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CLOTHES WASHER CONSUMER ANALYSIS 

TECHNICAL APPROACH 

DECEMBER 15, 1998 

ANALYSIS APPROACH 

The objective of this study is to determine which clothes washer features consumers 

value most and estimate how changes in these attributes resulting from an efficiency 

standard will affect clothes washer purchases and consumer utility. As discussed in 

this Technical Approach, focus group and conjoint analysis data will be used to estimate 

the probability of purchasing standard and high efficiency clothes washers. These 

purchase probabilities provide an intuitive context to evaluate clothes washer demand, 

since changes in equipment attributes will be expressed as a change in the likelihood of 

making a clothes washer purchase .. 

The estimation of purchase probabilities and elasticities guides virtually every stage of 

the analysis. Focus groups are used to determine the most important clothes washer 

attributes. These attributes are presented to respondents during conjoint analysis 

sessions. Using conjoint analysis has the advantage of presenting different washer 

attributes simultaneously, which forces respondents to make tradeoffs across attributes 

as they would if they were actually purchasing a washer. The conjoint data is combined 

with actual market data to estimate the probability of purchasing a clothes washer and 

calculate purchase elasticities. A detailed description of each analysis stage is presented 

below. 

PURCHASE DECISION STRUCTURE 

Exhibit 1 shows the two-step decision involved in purchasing a new clothes washer. 

The first decision is whether or not to enter the market and purchase a clothes washer; 

and is referred to here as the Purchase Probability. The second decision is, given that a 

purchase is going to be made, which equipment option will be chosen. This is labeled 

the Equipment Choice Probability. The product of these two yields the Total 

Probability, which is the probability that any one equipment option is purchased. 

Quantum Consulting Inc. 1 Technical Approach 
Exhibit 1 

Clothes Washer Purchase Decision Stages 

x 

FOCUS GROUPS 

The primary purpose of the focus groups is to identify the key washer characteristics to 

be used in the conjoint analysis. The focus groups are conducted to develop a list of all 

equipment characteristics that influence on the decision to purchase a clothes washer. 

This is accomplished by having the moderator guide the discussion to get an unsolicited 

list of important clothes washer attributes. Once the unaided list of attributes is 

obtained, the moderator will suggest any other attributes that were not volunteered 

initially for the group to discuss. Once the complete attribute list is determined, 

. questions are asked to determine which attributes are considered the most important in 

selecting a specific clothes washer. 

The focus groups are also used to identify key population segments that should be 

included in the conjoint session sample frame. For example, it may be that attitudes 

toward washers vary substantially by house type or some other demographic segment. 

These differences will be evaluated after the focus groups are completed to determine if 

the sample frame for the conjoint analysis should be stratified across these demographic 

segments as well. 

Focus groups will be conducted in five cities; Washington, DC, San Francisco, CA, 

Madison, WI, Miami, FL, Dallas, TX These cities were selected so that five different 

regions are represented in the focus groups. Ten focus groups will be conducted, two in 

each city, with a total of approximately 100 focus group participants divided evenly 

across the ten sessions. Focus group participants will be recruited randomly by phone 

to ensure a mix of demographic types. Each respondent will be paid a $50 incentive for 

participating in the focus group. 

Quantum Consulting Inc. 2 Technical Approach 
CONJOINT ANALYSIS 

Conjoint session design 

Conjoint analysis involves having respondents sort through and rank cards that reflect 

different clothes washer equipment options. Each card describes a separate clothes 

washer based on several equipment characteristics such as price, energy and water 

savings, and axis orientation. The actual equipment characteristics used in this analysis 

will be determined from the focus groups. Respondents rank the cards from most to 

least preferred. As discussed below, this ranking information is used to estimate the 

probability of purchasing different clothes washer options based on the equipment 

characteristics. 

The success of conjoint sessions rely on making sure that respondents are well informed 

as to what is expected during the sessions as well as being familiar with the equipment 

being evaluated. The moderator will explain that respondents should rank the set of 

cards from most preferred to least preferred. Photographs and additional information 

on high efficiency clothes washers will be available at each session. This will allow each 

respondent to become familiar with the high efficiency washers so that they can make 

informed decisions while doing the conjoint analysis. 

