VIII. Issues in measurement

A. Latent Variables and Measured Variables

1. Attributes as Latent Variables

a) physical and psychological constructs are unobservable
b) inferred from observed effects

2. Observed Scales as transformations of Latent Variables

a) temperature and heat
b) weight and mass
c) test score and ability

3. Scales and levels of measurement

a) scales defined in terms of their sensitivity to transformations
- (1) ordinal transformations
  - (a) preserve order but not distance: x>y <==> x' > y'
  - (b) without zero
  - (c) with zero
- (2) partial orders
  - (a) some distances are preserved
  - (b) some distances are indeterminant
- (3) interval scales preserve distance
  - (a) x-y > s-t <==> x'-y' > s' - t'
  - (b) Kelvin <-> Celcius <-> Farenheit
- (4) ratio scales preserve distance from 0
  - (a) x/y > s/t <==> x'/y'>s'/t'
  - (b) interval with zero point
  - (c) Meters to Miles
b) the meaning of transformations
- (1) statistics based upon observed data
- (2) inferences about latent variables
  - (a) what kind of inferences can one make about latent variables?
  - (b) main effect differences
  - (c) interactions

4. Examples of measurement induced inference

a) Impact of college upon students
- (1) Theoretical question: what is the influence of college quality upon student achievement
  - (a) student achievement as reflected in writing performance
  - (b) influence of college as reflected by change in writing performance
  - (c) college quality confounded with entering student ability
- (2) Change in reading score as a function of college quality
  - (a) pre-post measure on writing score
  - (b) 3 levels of college
    - i) non-selective
    - ii) selective
    - iii) very selective
  - (c) 2 types of test -- easy and hard
- (3) Hard test
  - (a) conclude that highly selective schools provide better education
- (4) Easy test
  - (a) conclude that highly selective schools provide an inferior education
b) Group differences in arousal
- (1) Theoretical question: do group differences in (e.g., anxiety) relate to arousal?
- (2) arousal as indexed by Skin Conductance or Skin Resistance
  - (a) SC = 1/SR
  - (b) SC as a measure of palmar activity -- high SC is high arousal
  - (c) SR as a direct measure of resistance to electric current
- (3) Which group is more aroused?
- (4) Group 2 in terms of SR, but Group 1 in terms of SC

B. Theory of Signal Detection

1. Observed score

a) the number of signals correctly detected
b) the number of non-signals incorrectly identified

2. Latent scores

a) Sensitivity to signal (d')
- (1) ability to detect signals in the presence of noise
- (2) dą = Signal + Noise distribution versus Noise distribution
b) Bias of responding (beta)
- (1) willingness to make false alarms
c)

3. Examples of a need to use Signal Detection

a) McGinnies, (1949) Emotionality and perceptual defense
- (1) Two classes of stimuli
  - (a) control words
  - (b) "taboo" words
- (2) two response measures
  - (a) GSR to words
  - (b) duration of signal needed for correct identification

Return to the Research Methods in Psychology (Psychology B05) syllabus.
Version of April 29, 1998