Anchored Max-Diff

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Anchored max-diff experiments supplement standard Max-Diff questions with additional questions designed to work out the absolute importance of the attributes. That is, while a traditional max-diff experiment identifies the relative importance of the attributes, an anchored max-diff experiment permits conclusions about whether specific attributes are actually important or not important.



These examples are from the data contained in File:AnchoredMaxDiff.QPack.

The table on the left shows the Probability % from a traditional max-diff experiment in which the attributes being compared are technology brands. Looking at the analysis we we can see that:

  • Google and Sony come in first and second place in terms of preference.
  • Apple has done better amongst the women than the men.
  • Intel and HP have done relatively better amongst the men than the women.

If you add up the percentages, each column adds to 100% and thus the analysis only focuses on relative preferences. Thus, while a naive read of the data would lead one to conclude that women like Apple more than do men, the data does not actually tell us this (i.e., it is possible that the men like every single brand more than do the women, but because the analysis is expressed as a percentage, such a conclusion cannot be obtained).

The table on the right shows the same analysis but in terms of the Coefficient. This is also uninformative, as these are indexed relative to the first brand, which is Apple. Thus, that men and women both have a score of 0 is an assumption of the analysis rather than an insight (the color-coding is because the significance test is comparing the relativities, and 0 is a relatively high score for the women).

UnanchoredMaxDiff.PNG MaxDiffCoef.PNG

Anchored max-diff resolves this conundrum by using additional data as a benchmark. In the table below, a question asking likelihood to recommend each of the brands has been used to anchor the max-diff experiment. In particular, a rating of 7 out of 10 by respondents has been used as a benchmark and assigned a coefficient of 0.[note 1] All of the other coefficients are thus interpreted relative to this benchmark value. Thus, we can see that Apple has received a score of less than seven amongst both men and women and so, in some absolute sense, the brand can be seen as performing poorly (as a score of less than seven in a question asking about likelihood to recommend is typically regarded as a poor score). The analysis also shows that men have a marginally lower absolute score than do women in terms of Apple (-0.68 versus -0.50), whereas Google has equal performance amongst the men and the women.


The significance tests indicated by the color-coding are showing relative performance. Thus, if we wish to test whether the difference between Apple by gender is significant we need to remove all the other brands from the analysis. This is shown on the left. The table on the right only contains the data for Intel; it shows that Intel is significantly more preferred, in an absolute sense, amongst men than women.

AnchoredApple.PNG AnchoredIntel.PNG

The two analyses above were created by selecting rows to remove, right-clicking and selecting Remove, and putting the brands back in again by right-clicking and selecting Revert. In each case, the automatic significance testing focuses on relativities.[note 2] To see how the brands perform in an absolute sense, we need to use gender as a filter rather than as the columns (as when using gender in the columns Q interprets this as meaning you are wanting to compare the genders).

The table output below shows the table with a Filter for women and with a Planned Test of Statistical Significance explicitly comparing Apple with the benchmark value of 0, which reveals that the absolute performance of Apple amongst women is significantly below the benchmark rating of 7 out of 10.


Types of anchored max-diff experiments

There are two common types of anchored max-diff experiments.

Dual response format

The dual response format involves following each max-diff question with another question asking something like:

Considering the four features shown above, would you say that...
○ All are important
○ Some are important, some are not
○ None of these are important.

Max-Diff combined with rating scales

Before or after the max-diff experiment, the respondent provides traditional ratings (e.g., rates all the attributes on a scale from 0 to 10).

The logic of standard max-diff analysis in Q

In order to understand how to set up max-diff experiments in Q it is necessary to first understand how Q interprets Max-Diff data. Q interprets each max-diff question as a partial ranking. Thus, if a respondent was given a question showing options A, B, C and F, and chose B as most preferred and F as least preferred, Q interprets this as the following ranking: B > A = C > F. Note that this is a different model to that used by Sawtooth Software.[note 3]

As discussed in Max-Diff Specifications, when each of the choice questions is set up in Q a 1 is used for the most preferred item, a -1 for the least preferred item, 0 for the other items that were shown but not chosen and NaN for the items not shown. Thus, B > A = C > D is encoded as:

A     B     C     D     E     F
0     1     0    NaN   NaN    -1     

where the alternatives not shown are coded as NaN.

Note that when analyzing this data Q only looks at the relative ordering and any other values could be used instead, provided that they imply the same ordering.

Setting up anchored max-diff experiments in Q

Setting up the dual response format anchored max-diff studies in Q

Anchoring is accomodated in Q by introducing a new alternative. In the case of the dual response, we will call this new alternative Zero. Consider again the situation where the respondent has been faced with a choice of A, B, C and F and has chosen B as best and F as worst, which leads to B > A = C > F.

The Zero alternative is always assigned a value of 0. The value assigned to the other alternatives is then relative to this zero value.

All are important

Where all of the items are important this implies that all are ranked higher than the Zero option:

A     B     C     D     E     F    Zero
2     3     2    NaN   NaN    1     0 

Some are important

Where some of the items are important this implies that the most preferred item must be more important than Zero, the least preferred item must be less preferred than Zero, but we do not know the relative preference of the remaining items relative to Zero, and thus this is coded as:

A     B     C     D     E     F    Zero
0     1     0    NaN   NaN    -1     0

Note that although this coding implies that A = C = Zero, the underlying algorithm does not explicitly assume these things are equal. Rather, it simply treats this particular set of data as not providing any evidence about the relative ordering of these alternatives.

None are important

 A     B     C     D     E     F    Zero
-2    -1    -2    NaN   NaN    -3    0 

Setting up the combined Max-Diff with ratings in Q

Prior to explaining how to use ratings to anchor the max-diff it is useful to first understand how ratings data can be combined with the max-diff experiment without anchoring. Again the situation where a max-diff task reveals that B > A = C > F. Consider a rating question where the six alternatives are rated, respectively, 9, 10, 7, 7, 7, 7 and 3. Thus, the ratings imply that: B > A > C = D = E > F and this information can be incorporated into Q as if just another question in the max-diff experiment:

A     B     C     D     E     F 
9    10     7     7     7     3 

Anchoring is achieved by using the scale points. We can use some or all of the scale points as anchors.[note 4] From an interpretation perspective it is usually most straightforward to choose a specific point as the anchor value. For example, consider the case where we decide to use a rating of 7 as the anchor point. We create a new alternative for the analysis which we will call Seven.

In the case of the max-diff tasks, as they only focus on relativities, they are set up in the standard way. Thus, where a max-diff question reveals that B > A > C = D = E > F, we include this new anchoring alternative, but it is assigned a value of NaN as nothing is learned about its relative appeal from this task.

 A     B     C     D     E     F    Seven
-2    -1    -2    NaN   NaN    -3    NaN

The setup of the ratings data is then straightforward. It is just the actual ratings provided by respondents, but with an additional item containing the benchmark value:

A     B     C     D     E     F    Seven 
9    10     7     7     7     3      7

See also


  1. This alternative has been moved to the top by dragging and dropping. This is necessary as Q will always default to comparing relative to the first option.
  2. However, as there are only two alternatives and one is an absolute benchmark, an analysis of their relative performance becomes a test of the absolute difference in gender.
  3. Sawtooth assumes that the difference between the appeal of B versus either A and C is equal to the difference between either A and C versus F.
  4. The data file for the Example contains an example involving dual anchors.
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