Statistics for ML #1 — Types of Data: Nominal, Ordinal, Interval, Ratio

Understanding data types is the most fundamental step before any analysis. Choosing the wrong statistical test or ML algorithm because you misidentified your data type is one of the most common mistakes in practice.

The Four Levels of Measurement (Stevens, 1946)

🔵 Nominal (Categorical, No Order)

Names or labels only. No ranking, no distance.

• Examples: Blood type (A, B, AB, O), Religion, Country, Gender, Disease category
• Operations allowed: = and ≠ only
• Central tendency: Mode
• In ML: One-hot encoding, label encoding

import pandas as pd
df['gender'] = pd.Categorical(df['gender'])
# One-hot encode
pd.get_dummies(df['gender'], prefix='gender')

🟢 Ordinal (Ordered, No Equal Spacing)

Categories with a meaningful order, but the gaps between ranks are not equal.

• Examples: Education level (Primary < Secondary < Tertiary), Likert scale (1=Strongly Disagree … 5=Strongly Agree), Cancer stage (I < II < III < IV), Wealth quintile in DHS surveys
• Operations allowed: = , ≠ , < , >
• Central tendency: Median, Mode
• In ML: Ordinal encoding, target encoding

⚠️ Critical mistake: Treating ordinal data as continuous (interval) inflates precision that doesn’t exist. The difference between “agree” and “strongly agree” is NOT necessarily the same as between “neutral” and “agree.”

🟡 Interval (Equal Spacing, No True Zero)

Equal gaps between values, but zero is arbitrary (does not mean “absence”).

• Examples: Temperature in °C or °F, Calendar year, IQ scores, pH scale
• Operations allowed: +, −, but NOT ×, ÷ ratios
• Note: 20°C is NOT “twice as hot” as 10°C. But the difference (10°) is meaningful.
• Central tendency: Mean, Median, Mode

🔴 Ratio (Equal Spacing + True Zero)

All arithmetic operations valid. Zero means absolute absence of the quantity.

• Examples: Height, Weight, Age, Income, Blood pressure, Number of ANC visits, Child mortality rate
• Operations allowed: +, −, ×, ÷ all valid
• Statement allowed: “A person earning $100K earns twice as much as one earning $50K.”
• Central tendency: Geometric mean, Harmonic mean also valid

Quick Reference Table

Why This Matters in Public Health & ML

In DHS survey data (Bangladesh, Nepal, Zambia):

• Wealth index → Ordinal (quintiles 1–5)
• Number of ANC visits → Ratio (true zero = no visits)
• Region/Division → Nominal (no ordering)
• Skilled birth attendance (Yes/No) → Nominal binary

Using the wrong encoding leads to:

• Inflated R² in regression
• Biased SHAP values
• Wrong distance metrics in clustering (k-means should NOT be used on nominal data directly)

R Code: Checking and Setting Data Types

library(dplyr)

df <- df %>%
  mutate(
    wealth_index = factor(wealth_index, ordered = TRUE,
                          levels = c("Poorest","Poorer","Middle","Richer","Richest")),
    region       = factor(region),           # nominal
    anc_visits   = as.integer(anc_visits),   # ratio/count
    temperature  = as.numeric(temperature)   # interval
  )

str(df)

Next post: #2 — Measures of Central Tendency
Series: Statistics for ML — Full Index