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📊 Topic 7: Measurement Scales & Summary

Topic 7/7 ⭐⭐ Applied ⏱️ ~20 min

Review nominal, ordinal, interval, and ratio scales, choose valid summaries for each, and consolidate everything learned in Week 1.

🎯 Learning Objectives

  • Differentiate nominal, ordinal, interval, and ratio scales.
  • Match real-world examples to each scale.
  • Select valid summary statistics for each measurement level.
  • Review the full week with a structured summary.

7.1 Four classical measurement scales

Scale Order? Equal differences? Meaningful ratios? Examples Valid summaries
Nominal No No No Blood group, type of browser Counts, mode
Ordinal Yes No fixed spacing No Customer satisfaction levels, ranks Medians, percentiles
Interval Yes Yes No true zero Temperature in deg C, calendar years Mean, standard deviation (with caution)
Ratio Yes Yes Yes Height, weight, income, response time Mean, variance, coefficient of variation

Interval scales allow addition and subtraction but not meaningful ratios because zero is arbitrary. Ratio scales allow all arithmetic operations.

7.2 Choosing statistics by scale

  • Nominal: use counts, proportions, and chi-square tests.
  • Ordinal: use medians, order-based charts, and non-parametric tests.
  • Interval: compare differences; z-scores are meaningful.
  • Ratio: apply all descriptive statistics, log transforms, and coefficient of variation.

7.3 Week 1 summary

Foundations

Statistics helps us learn from data through descriptive and inferential techniques.

Sampling

Clear definitions of population and sample plus representative sampling protect against bias.

Data management

Understand the context, document variables, and maintain data quality.

Classification

Classify variables by type and scale to choose appropriate statistical tools.

7.4 Reflection questions

  1. Can you articulate the difference between descriptive and inferential statistics without notes?
  2. Given any dataset, can you name the unit of analysis and list the variables?
  3. Are you comfortable identifying the measurement scale of a variable?
  4. Which sampling method would you use for your next project and why?
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