CONJOINT ANALYSIS


WHAT IS CONJOINT ANALYSIS?

We introduced conjoint analysis in Volume III of this series. Recall that conjoint analysis is a multivariate technique used specifically to understand how respondents develop preferences for products or services. It is based on the simple premise that consumers evaluate the value of a product/service/idea (real or hypothetical) by combining the separate amounts of value provided by each attribute.

It is this characteristic that is of interest in the DFSS methodology. After all, we want to know the bundle of utility from the customer's perspective. (The reader is encouraged to review Volume III, Chapter 11.) So in this section, rather than dwelling on theoretical statistical explanations , we will apply conjoint analysis in a couple of hypothetical examples. The examples are based on the work of Hair et al. (1998) and are used here with the publisher's permission.

A HYPOTHETICAL EXAMPLE OF CONJOINT ANALYSIS

As an illustration of conjoint analysis, let us assume that HATCO is trying to develop a new industrial cleanser. After discussion with sales representatives and focus groups, management decides that three attributes are important: cleaning ingredients , convenience of use, and brand name . To operationalize these attributes, the researchers create three factors with two levels each:

Factor

Level

Ingredients

Phosphate-free

Phosphate-based

Form

Liquid

Powder

Brand name

HATCO

Generic brand

A hypothetical cleaning product can be constructed by selecting one level of each attribute. For the three attributes (factors) with two values (levels), eight (2 — 2 — 2) combinations can be formed . Three examples of the eight possible combinations (stimuli) are:

  • HATCO phosphate-free powder

  • Generic phosphate-based liquid

  • Generic phosphate-free liquid

HATCO customers are then asked either to rank-order the eight stimuli in terms of preference or to rate each combination on a preference scale (perhaps a 1-to-10 scale). We can see why conjoint analysis is also called "trade-off analysis," because in making a judgment on a hypothetical product, respondents must consider both the "good" and "bad" characteristics of the product in forming a preference. Thus, respondents must weigh all attributes simultaneously in making their judgments .

By constructing specific combinations (stimuli), the researcher is attempting to understand a respondent's preference structure. The preference structure "explains" not only how important each factor is in the overall decision, but also how the differing levels within a factor influence the formation of an overall preference (utility). In our example, conjoint analysis would assess the relative impact of each brand name (HATCO versus generic), each form (powder versus liquid), and the different cleaning ingredients (phosphate-free versus phosphate-based) in determining the utility to a person. This utility, which represents the total "worth" or overall preference of an object, can be thought of as based on the part-worths for each level. The general form of a conjoint model can be shown as

(Total worth for product) ij... , n

=

Part-worth of level i for factor 1

   
  • + Part-worth of level j for factor 2 +...

   
  • + Part-worth of level n for factor m

where the product or service has m attributes, each having n levels. The product consists of level i of factor 2, level j of factor 2, and so forth, up to level n for factor m.

In our example, a simple additive model would represent the preference structure for the industrial cleanser as based on the three factors (utility = brand effect + ingredient effect + form effect). The preference for a specific cleanser product can be directly calculated from the part-worth values. For example, the preference for HATCO phosphate-free powder is:

Utility

=

Part-worth of HATCO brand

   
  • + Part-worth of phosphate-free cleaning ingredient

   
  • + Part-worth of powder

With the part-worth estimates, the preference of an individual can be estimated for any combination of factors. Moreover, the preference structure would reveal the factor(s) most important in determining overall utility and product choice. The choices of multiple respondents could also be combined to represent the competitive environment faced in the "real world."

AN EMPIRICAL EXAMPLE

To illustrate a simple conjoint analysis, assume that the industrial cleanser experiment was conducted with respondents who purchased industrial supplies . Each respondent was presented with eight descriptions of cleanser products (stimuli) and asked to rank them in order of preference for purchase (1 = most preferred; 8 = least preferred). The eight stimuli are described in Table 2.3, along with the rank orders given by two respondents.

