Theories and Domain Sampling:
Overview

• The Roles of Theories
• Sampling a Domain
  • Reliability
• Ostensible / Non-Ostensible Domains
• Variability
• Precision & Range

The Roles of Theories

• A constant touchstone for validity
• Often couched as models
  • Comprised of constructs
  • And the relationships between them
• Constructs often represent a conceptual “space”—or domain—that one tries to measure
  • Well-defined constructs are typically unitary
    • Varying in only one way
    • And representable as a dimension

Sampling a Domain

• Measurement can be seen as attempts to determine where one is in that theoretical space
• With repeated measurements benefiting from how consistently & accurately each point in that domain is quantified
  • Whence reliability

Ostensible / Non-Ostensible Domains

• Ostensible Domains
  • Directly measuring a phenomenon
  • E.g., heart rate, height, extent of a rash, severity of a burn
• Non-Ostensible Domains
  • Indirectly measuring a phenomenon
  • E.g., health-adjusted life expectancy, patient satisfaction, religiosity, lived experiences

Variability

• Research: Attempting to detect & interpret differences
  • E.g., where one is in that domain
    • More parsimoniously, where on a dimension
  • And why they are there
• We gain clarity in doing this by increasing interpretable variability
  • E.g., knowing where & why people at are different places on it

Precision & Range

Precision & Range (cont.)

Precision & Range (end)

Types of Measurement:
Overview

• Process vs. outcome measures
• Norm- vs. criterion-referenced
• Some other types of measurements

Process vs. Outcome Measures

Process vs. Outcome Measures (cont.)

Norm- vs. Criterion-Referenced

• Norms:
  • Comparing against a reference population
• Criteria:
  • Comparing against a standard
• Norms benefit from maximal discrepancy
• Criteria from maximal precision

Types of Stimuli & Responses

• Absolute vs. Comparative
  • We’re naturally better at comparative judgements
  • But the “anchors” used for comparison matter

Types of Stimuli & Responses (cont.)

• Preference vs. Similarity
  • Preference assumes dominance
    • “This” is better/more/etc. than “that”
  • Thus can use asymmetry to test validity
    • If A > B and B > C
    • Then can test if A > C
  • Similarity, however, is symmetric

Some Other Types of Measurements

• Qualitative
  • Good for understanding one event / individual
  • Without primary concern for referencing
• Quantitative
  • Good for comparisons
    • Esp. against norms or criteria

Some Other Types of Measurements (cont.)

• Behavioral Competencies
  • Aptitude: Propensity to succeed in a given domain
  • Achievement: Actual success in a specific, goal-direct task
  • Diagnoses: Level of achievement success / failure
    • Moderators / mediators to that success

Some Other Types of Measurements (cont.)

The Exciting Origins
of Modern Measurement

• Borne most directly from psychophysics
  • Study of relationships between actual and perceived intensities
  • Pioneered by Gustav Fechner
    • Attempting to find a measure of the mind
    • I.e., the basic building block of thought

Exciting Origins (cont.)

Absolute Threshold

• Fechner found that constant stimuli were not constantly noticed
  • There was “noise” in the responses
  • This noise is now typically—and, if unbiased, quite accurately—modeled as normally-distributed error

Just-Noticeable Difference (JND)

• Tested ability to tell if two stimuli were different
  • E.g., 2 weights as heavy, 2 lights as bright
• Found that the JND increased with stimulus intensity
  • It becomes harder to detect the
    same difference as the stimulus
    intensity increases
  • Typically called the Weber-
    Fechner law

Using Differences to Create a Scale

• Thurstone’s law of comparative judgement (Nunnally & Bernstein, p. ~26)
  1. Participants rate preferences to a series of stimuli, presented in pairs
  2. Proportion of preference is used to estimate distance between those 2 stimuli
  3. These distances are used to create an interval scale between all stimuli

“Rules” of Good Measurement

• Standardization
  • Creating a standard set of rules
    • (Thus related to scaling)
  • That facilitate cross-comparisons & generalizations
    • Between researchers, populations, etc.
  • Issue is usually not accuracy, but validity

“Rules” of Good Measurement (cont.)

• Good standardization rules are:
  1. Clear & unambiguous
     • Mathematical functions work well
  2. Easy & practical to apply
     • Helps with validity
  3. Objective
     • Rely little on the measurer, also helps validity

“Rules” of Good Measurement (end)

• Note how those rules apply as well to instrument use & administration
  • Clear & unambiguous instructions
  • Easily-followed response formats
  • That allow as objective a response as possible

How Likert Concieved Them

How Likert Concieved Them (cont.)

1. Construct a series of Likert response format items measuring positive attitudes towards target
2. Construct an equal number of items measuring negative attitudes
3. Q sort both directions to assess measurement of whole range
4. Use overall scores as interval-level measures

How Likert Concieved Them (end)

• Individual items were intended to be ordinal
  • But not intended to be interpretted alone
• Indeed, the concept of an overall Likert scale is almost meaningless
  • Nearly always, it’s items that employ a Likert response format
  • Except for domains easily measured with one item
    • E.g., pain scales

Likert Response Tendencies

• Respondents tend to assume equal distancing between categories (Westland, 2022)
  • Unless, e.g.:
    • Distances are strongly & explicitly stated
    • Items prompts or response anchors measure very strong/polarized beliefs
    • Response range is censored or levels binned
    • The scale includes a very wide range
      • Reminiscent of absolute thresholds

Likert Response Tendencies (cont.)

• Combined (e.g., summed) Likert-scaled items tend to act even more like an interval scale (Carifio & Perla, 2007)
  • Including approximating a normal distribution
  • This also tends to hold for dichotomous items
• Thus Likert-response data can typically be treated as interval
  • And relevant parametric tests employed
• And you should avoid item-level analyses anyway

Likert Response Tendencies (cont.)

• Kusmaryono et al. (2022)
  • 5+ response levels may generate more uniform patterns
  • Odd-numbered scales:
    • May generate more reliable & valid data
    • At the expense of respondents tended towards middle responses

Likert Response Tendencies (cont.)

• Weijters et al. (2010)
  • Studied marketing instruments administered online to the general (male) public
  • Investigated response formats on:
    • Net acquiescence response (NAR)
    • Extreme response (ER)
    • Misresponse to reversed items (MR)

Likert Response Tendencies (cont.)

Likert Response Tendencies (end)

• Adding more response levels:
  • Doesn’t change NARs
  • Reduces ER
  • Doesn’t change MR, but:
    • Also having only endpoints increases MR
      • But may improve criterion validity
    • Having a midpoint interacts with number of response levels to also increase MR