Measurement and Scaling

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Measurement and Scaling

• Week 7

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Study Materials for Module 7

• Cavana - Ch 8 9 pp. 360-62
• Jennings Ch 5 pp. 149-59
• Ch 8 pp. 247-252
• Ch 11 pp 353-56
• Reading 7.1 and 7.2
• Coakes and Steed Ch 3 normality, recoding
  missing values

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Lecture overview

• Nature of measurement
• Scaling
• Measurement scaling
• Measurement scales
• Parametric versus non - parametric statistics
• Methods of scaling
• Scale decisions
• Criteria for goodness of measure
• Ethics
• Report writing
• Summary
• Tutorial

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Nature of measurement

• Measurement in research consists of assigning
  numbers or symbols to characteristics of objects
  according to set of predetermined rules
• To do this we need to answer the question What
  is to be measured?
• Based on the research problem identify the
  relevant concepts/constructs ie brand loyalty
  service quality trust value of an attraction
• Conceptual definition define/ gives meaning to
  the concept in the context of the study.
  Specifies what the concept is and what it is not.
• Operational definitions an explanation that
  gives meaning to a concept by specifying the
  dimensions, activities, factors etc necessary to
  measure it.

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Example

• Concept - value consciousness
• Concept definition - the concern a consumer has
  for paying low prices contingent on some product
  quality expectation.
• Operational Statements (answer on 7 point likert
  scale)
• When grocery shopping, I compare the prices of
  different brands to be sure I get the best value
  for money.
• When I shop, I usually compare the price per
  gram information for brands I normally buy.
• When purchasing a product, I always try to
  maximise the quality I get for the money I spend
• etc. further statements would be developed

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Recap - What is measured?

• Variables studied in research are classified as
  objects or as properties.
• Objects i.e. people, books, cars
• Properties characteristics of the object i.e.
  persons physical properties height, age,
  posture psychological properties attitudes,
  intelligence social properties status,
  leadership abilities
• As researchers we do not measure objects or
  properties but indicators they are the
  operational measures

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Scaling

• Scaling an extension of measurement.
• involves creating a continuum upon which measured
  objects are located
• Example scale for locating consumers according
  to the characteristic attitude towards theme
  parks unfavourable 1 neutral 2 favourable
  3
• Measurement is the assignment of 1,2 or 3 to
  each respondent
• Scaling is the process by which respondents would
  be classified as having unfavourable, neutral or
  favourable attitude towards theme parks

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Measurement and Scaling

• Why do we need to understand Measurement and
  Scaling?
• As researchers we need to compare and contrast
  issues of concern.
• Measurement and scale provides us with the tools
  to make sense of the issues of concern in some
  structured and logical manner.

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Measurement and Scaling

• When choosing a measurement we must consider
• measurement scales (levels of measurement)
• Response scales
• criteria for good measurement
• Note there are also many other factors to
  consider when designing a questionnaire

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Measurement scales

• Nominal Scale
• numbers assigned to the object serve as labels
  for identification i.e. gender (male, female)
  store type accommodation type
• (mode, frequency, percentage)
• Ordinal Scale
• a scale that arranges objects or alternatives
  according to their magnitude in an ordered
  relationship i.e. preference ranking for a
  product social class
• (median, semi-interquartile range)

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Measurement scales

• Interval Scale
• a scale that both arranges objects according to
  their magnitude and also distinguishes this
  ordered arrangements in units of equal intervals
  i.e. attitudes, opinions (5 point likert scale)
• (mean, standard deviation, variance, range)
• Ratio Scale
• a scale that has absolute rather than relative
  quantities i.e. income, sales, costs, market
  share
• possess an absolute zero point and interval
  properties
• (mean, standard deviation, variance all lower
  level descriptive statistics)
• IMPORTANT SELECTED READING 7.1

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Parametric versus non - parametric statistics

• Statistical techniques can be classified as -
• Parametric statistics
• the use is based on the assumption that the
  population from which the sample is drawn is
  normally distributed and data are collected on an
  interval or ratio scale.
• Non-Parametric statistics
• makes no explicit assumptions regarding the
  normality of distribution in the population (less
  stringent requirements) and are used when the
  data are collected on a nominal or ordinal scale.
• (Refer to Appendix 1, Cavana et al p. 402)

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Methods of scaling

• Response scales
• rating scales estimates magnitude of a
  characteristic
• ranking scale rank order preference
• sorting scales arrange or classify concepts
• choice scales selection of preferred
  alternative

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Rating scale

• Rating tasks ask the respondent to estimate the
  magnitude of a characteristic, or quality, that
  an object possesses. The respondents position
  on a scale(s) is where he or she would rate an
  object.

