Data types and measurement scales
Choosing the right statistical tool depends entirely on the type of data you have. The exam tests this often: a question will describe a situation and ask which chart or test applies. Getting data types right is the gateway to every Measure-phase tool.
Continuous vs. discrete data
| Type | Description | Examples | Typical tools |
|---|---|---|---|
| Continuous (variable) | Any value within a range; can be subdivided infinitely | Fill weight (g), tablet thickness (mm), dissolution time (min), temperature | I-MR chart, X̅-R chart, histogram, Cp/Cpk |
| Discrete (attribute) | Countable; whole numbers only | Defect count per batch, number of rejects, pass/fail | p-chart, u-chart, Pareto, DPMO |
Measurement scales (NOIR)
| Scale | Properties | Example | Math allowed |
|---|---|---|---|
| Nominal | Categories, no order | Supplier code (A, B, C), shift name | Count, mode |
| Ordinal | Order matters; gaps unequal | Customer satisfaction (1–5 stars), severity rating | Median, percentiles |
| Interval | Equal gaps; no true zero | Temperature in °C or °F, calendar dates | Mean, standard deviation |
| Ratio | Equal gaps + true zero | Weight (g), length (mm), cycle time (s), count | All operations including ratios |
Memory aid: NOIR (Nominal, Ordinal, Interval, Ratio) — each level adds a property over the previous one.
Attribute vs. variable measurement systems
| Variable (continuous) | Attribute (discrete) | |
|---|---|---|
| Resolution | Any numeric value | Pass/fail or count |
| Information | More; shows how close to spec | Less; only in/out |
| MSA method | Gage R&R (ANOVA or X̅&R) | Attribute agreement analysis |
| Exam preference | Always preferred when feasible | Use when continuous measurement is impossible or very costly |
Data collection plan
Before collecting data in the Measure phase, build a data collection plan that defines:
- What to measure: specific metric (fill weight, not "quality")
- Operational definition: exactly how to measure it (which scale, which point in the process)
- Who measures: designated operators to ensure consistency
- When and where: sampling frequency and location in the process
- How many: sample size (see below)
- How to record: check sheet, form, or electronic system
Sampling basics
| Method | When to use |
|---|---|
| Random sampling | Every item has equal chance of selection; reduces bias |
| Stratified sampling | Population has known subgroups (shifts, lines); sample proportionally from each |
| Systematic sampling | Select every nth item; practical for continuous production |
| Subgroup (rational subgroup) | Group items produced under the same conditions; used for X̅-R charts |
Common exam traps
- Continuous data > attribute data. A tablet weight of 251.3 mg tells you much more than "pass" and enables Cp/Cpk. Use continuous measurement whenever feasible.
- Ordinal is not interval. The gap between "1 star" and "2 stars" is not necessarily the same as between "4 stars" and "5 stars." Calculating means from ordinal data is technically incorrect (though common in practice).
- Temperature in °C is not ratio. 20°C is not twice as hot as 10°C — there is no absolute zero. Kelvin is ratio.
- Larger sample ≠ better if collection process is flawed. Garbage in, garbage out. A well-defined operational definition matters more than sample size alone.
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