Full Profile Conjoint Analysis 

The conjoint analysis will .utilize a full profile conjoint analysis, where respondents rank 

cards in the order of their preference. Past experiencel as well as existing literature 

indicates that the most successful conjoint designs limit each exercise to ranking 16 

cards at a time with 4 to 6 features on each card. Including more cards or additional 

attributes tends to overwhelm respondents and results in less reliable data. To 

accommodate more features, such as the 8 to 12 mentioned in the original RFP, session 

participants may rank two different sets of cards of 4 to 6 characteristics each, with one 

or more features, such as price, common to both trades. This will allow the comparison 

of two separate models and allow for more washer characteristics to be evaluated~ 

The full profile conjoint design will utilize an orthogonal card design. The orthogonal 

design results in each of the card attributes being perfectly uncorrelated with the other 

attributes. This is critical to the analysis, as correlation across attributes results in a loss 

of precision and makes it difficult to estimate the importance that respondents place on 

each attribute. For example, consider the situation where price and rebate are two of 

the characteristics being evaluated and on each card rebate is 10 percent of the price. 

Since price and rebate are perfectly correlated, there is no way to determine from the 

data if a respondent is ranking the cards based on price or on rebate. For this reason, 

having an orthogonally designed study is essential. 

To address the likelihood of making a purchase, upon completing the rankings the 

respondents will be asked to determine those clothes washers that they would actually 

Quantum Consulting Inc. 3 Technical Approach 
purchase given their situation today. This is done by inserting a 'Participation Card' in 

the deck after the ranking is completed. Those cards ranked above the Partidpation 

Card are options that the respondent would purchase today while those below they 

would not purchase. As discussed below, Participation Card placement will be used to 

estimate the Purchase Propability. 

Sample Design 

The conjoint sample will be designed to include a mix of people across age and income 

groups. At least part of the sample should contain people that have recently purchased 

a new washer or that are planning to in the near future. These people are most likely to 

give answers that will match most closely with what they actually do in the market 

place. However, utilizing the Participation Card requires a sample of respondents who 

are not currently in the market for a clothes washer. Excluding these customers may 

bias the sample and ultimately make model predictions less accurate. Information 

obtained during the focus groups will also be used to determine if there should be any 

further sample stratification for the conjoint sessions. 

The conjoint sessions will be held in four different cities across the country: 

Washington, DC, San Francisco, CA, Madison, WI, and Dallas, TX. These cities have 

been chosen to mirror the focus groups sites and to ensure that a broad range of 

geographic regions are represented. Each session will _have 12 to 16 attendees with an 

average of 100 attendees for each city for a total of 400 conjoint session participants. 

Session participants will be recruited randomly by phone and will be paid a $50 

incentive for participation. 

PURCHASE PROBABILITY CALCULATIONS 

As shown in Exhibit 2, the decision to purchase a new washer is divided into the 

purchase probability and the equipment choice probability. The results of the conjoint 

analysis will be. used to estimate both of these probabilities. Once the probabilities are 

estimated, the probabilities will be calibrated to the actual distribution of purchases 

observed in the market. Once calibrated, the estimate probabilities can be used to 

estimate how purchases of washer_s will change given changes in the equipment 

characteristics used in the conjoint analysis. This provides a real world context for the 

conjoint analysis results and provides a powerful tool for predicting future market 

behavior. The remainder of this document describes how the conjoint analysis data will 

be used to estimate purchase probabilities and calculate the elasticities associated with 

clothes washer characteristics. : 

Exhibit 2 shows how the estimated probabilities will be combined with eligible market 

information to predict annual purchases. The first stage is multiplying the eligible 

market by the Purchase Probability to get the total number of washers purchased 

annually. Then, total purchases are multiplied by the Equipment .Purchase 

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Probabilities to get the number of annual purchases for each of the equipment options. 

This will give annual purchases for each of the standard and high efficiency washer 

options. 

Exhibit 2 

Clothes Washer Market Penetration, ·Model Stru.cture 

Sig~e Ma~~ ~~ 

Purchase Probability 

The decision to make a clothes washer purchase is the Purchase Probability shown in 

Exhibit 2. This probability is estimated from the conjoint analysis data based on the 

placement of the Participation Card. Since the purchase choice variable is discrete, the 

model is estimated using a standard logit model specification. In this application, the 

dependent variable has a value of one for those cards placed above the Participation 

Card and a value of zero for those below. The independent variables are the values for 

the characteristics on each card. In equation form, this is given by 

Purchase (0,1) =a+ LJB{Xijeii 

Where Purchase = 1 if card is ranked above the Participation Card, 0 if ranked below 

Xii= Value of attribute j on card i 

Bj = Coefficients to be estimated 

a = Constant to be estimated 

Quantum Consulting Inc. 5 Technical Approach 
Sij = random error termed assumed to be logistically distributed 

