Conjoint analysis provides various outputs for analysis, including part-worth utilities, counts and importance.

Here we discuss these measures and give guidelines for interpreting results and presenting findings to management. Before focusing on conjoint data, it is useful to review some fundamentals for interpreting quantitative data. The discussion of the nature of measurement scales follows the classic discussion of Stevens (1946), which has been adopted by numerous social scientists and business researchers.

**Nature of Quantitative Data**

There are four general types of quantitative data:

Nominal data - Here the numbers represent categories, such as (1=male, 2=female) or (20=Italy, 21=Canada, 22=Mexico). It is not appropriate to perform mathematical operations such as addition or subtraction with nominal data or to interpret the relative size of the numbers.

Ordinal data - These commonly occur in market research in the form of rankings. If a respondent ranks five brands from best 1 to worst 5, we know that a 1 is preferred to a 2. An example of an ordinal scale is the classification of strengths of hurricanes. A category 3 hurricane is stronger and more damaging than a category 2 hurricane. It is generally not appropriate to apply arithmetic operations to ordinal data. The difference in strength between a category 1 and category 2 hurricanes is not necessarily equal to the difference in strength between a category 2 and a category

3. Nor can we say that a category 2 is twice as strong as a category 1 hurricane.

Interval data - These permit the simple operations of addition and subtraction. The rating scales so common to market research provide interval data. The Celsius scale is an example of an interval scale. Each degree of temperature represents an equal heat increment. It takes the same amount of heat to raise the temperature of a cup of water from 10 to 20 degrees as from 20 to 30 degrees. The zero point is arbitrarily tied to the freezing point of distilled water. Sixty degrees is not twice as hot as 30 degrees, and the ratio 60/30 has no meaning.

Ratio data - These data permit all basic arithmetic operations, including division and multiplication. Examples of ratio data include weight, height, time increments, revenue, and profit. The zero point is meaningful in ratio scales. The difference between 20 and 30 kilograms is the same as the difference between 30 and 40 kilograms, and 40 kilograms is twice as heavy as 20 kilograms.

**Conjoint Utilities**

Conjoint utilities or part-worth are scaled to an arbitrary additive constant within each attribute and are interval data. The arbitrary origin of the scaling within each attribute results from dummy coding in the design matrix. We could add a constant to the part-worth for all levels of an attribute or to all attribute levels in the study, and it would not change our interpretation of the findings. When using a specific kind of dummy coding called effects coding, utilities are scaled to sum to zero within each attribute. A plausible set of part-worth utilities for fuel efficiency measured in miles per gallon might look like this:

__Fuel__

__Efficiency____Utility__

30 mpg -1.0

40 mpg 0.0

50 mpg 1.0

30 mpg received a negative utility value, but this does not mean that 30 mpg was unattractive. In fact, 30 mpg may have been acceptable to all respondents. But, all else being equal, 40 mpg and 50 mpg are better. The utilities are scaled to sum to zero within each attribute, so 30 mpg must receive a negative utility value. Other kinds of dummy coding arbitrarily set the part-worth of one level within each attribute to zero and estimate the remaining levels as contrasts with respect to zero.

Whether we multiply all the part-worth utilities by a positive constant or add a constant to each level within a study, the interpretation is the same. Suppose we have two attributes with the following utilities:

__Color __* Utility Brand Utility*

Blue 30 A 20

Red 20 B 40

Green 10 C 10

The increase in preference from Green to Blue (twenty points) is equal to the increase in preference between brand A and brand B (also twenty points). However, due to the arbitrary origin within each attribute, we cannot directly compare values between attributes to say that Red (twenty utiles) is preferred equally to brand A (twenty utiles). And even though we are comparing utilities within the same attribute, we cannot say that Blue is three times as preferred as Green (30/10). Interval data do not support ratio operations.

**Counts**

When using choice-based conjoint (CBC), the researcher can analyze the data by counting the number of times an attribute level was chosen relative to the number of times it was available for choice. In the absence of prohibitions, counts proportions are closely related to conjoint utilities. If prohibitions were used, counts are biased. Counts are ratio data. Consider the following counts proportions:

__Color__* Proportion Brand Proportion*

Blue 0.50 A 0.40

Red 0.30 B 0.50

Green 0.20 C 0.10

We can say that brand A was chosen four times as often as brand C (0.40/0.10). But, as with conjoint utilities, we cannot report that Brand A is preferred to Red.

**Attribute Importance**

Sometimes we want to characterize the relative importance of each attribute. We can do this by considering how much difference each attribute could make in the total utility of a product. That difference is the range in the attribute’s utility values. We calculate percentages from relative ranges, obtaining a set of attribute importance values that add to 100 percent, as illustrated in exhibit 9.1. For this respondent whose data are shown in the exhibit, the importance of brand is 26.7 percent, the importance of price is 60 percent, and the importance of color is 13.3 percent. Importance depends on the particular attribute levels chosen for the study. For example, with a narrower range of prices, price would have been less important.

Relative importance of attributes

When summarizing attribute importance for groups, it is best to compute importance for respondents individually and then average them, rather than computing importance from average utilities. For example, suppose we were studying two brands, Coke and Pepsi. If half of the respondents preferred each brand, the average utilities for Coke and Pepsi would be tied, and the importance of brand would appear to be zero.

Importance measures are ratio-scaled, but they are also relative, study-specific measures. An attribute with an importance of twenty percent is twice as important as an attribute with an importance of ten, given the set of attributes and levels used in the study. That is to say, importance has a meaningful zero point, as do all percentages. But when we compute an attribute’s importance, it is always relative to the other attributes being used in the study. And we can compare one attribute to another in terms of importance within a conjoint study but not across studies featuring different attribute lists.

When calculating importance from CBC data, it is advisable to use partworth utilities resulting from latent class (with multiple segments) or, better yet, HB estimation, especially if there are attributes on which respondents disagree about preference order of the levels. (Recall the previous Coke versus Pepsi example.)

One of the problems with standard importance analysis is that it considers the extremes within an attribute, irrespective of whether the part-worth utilities follow rational preference order. The importance calculations capitalize on random error, and attributes with very little to no importance can be biased upward in importance. There will almost always be a difference between the part-worth utilities of the levels, even if it is due to random noise alone. For that reason, many analysts prefer to use sensitivity analysis in a market simulator to estimate the impact of attributes.

By

*Shruthi Mylaram*

*Operations - 2*

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