Table 2.3: Stimuli Descriptions and Respondent Rankings for Conjoint Analysis of Industrial Cleanser
 

Stimuli Descriptions

Respondent Rankings

 

Form

Ingredients

Brand

Respondent 1

Respondent 2

1

Liquid

Phosphate-free

HATCO

1

1

2

Liquid

Phosphate-free

Generic

2

2

3

Liquid

Phosphate-based

HATCO

5

3

4

Liquid

Phosphate-based

Generic

6

4

5

Powder

Phosphate-free

HATCO

3

7

6

Powder

Phosphate-free

Generic

4

5

7

Powder

Phosphate-based

HATCO

7

8

8

Powder

Phosphate-based

Generic

8

6

As we examine the responses for respondent 1, we see that the ranks for the stimuli with the phosphate-free ingredients are the highest possible (1, 2, 3, and 4), whereas the phosphate-based product has the four lowest ranks (5, 6, 7, and 8). Thus, the phosphate-free product is much more preferred than the phosphate-based cleanser. This can be contrasted to the ranks for the two brands, which show a mixture of high and low ranks for each brand. Assuming that the basic model (an additive model) applies, we can calculate the impact of each level as differences (deviations) from the overall mean ranking. (Readers may note that this is analogous to multiple regression with dummy variables or ANOVA.) For example, the average ranks for the two cleanser ingredients (phosphate-free versus phosphate-based) for respondent 1 are:

Phosphate-free: (1 + 2 + 3 + 4)/4 = 2.5

Phosphate-based: (5 + 6 + 7 + 8)/4 = 6.5

With the average rank of the eight stimuli of 4.5 [(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8)/8 = 36/8 = 4.5], the phosphate-free level would then have a deviation of -2.0 (2.5 - 4.5) from the overall average, whereas the phosphate-based level would have a deviation of +2.0 (6.5 - 4.5). The average ranks and deviations for each factor from the overall average rank (4.5) for respondents 1 and 2 are given in Table 2.4. In our example, we use smaller numbers to indicate higher ranks and a more preferred stimulus (e.g., 1 = most preferred). When the preference measure is inversely related to preference, such as here, we reverse the signs of the deviations in the part-worth calculations so that positive deviations will be associated with part-worths indicating greater preference. Deviation is calculated as: deviation = average rank of level - overall average rank (4.5). Note that negative deviations imply more preferred rankings.

Table 2.4: Average Ranks and Deviations for Respondents 1 and 2

Factor Level

Ranks Across Stimuli

Average Rank of Level

Deviation from Overall Average Rank

Respondent 1

Form

     

Liquid

1, 2, 5, 6

3.5

-1.0

Powder

3, 4, 7, 8

5.5

+1.0

Ingredients

     

Phosphate-free

1, 2, 3, 4

2.5

-2.0

Phosphate-based

5, 6, 7, 8

6.5

+2.0

Brand

     

HATCO

1, 3, 5, 7

4.0

-.5

Generic

2, 4, 6, 8

5.0

+.5

Respondent 2

Form

     

Liquid

1, 2, 3, 4

2.5

-2.0

Powder

5, 6, 7, 8

6.5

+2.0

Ingredients

     

Phosphate-free

1, 2, 5, 7

3.75

-.75

Phosphate-based

3, 4, 6, 8

5.25

+.75

Brand

     

HATCO

1, 3, 7, 8

4.75

+.25

Generic

2, 4, 5, 6

4.25

-.25

The part-worths of each level are calculated in four steps:

  • Step 1: Square the deviations and find their sum across all levels.

  • Step 2: Calculate a standardizing value that is equal to the total number of levels divided by the sum of squared deviations.

  • Step 3: Standardize each squared deviation by multiplying it by the standardizing value.

  • Step 4: Estimate the part-worth by taking the square root of the standardized squared deviation.

Let us examine how we would calculate the part-worth of the first level of ingredients (phosphate-free) for respondent 1. The deviations from 2.5 are squared. The squared deviations are summed (10.5). The number of levels is six (three factors with two levels apiece). Thus, the standardizing value is calculated as .571 (6/10.5 = .571). The squared deviation for phosphate-free (2 2 ; remember that we reverse signs) is then multiplied by .571 to get 2.284 (2 2 — .571 = 2.284). Finally, to calculate the part-worth for this level, we then take the square root of 2.284, for a value of 1.1511. This process yields part-worths for each level for respondents 1 and 2, as shown in Table 2.5.

