Small Sample Quantitative Methods
November 21, 2002
Small Sample Quantitative Techniques
•Two choices when it comes to conducting research
-Collect a lot of information from a few
-Collect less information across more individuals.
•Rule of Thumb
-The more information you collect from any single
individual, the fewer the number of cases you will
need in order to achieve a stable sample estimate.
• Conjoint analysis uses this rule of thumb by
measuring a phenomenon systematically in
every possible light; hence, the statistical
stability without the large, expensive
Scales and Use of Sophisticated
• If you can assume that the differences in the way
people standardize their perceptions and the
widths of the intervals will average themselves out
--in other words, those who are more stringent
balance out those who are less stringent-- then you
can treat scales as though they were ratio scales
and calculate averages using the more powerful
analytical quantitative statistical procedures.
• For most marketing and B2B market research
purposes, attitude scales are used as though they
are ratio- and equal-interval scales.
• A technique that quantifies people’s preferences or
priorities when faced with the task of evaluating a set of
products or services and choosing the most preferred
• Often labeled trade-off analysis
• Parallels a purchase situation
– Product purchase example
• Computer brands and descriptors:
– HD memory
– monitor size
•Important first step in conjoint analysis is to determine the
appropriate features to test for. (Qualitative research)
•Second step is to determine an appropriate number of
realistic levels (attribute configurations) for each feature.
Basics of Conjoint Analysis
•Suppose you wanted to book an airline flight and you had a choice
of spending $400 or $700 for a ticket. Which would you choose?
•What if the only consideration was sitting in a regular or an
extra-wide seat? Likely would choose the extra-wide seat.
•Suppose you can take either a direct flight which takes three hours
real purchase situations, consumers do Choice is clear.
•In or a flight that stops once and takes five hours. not make choices based
on a single attribute like comfort or cost.
•Consumers examine a range of features or attributes and them
make judgments or trade-offs to determine their final purchase
•Conjoint analysis examines the trade-offs to determine the
combination of attributes that will be most satisfying to the customer.
A Practical Example of Conjoint Analysis
Conjoint analysis presents choice alternatives between products/
services defined by sets of attributes.
•Would you prefer a flight with regular seats, that costs $400
and takes 5 hours, or a flight which costs $700, has extra-wide
seats and takes 3 hours?
•If, for example, we see seat comfort, price and duration
are the only relevant attributes, there are potentially eight
Airline Flight Example
Choice Seat Price Duration
1 Extra-wide $700 5 hours
2 Extra-wide $700 3 hours
3 Extra-wide $400 5 hours
4 Extra-wide $400 3 hours
5 Regular $700 5 hours
6 Regular $700 3 hours
7 Regular $400 5 hours
8 Regular $400 3 hours
Utility or “Part-worth”
•Utility is defined as a number which represents the value or relative
“worth” consumers place on an attribute or “part.”.
•A low utility indicates less value; a high utility indicates more value.
Hypothetical utilities for an individual consumer
ATTRIBUTE UTILITY RANGE
3 hours 42 20
5 hours 22 (42MINUS 22=20)
Comfort seat 15 3
extra-wide 12 (15 MINUS 12= 3)
$400 61 56
$700 5 (61 MINUS 5= 56)
Using the Computer
•Reveals consumer preference for specific products defined by the
Flight 1: $300 5 hours two stops meal
Flight 2: $400 4 hours one stop snack
Flight 3: $500 3 hours direct no meal
• Will a price change of $50 influence the consumer’s choice?
•Would the consumer be willing to pay $50 more if s/he got a meal?
Data collection involves showing respondents a series of cards that
contain a written description of the product or service.
A typical card examining the business traveler might look like
“On your next business flight overseas, how likely would you be to
choose a flight that has all the following characteristics? Please circle
the appropriate number from 1 to 10 to indicate your feelings.’
•One stop en route
•Departure time: before 8:00 AM
•“Double” mileage points
•$200 fee to change ticket
Would never Would definitely
choose this flight choose this flight
1 2 3 4 5 6 7 8 9 10
See Exhibit 5.4 Hypothetical Conjoint
Output for FAX that follows.
