Statistical hygiene

Once you’ve declared a variable’s measurement scale (nominal, ordinal, interval, ratio), the next step is: only use statistic or plot types valid for that scale. Below is a compact guide.

Scale	Allowed summaries / metrics	Allowed visualizations	Not allowed / misuse to avoid
Nominal	counts, proportions, mode	bar chart, pie (small categories)	mean, standard deviation, histogram (meaningless)
Ordinal	median, rank correlations (e.g. Spearman)	bar chart (ordered), boxplot of ranks	arithmetic mean (unless evenly spaced), variance with caution
Interval	mean, standard deviation, differences	histogram, density plot, boxplot	true “zero‑based” ratios (only differences meaningful)
Ratio	all interval metrics + meaningful ratios	same as interval + log scales if needed	none in the standard sense (all metrics valid)

Procedure:

1. For each variable, annotate its scale (in data dictionary or schema).
2. When choosing a summary or statistic, refer back to this table.
3. For visualizations, match type to permissible plots above.
4. If you ever see code taking a mean of a nominal code (e.g. 0/1 categories), flag for correction.

# Example: binary treatment (nominal) → use proportion & bar, not mean code:
import pandas as pd
df = pd.DataFrame({"group": ["A","B","A","B","A","A","B"], "outcome": [0,1,0,1,0,1,1]})
counts = df.groupby("group")["outcome"].value_counts(normalize=True).unstack(fill_value=0)
print(counts)
counts.plot(kind="bar", stacked=True)

You can also encode nominal codes as pd.Categorical (unordered) so that accidental numeric ops error out.

3) Where it goes

Page: 0.1 Measurement Scales & Variable Types
Section: After the definitions / examples of nominal, ordinal, interval, ratio — insert a new subheading “0.2 From Scales → Choosing Summaries & Visuals (Statistical hygiene)”

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4) Micro‑exercises (with brief answers)

1. Variable “color of car” (red/blue/green) → what summary metric and plot do you choose?
   Answer: counts / proportions; bar chart (categorical); not mean or histogram.

2. Variable “customer satisfaction” rated 1–5, with ordinal scale → is taking the mean valid?
   Answer: only if you assume equal spacing; safer to use median, rank correlation, or treat it as ordinal in box/rank plots.

3. You see code df["gender_code"].mean() where gender_code is encoded 0 = male, 1 = female. What’s wrong and what to replace?
   Answer: Taking a mean of nominal binary is meaningless — instead compute proportion df["gender_code"].mean() is okay but only if clearly documented and interpreted as proportion; better: treat as nominal and show counts/proportions with bar chart.

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5) Expand Path (optional)

Next pages / sections to build:

• 1. Probability → as earlier patch suggested: events, conditional, Bayes, total probability.
• 2. Descriptive Statistics → deeper: variance, covariance, quantiles; tie to scale table above.
• 3. Visualization → mapping plot types to data shapes and objectives (e.g. scatter, line, faceting).
• 4. Data Cleaning / Type Enforcement → enforcing categorical dtype, safe coercion, missingness policies.
• 5. Inference / Hypothesis Testing → building on probability + descriptive foundations.

That single inserted “scale → summary/plot” guide will reduce many future misapplications, and anchor all downstream choices to sound foundations.

Micro‑exercises:

• Q1: A variable “browser type” (Chrome, Firefox, Safari) — what summary metric and plot should you use?
  A1: counts or proportions; bar chart. (Not mean or histogram of codes.)
• Q2: A satisfaction rating 1‑5 (ordinal) — is it always valid to compute the mean?
  A2: No — only if spacing is truly equal and you treat it as interval; safer: median or percentiles.
• Q3: A variable “time since signup (in days)” (ratio) — what summaries/plots are valid?
  A3: mean, sd, ratios (e.g., twice as long), histogram, density plot; log scale if heavy tail.