Table 2.5: Estimated Part-Worths and Factor Importance for Respondents 1 and 2
 

Estimated Part-Worths

Calculating Factor Importance

Factor Level

Reversed Deviation [a]

Squared Deviation

Standardized Deviation [b]

Estimated Part-Worth [c]

Range of Part-Worths

Factor Importance [d]

Respondent 1

Form

           

Liquid

+1.0

1.0

+.571

+.756

   

Powder

-1.0

1.0

-.571

-.756

1.512

28.6%

Ingredients

           

Phosphate- free

+2.0

4.0

+2.284

+1.511

   

Phosphate-based

-2.0

4.0

-2.284

-1.511

3.022

57.1%

Brand

           

HATCO

+.5

.25

+.143

+.378

   

Generic

-.5

.25

-.143

-.378

.756

14.3%

Sum of squared deviations

 

10.5

       

Standardizing value [e]

 

.571

       

Sum of part-worth ranges

       

5.290

 

[a] Deviations are reversed to indicate higher preference for lower ranks. Sign of deviation used to indicate sign of estimated part-worth.

[b] Standardized deviation equal to the squared deviation times the standardizing value.

[c] Estimated part-worth equal to the square root of the standardized deviation.

[d] Factor importance equal to the range of a factor divided by the sum of the ranges across all factors, multiplied by 100 to yield a percentage.

[e] Standardizing value equal to the number of levels (2 + 2 + 2 = 6) divided by the sum of the squared deviations.

Respondent 2

Form

           

Liquid

+2.0

4.0

+2.60

+1.612

   

Powder

-2.0

4.0

-2.60

-1.612

3.224

66.7%

Ingredients

           

Phosphate- free

+.75

.5625

+.365

+.604

   

Phosphate-based

-.75

.5625

-.365

-.604

1.208

25.0%

Brand

           

HATCO

-.25

.0625

-.04

-.20

   

Generic

+.25

.0625

+.04

+.20

.400

8.3%

Sum of squared deviations

 

9.25

       

Standardizing value

 

.649

       

Sum of part-worth ranges

       

4.832

 

[a] Deviations are reversed to indicate higher preference for lower ranks. Sign of deviation used to indicate sign of estimated part-worth.

[b] Standardized deviation equal to the squared deviation times the standardizing value.

[c] Estimated part-worth equal to the square root of the standardized deviation.

[d] Factor importance equal to the range of a factor divided by the sum of the ranges across all factors, multiplied by 100 to yield a percentage.

[e] Standardizing value equal to the number of levels (2 + 2 + 2 = 6) divided by the sum of the squared deviations.

Because the part-worth estimates are on a common scale, we can compute the relative importance of each factor directly. The importance of a factor is represented by the range of its levels (i.e., the difference between the highest and lowest values) divided by the sum of the ranges across all factors. For example, for respondent 1, the ranges are 1.512 [.756 - (-.756)], 3.022 [1.511 - (-1.511)], and .756 [.378 - (-.378)]. The sum total of ranges is 5.290. The relative importance for form, ingredients, and brand is calculated as 1.512/5.290, 3.022/5.290, and .756/5.290, or 28.6, 57.1, and 14.3 percent, respectively. We can follow the same procedure for the second respondent and calculate the importance of each factor, with the results of form (66.7 percent), ingredients (25 percent), and brand (8.3 percent). These calculations for respondents 1 and 2 are also shown in Table 2.5.

To examine the ability of this model to predict the actual choices of the respondents, we predict preference order by summing the part-worths for the different combinations of factor levels and then rank ordering the resulting scores. The calculations for both respondents for all eight stimuli are shown in Table 2.4. Comparing the predicted preference order to the respondent's actual preference order assesses predictive accuracy. Note that the total part-worth values have no real meaning except as a means of developing the preference order and, as such, are not compared across respondents. The predicted and actual preference orders for both respondents are given in Table 2.6.

