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Unit 4: Measurement & Scaling - Coggle Diagram
Unit 4: Measurement & Scaling
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.
Scaling
Extension of measurement creating a continuum for measurement placement.
Example: Satisfaction level from 1 to 11.
Types of Measurement Scales
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.
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.
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.
Ratio Scale
Ratios of measurements have meaningful interpretation.
Examples: Number of shops, students enrolled, distance traveled.
All mathematical operations are applicable.
Classification of Scales
Single Item Scale
: Satisfaction with job, for instance.
Multiple Item Scale
: Satisfaction with aspects of a job.
Comparative Scales
Paired Comparison
Constant Sum
Rank Order
Q-Sort and other procedures
Non-Comparative Scales
Graphic Rating Scale
Itemized Rating Scale: Likert, Semantic Differential, Stapel
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.
Criteria of a Good Measurement
Reliability
: Consistency, accuracy, and predictability of a measurement.
Validity
: Free from systematic and random errors.
Sensitivity
: Ability to accurately measure variability in a concept.