Transcript Statistics for Marketing and Consumer Research

Measurement errors and
data for consumer research
Chapter 1
Statistics for Marketing & Consumer Research
Copyright © 2008 - Mario Mazzocchi
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Outline
• The problem of measurement in relation to
consumer research
• Measurement scales and data types
• Two data-sets
• Commercial software for data analysis
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What is measurement?
Measurement is the assignment of numerals to
objects or events according to rules
(Stevens, 1946)
A measurement rules with its mathematical
and statistical properties is called
measurement scale
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Measurement vs.reality
• Suppose that the following are average
measures of attitude towards mathematics
(on a 10 points scale) taken on Year 1
undergrads in three different years:
2005 – 6.78
2006 – 7.09
2007 – 7.13
• Can we conclude that as time goes by, new
undergrads increasingly like mathematics?
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Errare humanum est
• Empirical measures are an approximation of the
(unknown) true value
Empirical measure =
True value + Systematic Error + Random Error
Systematic error: a bias in measurement which
makes each of the measures systematically too
high or too low
Random error: fluctuation in measurement which
does not follow any systematic direction, but is
due to factors that act in a random fashion
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Statisticians and random errors
• Across a sufficiently large sample of
measurements, positive random errors
compensate negative random errors, so that
a sum of all random errors is close to 0.
• With a single measurement it is not possible
to quantify the amount of random error, but
over many multiple measurements the
average (or total) random error would
become zero.
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A theory of errors
• Thus, the sample mean is the best possible
measure for the true value, provided that there
are no systematic errors
• The normal (or Gaussian) curve is the probability
distribution representing perfect randomness
around a mean value and is bell-shaped.
• The larger are the random errors (less precise
measurements), the flatter is the bell-shaped
curve.
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Carl Friedrich Gauss
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The Gaussian (normal) curve
• Assume the width of a book"s cover is 30.8
• Consider 100,000 measurements
• This is how the distribution of measurements looks like:
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More on the Gaussian curve…
• The average value (30.8 cm) is also the most likely
one and — provided there are no systematic errors
— corresponds to the true value.
• As one moves away from the mean value,
probability decrease symmetrically. Thus, the
probability of committing a 1 cm error in excess is
equal to the probability of a 1 cm error in defect.
• Besides error, the normal curve well represent the
influence of other random factors (see Appendix).
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Measurement (again)
From the Oxford English Dictionary:
A dimension ascertained by measuring; a magnitude,
quantity, or extent calculated by the application
of an instrument or device marked in standard
units
• A dimension is latent; it is real and unique, but
measurement is artificial and not unique
• The latent dimension cannot be defined and
measured in an unequivocal and verifiable way
• The researcher needs to choose an instrument for
translating the latent dimension into units.
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Examples of latent dimension
•
•
•
•
Attitude towards mathematics
Quality of a product
Customer satisfaction
The width of a book"s cover
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Measuring latent dimensions
• Measurement scale types
QUANTITATIVE
• Interval scale
• Ratio scale
QUALITATIVE
• Nominal
• Ordinal
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Quantitative scales
Interval scales — no unique reference point
(e.g. temperature in Celsius or Fahrenheit)
— distance is meaningful
Ratio scales — unique reference point (e.g.
money in a bank account — zero, positive
and negative values are meaningful
independent of the currency unit; ratios do
not vary with currency conversion)
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Qualitative scales
Nominal: nominal assignment to a specific class
which only allows comparison of whether two
elements are equal (they belong to the same class)
or different (they belong to different classes). No
ranking or distance measurement is possible.
Example: job type.
Ordinal: classes can be ranked according to some
criterion which allows determination of which class
is greater and which is smaller albeit no distance
measurement is possible. Example: consumer
perception of quality.
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Scaling techniques
COMPARATIVE SCALING
Measurement is based on the comparison
between objects
NON-COMPARATIVE SCALING
Measurement is based on individual
assessment of each of the objects
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Comparative scaling techniques
Q: Distribute 100 hours of leisure time to
the following activities, according to your
preferences:
A:
1) Going out at night
2) Playing sports
Q: Do you prefer statistics or football?
