0.1 Measurement Scales & Variable Types

Purpose: choose the right summaries and charts by naming what your data is.

1) Variable families (what the thing is)

• Categorical or Cualitative
  • Nominal (no order): color, country, user_id (identifier, not a “category” for averaging).
  • Ordinal (order, uneven steps): low/med/high, Likert 1–5.
• Numeric
  • Interval (equal steps, no true zero): °C, dates.
  • Ratio (equal steps, true zero): length, income, counts.
  • Boolean: Logic (True/False)
• Specials: datetime, text, geospatial, images.

2) What you may do (legitimate operations)

Scale	Allowed ops (examples)	Typical stats	Typical visuals
Nominal	=, ≠, mode, counts	Mode, frequency %	Bar chart, stacked bars
Ordinal	order comparisons (<, >), median	Median, percentiles	Ordered bars, dot plot
Interval	+/−, mean differences	Mean, SD, z-scores	Line (time), histogram
Ratio	×/÷, geometric mean, CV	Mean, SD, ratios, rates	Histogram, box plot, scatter

Heuristic: position > length > angle/area > color for quantitative precision.

3) Common pitfalls (and fixes)

• IDs as categories: never average an identifier; use for joins/keys only.
• Ordinal ≠ Interval: a 4 isn’t “twice” a 2 on a Likert scale; report medians/quantiles.
• Unit traps: °C is interval (no true zero) → ratios like “30°C is 2× 15°C” are invalid; Kelvin is ratio.
• Implicit missingness: “0” might mean “unknown”; encode NaN/NA explicitly.
• Re-encoding danger: integer-coding categories does not make them numeric.

4) Mapping to pandas (practical handles)

Concept	pandas dtype / tool	Note
Nominal	category / string	Memory-friendly categories.
Ordinal	CategoricalDtype(ordered=True)	Define order explicitly.
Interval	float64, datetime64[ns]	Beware time zones.
Ratio	int64 / float64	Keep units in column name.
Binary	bool	Encode missing as pd.BooleanDtype().
Datetime	to_datetime, dt accessor	Store as UTC internally.
Geo	geopandas.GeoDataFrame (geometry)	Track CRS; don’t mix.

5) Mini-checklist (before any analysis)

1. Name each column’s scale (nominal/ordinal/interval/ratio).
2. Set dtype accordingly (categories ordered where needed).
3. Write the unit and missingness policy.
4. Choose summaries & charts that the scale permits.

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Scale → Valid Statistics & Plots: Decision Table

Scale	Permitted comparisons / operations	Safe descriptive stats	Bad/misleading stats to avoid	Recommended plots
Nominal	equality / membership	counts, proportions, mode	mean, standard deviation, correlations	bar charts (counts / proportions), mosaic
Ordinal	order, ranking, percentiles	median, percentiles, rank‑based	mean on raw codes, linear regressions	ordered bar, box / violin by group (on ranks)
Interval	differences meaningful (no absolute zero)	mean, standard deviation, z‑scores	ratios (e.g. “twice as big”)	histogram, KDE, line plot
Ratio	full arithmetic ( + − × ÷ )	mean, geometric mean (if >0), CV	(still avoid mixing types blindly)	histogram (possibly log scale), scatter

Rule of thumb: If your data is non‑numeric or has arbitrary codes, treat as nominal/ordinal — don’t compute mean or Pearson correlations until it's truly interval/ratio.