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Measurement Scales Pyramid

Run the Measurement Scales Pyramid Fullscreen

About This MicroSim

This interactive infographic visualizes the four measurement scales as a hierarchy where each level adds mathematical capabilities. The pyramid shape reinforces that:

  • More variables fit into the lower categories (wider base)
  • More operations are possible at higher levels (narrower top = more exclusive)

How to Use

  • Hover over any layer to see 5 example variables of that measurement type
  • Click a layer to see which statistical tests are appropriate for that scale
  • Click again to deselect and return to hover mode

The Four Measurement Scales

1. Nominal (Base)

  • Operations: Equality only (= ≠)
  • Example: Jersey numbers, eye color, blood type
  • Statistics: Mode, chi-square tests, frequency tables

2. Ordinal

  • Operations: Equality + ordering (= ≠ < >)
  • Example: Race positions, Likert scales, pain ratings
  • Statistics: Median, Spearman correlation, Mann-Whitney U

3. Interval

  • Operations: Equality + ordering + equal intervals (= ≠ < > + −)
  • Example: Temperature in Fahrenheit, IQ scores, calendar dates
  • Statistics: Mean, t-tests, Pearson correlation, regression

4. Ratio (Top)

  • Operations: Full arithmetic (= ≠ < > + − × ÷)
  • Example: Height, weight, age, income
  • Statistics: All statistical tests, geometric mean, coefficient of variation

Why This Matters

Choosing the wrong statistical test for your measurement scale can lead to meaningless results. For example:

  • Computing the mean of jersey numbers is meaningless (nominal data)
  • You can't say "80°F is twice as hot as 40°F" (interval, not ratio)
  • Race positions 1st, 2nd, 3rd don't tell you the time gaps (ordinal)

Learning Objectives

After exploring this visualization, students should be able to:

  1. Remember (L1): Name the four measurement scales in order
  2. Understand (L1): Explain what operations are valid for each scale
  3. Apply (L2): Classify any variable into the correct measurement scale
  4. Analyze (L3): Select appropriate statistical tests based on measurement scale

Embed This MicroSim

You can include this MicroSim on your website using the following iframe:

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<iframe src="https://dmccreary.github.io/data-science-course/sims/measurement-scales-pyramid/main.html"
        height="502px"
        width="100%"
        scrolling="no"></iframe>