3) Listening to music
A:
1) Statistics
4) Eating out
2) Football
5) Studying statistics
3) No preference
…
Q: Rank the following activities according to your
preferences:
Q: State the level of agreement with the following
A:
1) Going out at night
sentences:
2) Playing sports
A:
1) I do not like statistics
3) Listening to music
2) I hate statistics
4) Eating out
3) Statistics should be taken off
5) Studying statistics
academic programs
…
4) Books about statistics should be burnt
…
• Pairwise scaling: compare two objects
• Guttman scaling: measure one dimension
through agreement towards ranked set of
items, ordered from least extreme to most
extreme position
• Rank order scaling: rank more than two
objects
• Constant sum scaling: allocate a given number
of points (e.g. 100) to several objects
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Non-comparative scaling techniques
• Continuous rating: tick in a continuous line which
runs between two extremes of a single attribute
• Semantic differential scale: line with itemized
ordered categories associated with
numbers/descriptions, two bipolar attributes
• Likert scale: intensity of a single attribute, usually
measured through agreement with a sentence
• Stapel scale: unipolar scale on a single attribute
with ten points from minus five to plus five – no
neutrality
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Some desirable properties of
measurement scales
Accuracy: how closely does the measurement value reflect
the true value of the latent dimension?
Precision: how detailed are measurements? If repeated
measures are taken, how much do they change over the
span of measurement?
Reliability: when several items are used to measure the same
construct across people or over time, are they consistent?
Validity: does the measurement scale adequately represent
the unobservable latent concept? Could it be used to
predict the latent concept?
Generalizability: can the measurement be generalized to
different samples, administration methods, timings, etc.?
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Some general findings on measurement
scale
• In general, choice of the measurement scale does not
affect results
• However, the following choices do have an impact:
• Number of items in the final scale
• Number of scale points
• A larger number of items increases reliability measures
• Higher numbers of points in the scales also increase
reliability
• Other choices (e.g. comparative vs. non-comparative
scaling) may also affect results, but not in an unequivocal
direction – pros and cons should be evaluated on a case by
case basis
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Measuring reliability:
Cronbachs Alpha
• It measures internal consistency of measurement scales composed of
several items
• A reliable scale is expected to show as much variability as the true
latent dimension
• However the latent dimension is unknown
• The Cronbachs Alpha measures reliability by looking at the correlations
between items across respondents
• High correlations mean high reliability
• Cronbachs Alpha is equal to one when there is perfect correlation – in
this case the sum of the individual items allows one to build a
measurement which reflects the variability of the latent dimension
• Cronbachs Alpha is zero when there is no correlation and may be lower
in the presence of negative correlation
• As a rule of thumb one should not rely on scales with a Cronbachs Alpha
below 0.70
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Two sample data-sets
• EFS.sav – A sample data-set from the 2004-5
UK Expenditure and Food Survey. An
example of secondary data.
• Trust.sav – A sample data-set from an
international survey within the EU project
Trust (www.trust.unifi.it). An example of
primary data.
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The EFS data-set
• The EFS data set is a subset from the 2004-05 UK
Food and Expenditure Survey
• The file includes a simple random sample of 500
households and a selection of 420 variables out of
the 1952 available in the officially released data
set (www.data-archive.ac.uk)
• The survey records household expenditures and
other household characteristics, following a
standard codification of purchases called COICOP.
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The trust data-set
• The aim of the original survey was to collect
attitudinal and psychographic data to explain
chicken purchasing behaviour in five European
countries
• The simplified sample data-set contains 500 cases
(100 per country selected randomly) out of the
original 2,725 household surveyed and 138
variables
• The Trust survey is a good example of the outcome
of primary data collection, which means that the
data were explicitly collected for the purpose of
the consumer research.
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Statistical software: SPSS
Advantages:
• a good range of methodologies with a relative ease of use
• the data management design allows one to deal with large data-sets and is
calibrated to fit very well with marketing research
• user-friendly interface with dialog boxes
• a syntax editor allows one to save sequences of commands for repetitive
tasks
• probably the most accessible software for those with a limited background
in statistics
Issues:
• Reduced control on options for some methodologies (“black box” problem)
• Some complex tasks (e.g. simultaneous estimation of multiple equation
systems) cannot be accomplished in SPSS
An evaluation copy of SPSS which fully works for 15-days can be
downloaded from www.spss.com
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Statistical software: SAS
Advantages:
• increased control on statistical methodologies and
flexibility
• powerful as a statistical programming language
• very well documented on-line users guide
• a good range of methodologies with a relative ease of
use
• Includes virtually any existing statistical technique
Issues:
• Less user-friendly than SPSS
• Require a stronger background in statistics
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Other packages
• LISREL– structural equation systems
• LIMDEP – econometrics with a specific
versatility for discrete choice and limited
dependent variable models
• Eviews – econometrics, particularly helpful
for dealing with advanced time series
models and simultaneous equation systems
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