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Statistics for Marketing & Consumer ResearchCopyright © 2008 - Mario Mazzocchi

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Measurement errors and data for consumer

researchChapter 1


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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 ErrorSystematic 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 typesQUANTITATIVE

• 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

• 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

Q: Do you prefer statistics or football?A: 1) Statistics

2) Football3) No preference

Q: State the level of agreement with the following sentences:A: 1) I do not like statistics

2) I hate statistics3) Statistics should be taken off

academic programs4) Books about statistics should be burnt…

Q: Rank the following activities according to your preferences:A: 1) Going out at night

2) Playing sports3) Listening to music4) Eating out5) Studying statistics…

Q: Distribute 100 hours of leisure time to the following activities, according to your preferences:A: 1) Going out at night

2) Playing sports3) Listening to music4) Eating out5) Studying statistics…


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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 statisticsIssues:

• 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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