Using the estimation results from this purchase logit, the probability of making any 

equipment purchases Prob(Purchase) is given by 

Prob(Purchase) = exp(J3'X) / (1 + exp(j3'X)) 

Equipment Choice Probability 

The second stage of the model is the choice of a specific equipment option given that a 

purchase will definitely be made, which is the Equipment Choice Probability in Exhibit 

2. Using a slightly different version of the logit model, the rankings of the cards are 

regressed against the attribute levels on the cards. This has a different appearance than 

the standard conditional logit since the dependent variable is the actual ranking rather 

than a zero or one value.1 However, estimation of this model is conducted the same as 

with the more familiar logit specification. The equation to be estimated in this stage is 

given by 

Where Ranl<i ~ The ranking of card i 

Xii= Value for attribute j from card i 

J3i =Coefficients to be estimated 

Sij = Random error terin assumed to be logistically distributed 

Using these estimated results, a clothes washer choice set will be constructed that 

re~ects both standard and high efficiency equipment options. Using the logit density 

function, the probability of choosing any option n among M different equipment 

options given that a purchase i~ made is 

Prob(Equipn I Purchase)= exp(f3'Xn) / }:M (exp(f3'Xm)) 

The Total Probability is then calculated by multiplying the Purchase Probability by the 

Eq1:1ipment Choice Probability~ or 

Prob(Total) "."' Prob(Purchase) * Prob(Equipn I Purchase) 

1 A more complete description of how ranked conjoint data can be analyzed using this logit specification is 

contained in "Logit Models for Sets of Ranked Items", Nicholos Christakis and Paul Allison, Sociological Methodology, 

Volume 24, 1996, pp. 199-228. · 

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Model Calibration· 

Both of the probabilities described above are determined using the conjoint analysis 

data. However, relying entirely on stated preference data can be risky, since there is 

always the chance that the decisions respondents make in a controlled experiment do 

not accurately reflect what they would do in the market place. 

To account for this, both estimated probabilities will be adjusted to match observed 

market data. The constant in the Purchase Probability will be adjusted so that the 

estimated probability of making a purchase matches the observed proportion in the 

population nationwide. Similarly, the Equipment Choice Probability will be adjusted 

so that the estimated, distribution across · standard and high efficiency equipment 

options matches the actual distribution in the market place. This calibration adjusts the 

estimation results to account for unobserved customer characteristics that are not 

accounted for in the model. The result is a model that utilizes the tradeoff information 

obtained during the stated preference sessions while anchoring the model to observed 

market behavior. 

PURCHASE SCENARIOS 

The estimated probabilities provide a variety. of options for estimating the effect of 

changes in equipment design due to an efficiency standard. In addition to elasticities, 

changes in purchases due to changes in equipment features will be estimated by 

examining how these changes affect the purchase probabilities. The analysis of 

purchase scenarios using both the elasticities and probability changes is discussed 

below. 

Probability Scenarios 

The probability estimates are used to estimate the change in purchases due to changes 

in clothes washer design resulting from an efficiency standard. To evaluate the effect 

these changes will have on purchases, the purchase probabilities will be calculated 

using the values for attributes of the original equipment before the standard. For 

example the pre-standard purchase probability is given by 

Probi = exp(13'X) / (1 + 13'X) 

Where ~ = Estimated coefficients from the purchase logit 

X = Attribute values such as price, savings, axis orientation for the pre-standard 

equipment design. 

This pre-standard purchase probability is compared with the post-standard purchase 

probability. The post-standard probability is calculated using the same formula with 

post-standard values for price, savings, and other equipment attributes 

Quantum Consulting Inc. 7 Technical Approach 
Probi = exp(13'X) / (1 + 13'X) 

Where p = Estimated coefficients from the purchase logit 

X = Attribute values such as price, savings, axis orientation for the post-standard 

equipment design. · 

The effect of the standard can be shown by comparing the difference in purchase 

probabilities before and after the standard 

Effect of Standard= (Probi - Prob2)/ Probi. 

For example, if the pre-standard purchase probability is 0.15 and the post-standard 

purchase probability is 0.10 then the effect of the standard is (0.15 - 0.10)/0.15 or 0.33, 

which indicates a 33 percent reduction in the likelihood of purchasing this clothes 

washer. 