Table 2.6: Predicted Part-Worth Totals and Comparison of Actual and Estimated Preference Rankings

Stimuli Description

Part-Worth Estimates

Preference Rankings

Size

Ingredients

Brand

Size

Ingredients

Brand

Total

Estimated

Actual

Respondent 1

Liquid

Phosphate-free

HATCO

.756

1.511

.378

2.645

1

1

Liquid

Phosphate-free

Generic

.756

1.511

-.378

1.889

2

2

Liquid

Phosphate-based

HATCO

.756

-1.511

.378

-.377

5

5

Liquid

Phosphate-based

Generic

.756

-1.511

-.378

-1.133

6

6

Powder

Phosphate-free

HATCO

-.756

1.511

.378

1.133

3

3

Powder

Phosphate-free

Generic

-.756

1.511

-.378

.377

4

4

Powder

Phosphate-based

HATCO

-.756

-1.511

.378

-1.889

7

7

Powder

Phosphate-based

Generic

-.756

-1.511

-.378

-2.645

8

8

Respondent 2

Liquid

Phosphate-free

HATCO

1.612

.604

-.20

2.016

2

1

Liquid

Phosphate-free

Generic

1.612

.604

.20

2.416

1

2

Liquid

Phosphate-based

HATCO

1.612

-.604

-.20

.808

4

3

Liquid

Phosphate-based

Generic

1.612

-.604

.20

1.208

3

4

Powder

Phosphate-free

HATCO

-1.612

.604

-.20

-1.208

6

7

Powder

Phosphate-free

Generic

-1.612

.604

.20

-.808

5

5

Powder

Phosphate-based

HATCO

-1.612

-.604

-.20

-2.416

8

8

Powder

Phosphate-based

Generic

-1.612

-.604

.20

-2.016

7

6

The estimated part-worths predict the preference order perfectly for respondent 1. This indicates that the preference structure was successfully represented in the part-worth estimates and that the respondent made choices consistent with the preference structure. The need for consistency is seen when the rankings for respondent 2 are examined. For example, the average rank for the generic brand is lower than that for the HATCO brand (refer to Table 2.4), meaning that, all things being equal, the stimuli with the generic brand will be more preferred. Yet, examining the actual rank orders, this is not always seen. Stimuli 1 and 2 are equal except for brand name, yet HATCO is preferred. This also occurs for stimuli 3 and 4. However, the correct ordering (generic preferred over HATCO) is seen for the stimuli pairs of 5 “6 and 7 “8. Thus, the preference structure of the part-worths will have a difficult time predicting this choice pattern. When we compare the actual and predicted rank orders (see Table 2.6), we see that respondent 2's choices are many times mispredicted but most often just miss by one position due to the brand effect. Thus, we would conclude that the preference structure is an adequate representation of the choice process for the more important factors, but that it does not predict choice perfectly for respondent 2, as it does for respondent 1.

THE MANAGERIAL USES OF CONJOINT ANALYSIS

It is beyond the scope of this section to discuss the statistical basis of conjoint analysis. However, in DFSS, we should understand the technique in terms of its role in decision making and strategy development. The simple example we have just discussed presents some of the basic benefits of conjoint analysis. The flexibility of conjoint analysis gives rise to its application in almost any area in which decisions are studied. Conjoint analysis assumes that any set of objects (e.g., brands, companies) or concepts (e.g., positioning, benefits, images) is evaluated as a bundle of attributes. Having determined the contribution of each factor to the consumer's overall evaluation, the marketing researcher could then:

  1. Define the object or concept with the optimum combination of features

  2. Show the relative contributions of each attribute and each level to the overall evaluation of the object

  3. Use estimates of purchaser or customer judgments to predict preferences among objects with differing sets of features (other things held constant)

  4. Isolate groups of potential customers who place differing importance on the features to define high and low potential segments

  5. Identify marketing opportunities by exploring the market potential for feature combinations not currently available

The knowledge of the preference structure for each individual allows the researcher almost unlimited flexibility in examining both individual and aggregate reactions to a wide range of product- or service-related issues.




Six Sigma and Beyond. Design for Six Sigma (Vol. 6)
Six Sigma and Beyond: Design for Six Sigma, Volume VI
ISBN: 1574443151
EAN: 2147483647
Year: 2003
Pages: 235

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