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Ranking scale

• Ranking tasks require that the respondent rank
  order a small number of objects in overall
  performance on the basis of some characteristic
  or stimulus.

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Other scales

• Sorting might present the respondent with several
  concepts typed on cards and require that the
  respondent arrange the cards into a number of
  piles or otherwise classify the concepts.
• Choice between two or more alternatives is
  another type of measurement - it is assumed that
  the chosen object is preferred over the other.

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Rating scales

• category scale
• Likert scale
• semantic differential
• numerical scale
• staple scale
• itemised rating scale
• constant sum rating scale
• graphic rating scale

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Category Scale

• a category scale is a more sensitive measure than
  a scale having only two response categories - it
  provides more information.
• Nominal or ordinal (example is ordinal)
• if interval between each category is regarded as
  equal interval
• dichotomous scale - 2 response categories (yes
  or no agree or disagree) nominal

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EXAMPLE OF CATEGORY SCALE

• How important were the following in your decision
  to visit Sydney (tick one response for each item)
• VERY SOMEWHAT NOT TOO
• IMPORTANT IMPORTANT IMPORTANT
• CLIMATE ___________ ___________ ___________
• COST OF TRAVEL ___________ ___________ ___________
  
• FAMILY ORIENTED ___________ ___________ __________
  _
• EDUCATIONAL
• /HISTORICAL ASPECTS _________ ___________ ________
  ___
• FAMILIARITY WITH
• AREA ___________ ___________ ___________

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The Likert Scale

• An extremely popular means for measuring
  attitudes. Respondents indicate their own
  attitudes by checking how strongly they agree or
  disagree with statements.
• response alternatives strongly agree,
  agree, uncertain, disagree, and strongly
  disagree.
• generally 5 points but can vary
• not all 5 point scales are Likert scale
• debate as to the level of measurement of this
  scale (interval)
• If several scale item are used to measure a
  variable, then an index may be formed by adding
  the responses to each scale item together.
• If a scale is negatively worded, then recode
  prior to creating the index (refer to Coakes
  Steed p. 40)

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LIKERT SCALE FOR MEASURING ATTITUDES TOWARD TENNIS

• It is more fun to play a tough, competitive
  tennis match than to play an easy one.
• ___Strongly Agree
• ___Agree
• ___Neither agree nor disagree
• ___Disagree
• ___Strongly Disagree

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Semantic Differential

• Bipolar adjectives to anchor each end of scale
  (seven point scale) eg
• good ______________ bad
• sweet ______________ sour
• hot ______________ cold
• Rotation required to avoid halo effect ???
• Image profile - graphic representation for
  competing brands, services to highlight
  comparison (based on mean or median)

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Numerical Scale

• Numerical scales have numbers as response
  options, rather than semantic space or verbal
  descriptions, to identify categories (response
  positions).
• Similar to semantic differential bipolar
  adjectives on a 5 - point or 7 - point scale
• How satisfied are you with your new computer?
• Extremely satisfied 7 6 5 4 3 2 1
  Extremely dissatisfied

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Stapel Scales

• measures both direction intensity of an
  attitude towards an object
• up to a 10 point scale 5 to -5
• presented vertically
• considered interval

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A Stapel Scale for Measuring a Stores Image

• Department
• Store Name
• 3
• 2
• 1
• Wide Selection
• -1
• -2
• -3
• Select a positive or negative number that you
  think describe the store accurately for each
  descriptive word.

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Itemised rating scale

• Similar to category scale
• 5 or more point scale
• Each point is numbered and labelled
• 1 Very unlikely 2 Unlikely 3 neither
  unlikely nor likely 4 Likely 5 Very likely
• A number of statements are rated using scale
• Interval scale

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Constant sum rating scale

• Respondent is asked to distribute a given number
  of points across various items (attributes) of a
  product to indicate the importance to each
  attribute.
• Example distribute 100 point among the
  following attributes to indicate the importance
  of each for the product - soap.
• fragrance size shape texture colour

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Graphic Rating Scale Stressing Pictorial Visual
Communications
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Ranking Scales

• Paired comparison helps to identify preferences
• Forced choice rank a set of objects (eg.
  destinations) from preferred to least preferred
• Comparative scale - use a benchmark to compare
  another product with.
• Ranking scales provide ordinal data

