# How to Interpret Partworth Utilities

Partworth utilities (also known as attribute importance scores and level values, or simply as conjoint analysis utilities) are numerical scores that measure how much each feature influences the customer’s decision to select an alternative. Because partworths of attributes and levels in conjoint analysis are interrelated, in this post we will look at them using the same example of a mobile plan.

Suppose a company wants to find out customers’ preferences for mobile plan to reassess its product range, as a pathway to growth. They are investigating the following four attributes, to see which combination of levels within the attributes creates an optimal plan.

## Relative value by level (Level partworths)

Level partworths allow you to dive deeper to understand what specific levels within an attribute drive customers' choice. In this example, unlimited data plan is strongly preferred to 500MB data and 1GB plan and somewhat to 10GB data plan.

Level partworths are calculated based on the average preference scores for each level. Levels that are strongly preferred by customers are assigned higher scores, levels that perform poorly (in comparison) are assigned lower scores. The chart is scaled so that, for each attribute, the sum of all positive values equals (the absolute value of) the sum of all negative values.

Again, it is important to remember that these partworths are relative. If we add a new level for the attribute “Data included”, the relative value of each level will change.

## Distribution of preferences for levels

This chart shows the distribution of preferences for various levels. It answers the question: Assuming that each consumer has a preference for different levels, what is the distribution of preferences for different levels (within each attribute) across consumers?

This information allows you to dive deeper to understand the preference distribution for various levels within an attribute. In this example regarding data plans, 83.2% of total preference goes to unlimited, 10.3% for 10GB, 3.6% for 1GB, 2.9% for 500MB. Unlimited data plan is strongly preferred to 500MB data and 1GB plan and somewhat to 10GB data plan.

Distribution of preferences for levels are based on the ratio of preference scores for levels within the attribute for each respondent. Levels with high percentages of preferences are more preferred within attribution across all respondents.

## Distribution of most preferred levels

This chart shows the distribution of levels most preferred by consumers. It answers the question: Assuming that each consumer likes different levels, how many consumers have each level as their most preferred

Following the same example of mobile data plans, 97.9% of respondents most-preferred plan unlimited data, with 2.1% of respondents most preferring 1GB. Therefore, unlimited data is easily the most preferred level among mobile data.

Distribution of most preferred levels is calculated with the percentage of respondents choosing the specific level as the top preferred option within attributes. High percentage of this value represents the level is most preferred by big percentage of consumers.

## Ranked list of product concepts

For each report, Conjoint.ly will present a “ranked list of product concepts as preferred by customers”. This is a list of up to 500 potential combinations of features and prices that represent product concepts. The column “Value to customers'' will contain a single number for each concept combination (row) with specific features and price levels. This number is calculated as the average partworths across individual respondent’s total partworth utility scores for the combination. It is scaled with 0 as the average value.

The first rank combination is the most preferred concept across respondents. In this example, a mobile plan of \$30 per month, unlimited data included, 300 min internal included and unlimited text included has the highest overall utilities across respondents.

## FAQs

### Do partworth utilities show variability of preferences across consumers?

No, partworth utilities (both attribute importance scores and level preference scores) show only mean (average) preferences and importances. In order to gauge variability of preferences, you may want to look at distribution of individual-level HB co-efficients or perform simulations.

### Why do importance scores not sum up to 100% in brand-specific conjoint?

In brand-specific conjoint, importance scores do not necessarily sum up to 100% within each brand. Instead, we scale then so that they can be comparable across brands.

Effectively, you can omit “%” because the scale is arbitrary. Or you can re-scale them to 100% within each brand (but that will remove comparability across brands).