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Measurement & scaling: defs + why?

2 reasons

measure = assign numbers

scale = create a continuum upon which measured objects are located



1. to apply statistics

2. to communicate more clearly


4 (5) types of scales, in order from lower to higher level of measurement

  1. nominal scale = mutually exclusive and exhaustive categories
  2. ordinal scale = numbers expressing ranking

    (2.5) rating scale = like preference ranking... it is in between, and really an ordinal scale, but often interpreted as interval --> to do statistics
  3. interval scale = numbers with intervals being equal
  4. ratio scale = interval scale with an absolute zero --> you know ratios between ratios, e.g. Kelvin VS Celsius degrees


6 steps of measuring: 3+2+1


  1. Identify the concept of interest
    (can be simple like gender or complex like intelligence)
  2. Develop a construct
  3. Define the concept constitutively
    (the central idea under study)


  1. Define the concept operationally
    (operational definition what to measure)
  2. Develop a measurement scale


  1. Evaluate the reliability and validity of measurement


effect of using brackets, e.g. for age,
on the measurement level

--> moving down from ratio scale to ordinal scale

...it is better to ask for the age number instead!


scaling technique 3-level taxonomy (for rating scales)

  • comparative
    • pair comparison
    • rank order
    • constant sum
  • non-comparative
    • itemized rating scale
      • semantic differential = 7-point scale of bipolar labels, eg hot VS cold, careful VS careless
      • Stapel = 10-point unipolar scale (on attribute), from -5 to +5 with no neutral zero rating
      • Likert ('li:kert) = degree of agreement from 1=strongly disagree to 5/7=strongly agree
    • continuous rating scale


when to ask w comparative scales? 3 reasons

  • when you need a decision, eg on preferences
  • when you are interested in the effects of small differenes
  • to avoid carry-over effects (respond as above) and halo effects


how to design a scale? 
4=2+2 issues to consider

2 item Nr-related factors:

  • how many items? odd (w neutral) or even (--> take sides)?
    • suggestion: do not force to take sides, offer a neutral or 'do not know' answer
    • relatedly: do not force answers, esp. on sensitive Qs where ppl might not want to answer, like income; rather, request --> it is softer
  • constant number of scale categories: do not switch from 5- to 7-point scale mid-survey, coz it confuses participants and makes your analysis more difficult to standardize

2 scale type-related factors:

  • switch bw scale types instead, while keeping the same Nr of options, to avoid boredom & carry-over or halo effects
  • tradeoff bw single-item or multi-item scales: multi-items means several similar Qs to measure all facets more precisely, but it is fatiguing for participants


scale evaluation: is our measurement good?

2 criteria

2 types of errors

 2 criteria:

  • validity --> am I measuring the intended construct?
  • reliability --> repeatability

NB: validity presupposes reliability.


2 error types:

  • random errors = noise
  • systematic errors



key issue


2 methods to achieve it

key issue --> are we correctly representing the correct target population?

goal --> external validity

methods to achieve it --> correct sample selection & sample size


4 basic concepts in sampling + 2 errors

population --> sample frame

sample = set of (sample units)

sampling error = units chosen outside, or otherwise not representatively of the target population

sample frame error = differences bw population and sample frame


sample size tradeoff

the larger,
the more accurate, but also the more expensive