research Methodology 8 (1): 76. doi:10.1186/1471-2288-8-76. ISSN 1471-2288. PMC 2600822. PMID 19017376.