Unit 4: Measurement & Scaling

  1. Measurement
  • Definition: Assigning numbers or symbols to characteristics or objects for statistical operations and better communication of results.
  • Example: Assigning rupee figures to households with the same income.
  1. Scaling
  • Extension of measurement creating a continuum for measurement placement.
  • Example: Satisfaction level from 1 to 11.
  1. Types of Measurement Scales
  1. Nominal Scale
  • For identification purposes.
  • Numbers assigned do not imply superiority or inferiority.
  • Examples include religious affiliation.
  • Statistical operations: frequency distribution, Chi-square test, contingency coefficient, binomial test.
  1. Ordinal Scale
  • Indicates higher or lower status but not the magnitude of difference.
  • Examples: Rankings in a competition, CAT score percentiles.
  • Statistical operations: Median, percentile, quartiles, rank order correlation, sign test, plus nominal scale operations.
  1. Interval Scale
  • Differences between scores have meaningful interpretation.
  • Example: Rating scales for likelihood, satisfaction, or agreement.
  • Statistical operations: Addition, subtraction, mean, standard deviation, correlation coefficient, T-test, Z-test, regression, factor analysis.
  1. Ratio Scale
  • Ratios of measurements have meaningful interpretation.
  • Examples: Number of shops, students enrolled, distance traveled.
  • All mathematical operations are applicable.
  1. Classification of Scales
  • Single Item Scale: Satisfaction with job, for instance.
  • Multiple Item Scale: Satisfaction with aspects of a job.
  • Comparative Scales
  1. Paired Comparison
  1. Constant Sum
  1. Rank Order
  1. Q-Sort and other procedures
  • Non-Comparative Scales
  1. Graphic Rating Scale
  1. Itemized Rating Scale: Likert, Semantic Differential, Stapel
  1. Measurement Error
  • Occurs when the observed measurement differs from the true state.
  • Caused by environmental variations, interviewer bias, ambiguous questions, or coding errors.
  • Formula: Observed measurement = True score + Systematic Error + Random Error.
  1. Criteria of a Good Measurement
  1. Reliability: Consistency, accuracy, and predictability of a measurement.
  1. Validity: Free from systematic and random errors.
  1. Sensitivity: Ability to accurately measure variability in a concept.