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Other response sets

• Scenarios then provide a set of possible
  responses to select from
• Open-ended questions

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Scale decisions

• type of response scale
• number of scale categories
• balanced versus unbalanced
• even/odd number of categories
• forced versus non-forced scales
• nature degree of verbal description
• physical form of the scale

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Type of response scale

• depends on research problem and objectives
• depends on the statistical analysis techniques
  that may be used for both descriptive and
  inferential statistics

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Number of categories

• greater the option, greater the sensitivity
• most respondent can only handle 5 to 9
• options increase as object knowledge increases.
• nature of object
• mode of data collection
• analysis of the data - correlation coefficient
  decreases with the reduction of categories

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Balanced versus unbalanced

• balanced equal no. of favourable unfavourable
  categories
• to obtain objective data need balanced scale
• if you know the response will be skewed use an
  unbalance scale in-line with the skewness
• unbalanced scale has data analysis implications

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Even/odd number of categories

• depends on the need for a central or neutral
  position odd number of categories results in a
  neutral point
• example Likert scale is a balanced rating with
  an odd number of categories i.e. 5 or 7
• even scales will force respondent to a position
  either positive or negative.
• if a neutral or indifferent response is possible
  from some respondents odd number of categories
  should be used

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Forced versus non-forced scales

• forced scale - the respondent is forced to give
  an answer
• forced scale omits no opinion or no knowledge
  option
• forced scale can distort the response thus the
  measures of central tendency variance
• offering a no opinion can allow respondents to
  be lazy and not respond

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Nature degree of verbal description

• degree of verbal description associated with the
  scale can influence the response
• categorising helps the respondent understand the
  scale
• recommend that all or most scale points need
  categorising/ description
• strength of adjectives to anchor scale generally
  agree vs strongly agree

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Physical form of the scale

• presentation of scale can be in many formats
• in selecting a scale format - consider the
  audience and the format likely to receive the
  highest response rate

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Selecting an appropriate scale

• no one is best - decision is situational
• want maximum information
• nature of item being measured
• ease of use of technique by respondent
• analysis required
• method of communication

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Criteria for goodness of measure

• 3 major criteria for evaluating good measurement
  are
• reliability
• validity
• sensitivity
• Other factors to consider are
• relevant
• versatile
• ease of response

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Reliability

• refers to the extent to which a scale (number of
  items) produces consistent results if repeated
  measurements are made
• degree to which the scale is free from random
  error and yields consistent results
• Is the scale a stable measure of the concept? and
  how well do the items in a scale hold together?
• main methods test-retest inter-item
  consistency reliability
• reliability is a necessary but insufficient
  condition of the test of goodness of a measure

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Validity

• ability of a scale to measure the intended
  concept and not some other concept
• content validity measure includes an adequate
  representative set of items that tap the concept
• literature
• qualitative research
• judgement of a panel of experts
• Note other forms of validity

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Reliability and validity on target
Old Rifle New Rifle New Rifle
Sunglare Neither reliability nor High
reliability Reliable but not valid valid
(Target A) validity(Target B) (Target C)
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Sensitivity

• sensitivity of a scale is important when
  investigating changes in attitudes
• a measurement instruments ability to accurately
  measure variability in responses
• avoid 2 or 3 point scales use 5 or 7 point
  scales to increase the scales sensitivity
• avoid basing a scale on one item or one question
  use multiple items and create an index measure

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Ethics

• researches are obligated to use the best scale
  for the given objectives
• researchers must ensure the correct scale is used
  to allow the analysis design to be effective

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Report writing

• Researchers need to disclose any scales that is
  unique to the study. They need to identify the
  process used to test the adopted scale.
• Presentation techniques refer to study book
  text reading

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Next topic

• Questionnaire and form design

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Summary

• nature of measurement scaling
• conceptual operational definitions
• measurement scales
• nominal
• ordinal
• interval
• ratio
• parametric versus non-parametric statistical
  techniques
• methods of scaling rating, ranking, sorting,
  choice
• scaling decisions type, odd/even,
  balanced/unbalanced, forced/non-forced, no. of
  scale categories, etc
• criteria for goodness of measure reliability,
  validity, sensitivity

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Tutorial

• Presentation
• Assignments returned feedback
• Measurement scaling exercises - bring study
  materials
• SPSS Ch 3 normality recoding missing
  variables