•Price is the most important feature in the
purchase decision for this one individual, and
the lowest price of $499 is the most preferred
•Print speed is next in importance, and the highest
speed of 10ppm speed is the most preferred
•Color and brand name have less impact on
preference because the utilities are much lower
for these features
(Block & Block)
5.4 Hypothetical Conjoint Output for FAX Machine
Partsworth Difference Relative Weight
No .01 .59 18%
No .1 .4 12
No .5 .3 9
10ppm 1.0 .7 21
HP .6 .2 6
Gray .2 .1 6
$899 .5 1.0 31
Total Utility 3.29 100%
See Exhibits 5.5 & 5.6 that follow.
•Partsworth diagrams for hypothetical FAX example
– A change in price from $499 to $699 greatly
reduces preference, and with a price point of
$899, preference dips considerably lower.
– Difference between highest and lowest utility is
an indication of the impact of this feature on
– Note that the “elasticity” of the color feature is
small and flat while price elasticity is steep.
(Block & Block)
5.5 Partworth Diagrams for Hypothetical FAX Example
Black Beige Gray
Yes No Yes No
Paper Cutter Answering Machine Color
Sharp Panasonic Brother Hp
Yes No $499 $699 $899
Telephone Handset Price
5ppm 8ppm 10ppm
5.6 Partworths for FAX Machine
0 Paper Teleph one An swering Print Brand Color Price
Cu tter Handset Machine Sp eed Name
Alternative Measurement Techniques in
• The paired comparison
– Two alternatives presented
• Rating Scales
– Added to paired comparison to get more data
• Conjoint simulation using a computer
– Lets you estimate the ideal feature
• Computer-aided Interviewing
– Computer models used to present and compute conjoint
• Full-profile conjoint analysis
Trade-Off Conjoint Analysis or
“Two -Factor Approach”
See Exhibit 5.8 Trade-Off Conjoint Matrices that follows.
– Respondents are presented with a series of
combinations based only on pairs of features
– Requires respondent to make choices about every
combination of features and levels.
– This intense data collection adds to the stability of the
utilities for even small samples.
– Works best when features do not interact with one
another, or in others words, the preference or utility of
one variable compared to another does not depend on
the circumstances of a third feature.
– Computer model analyzes the data to get utility values
(Block & Block)
5.8 Trade-Off Conjoint Matrices
Print With Without Print $499 $699 $899
Speed Handset Handset Speed
5ppm 5ppm 3
8ppm 3 4 10ppm 1 4
10ppm 1 2
Telephone $499 $699 $899
These are merely
examples of possible
responses. With 1 3 4
Full Profile Conjoint Analysis or
“Multi Factor Approach”
See Exhibit 5.9 - Product Descriptions in a
full profile conjoint analysis that follows.
•Respondents are presented with a complete profile of
alternative products, each alternative profiled in terms
of information for each and every feature of interest.
•Rather than pairs of features, in full profile CA the
individual is confronted with many alternatives for
which s/he must consider all the various features before
indicating a rank-ordered preference among them.
•Using computers to model and crunch the data, full-
profile CA is the dominant method used today.
(Block & Block)
Product Description in a Full Profile Conjoint Example
Card Print Speed Handset Price
1 5ppm Yes $499
2 5ppm Yes $699
3 5ppm Yes $899
4 5ppm No $499
5 5ppm No $699
6 5ppm No $899
7 8ppm Yes $499
8 8ppm Yes $699
9 8ppm Yes $899
10 8ppm No $499
11 8ppm No $699
12 8ppm No $899
13 10ppm Yes $499
14 10ppm Yes $699
15 10ppm Yes $899
16 10ppm No $499
17 10ppm No $699
18 10ppm No $899
Conjoint Analysis Demonstration
Summary Conjoint Basics
• Involves presenting respondents with alternative
choice situations and having them rank the
• Computer model “decomposes” these preferences
by analyzing what features have been consistently
present or traded-off in the way choices were
• Output of model is a set of numerical values
associated with every feature and feature level,
which portrays the relative importance of each to