Since the adoption of an efficiency standard will likely increase the price of all clothes 

washer options, it will be useful to evaluate the effect of the standard on purchases 

while holding price constant. Holding price constant allows the evaluation of different 

equipment configurations that will comply with the standard independent of price 

considerations. For example, suppose that there are two different equipment designs 

that comply with the new standard. The first option meets the standard utilizing a 

horizontal axis. The second option meets the standard using a vertical axis and no hot 

water option for the rinse and wash cycles. The same probability calculations can be 

used to determine which equipment configuration will be more popular holding price 

constant 

ProbA1 = exp(f3'X) / (1 + exp(j3'X) 

Where f3 = Estimated coefficients from the logit purchase model 

X =Pre-Standard equipment features (vertical axis) for choice A with the poststandard equipment price. 

The post-standard purchase probability for Option A is given by 

·ProbA2 = exp(j3'X) / (1 + exp(j3'X) 

Where f3 = Estimated coeficients from the logit purchase _model 

X = Post-Standard equipment options (horizontal axis) with the post-standard 

equipment price. 

The same method is used to calculate pre-standard and post-standard purchase 

probabilities for Option B with and without the hot water feature: 

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ProbB1 = Purchase probability with pre~standard options (hot water) and post 

standard price. 

ProbB2 =Purchase probability with post-standard options (no hot water) and poststandard price. 

The effect of the standard on these two different equipment options can be evaluated 

the same as before. Suppose that the options have the following probabilities: 

ProbA1 = 0.20 ProbB1 = 0.15 

ProbA2 = 0.10 ProbB2 = .010 

The effect of the efficiency standard on Option A is (0.20 - 0.10) / 0.20 = 0.50 or a 50 

percent reduction in the likelihood of making a purchase. Similarly, for Option B the 

change is a 33 percent reduction in the purchase probability. In this example, meeting 

the standard using the Option B equipment design utilizes more popular equipment 

features and will have less of a detrimental effect on purchases. 

Elasticity Scenarios 

The sensitivity of purchases to changes in equipment features can also be evaluated by 

calculating the elasticity associated with each equipment characteristic. The purchase 

elasticities are calculated using the price and equipment options as well as the estimated 

purchase probabilities. For the elasticity with respect to price, the elasticity is calculated 

by 

Price Elasticity=(~ Prob/~ Price)* (Price/ Prob) 

Where ~ Prob = Change in purchase probability due to the change in price 

~ Price = Change in price resulting from the efficiency standard 

Prob = Pre-standard purchase probability 

Price= Pre-standard price. 

This number reflects how sensitive the purchase probability is to changes in price. In 

general, an elasticity with an absolute value of less than one is considered inelastic or 

insensitive to changes in price while an elasticity greater than one is elastic or sensitive 

to changes in price. 

Elasticities can also be caiculated with any of the equipment options that were used in 

the conjoint analysis and the logit purchase model. For example, the sensitivity of the 

purchase probability to a horizontal versus vertical axis is determined by . 

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Axis Elasticity=(~ Prob/~ Axis)* Axis/ Prob 

Where ~ P = Change in the purchase probability due to a switch from a vertical to a 

horizontal axis 

~ Axis = Chan_ge in axis orientation (denoted by a dummy variable in the model) 

Prob = Pre-standard purchase probability 

Axis = Original vertical axis orientation. 

By calculating the elasticities, the sensitivity of washer purchases to changes in each of 

the equipment attributes used in the purchase decision can be evaluated. However, 

each elasticity provides information on only one individual attribute while holding all 

other attributes constant. To evaluate the effect of changing several equipment 

attributes simultaneously, examining the change in overall purchase probabilities as 

described above is appropriate. 

SUMMARY 

A combination of· focus groups and conjoint analysis will be used to determine the 

clothes washer features that consumers value most and to estimate the effect that 

changes in these features due to an efficiency standard will have on clothes washer 

purchases. The attributes that are used in conjoint sessions will be determined from 

focus groups to ensure input from as broad a range of customers as possible. As 

described above, the conjoint analysis results will be used to estimate clothes washer_ 

purchase probabilities. 

The purchase probabilities will be used to evaluate how sensitive the purchase decision 

is to changes in the equipment attributes that are likely to be affected by an efficiency 

standard. The conjoint analysis and logit specification allows these issues to be 

addressed in a variety of ways. Purchase sensitivity will be evaluated by calculating 

elasticities as well as looking at how purchase probabilities change with changes in 

equipment features due to ari efficiency standard. Purchase scenarios will be conducted 

allowing price to vary and with holding price constant. Holding price constant in the 

purchase scenarios provides an opportunity to evaluate changes in non-price attributes 

without having the change in price overwhelm the changes in other equipment 

features. 

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