Data Types & Measurement Scales

Data Types & Measurement Scales

Quick Answer: Six Sigma data are continuous (variables) or discrete (attributes). Measurement scales—nominal, ordinal, interval, ratio—define what arithmetic is valid. Green Belts classify data before choosing control charts, descriptive statistics, or hypothesis tests so analysis matches the information the numbers actually carry.

Why Classification Comes First

Every DMAIC project lives or dies on data quality—and “quality” starts with knowing what kind of data you have. Applying a mean and standard deviation to pure category codes, or treating Likert ranks as if they were precise temperatures, produces polished nonsense. CSSGB BoK III.D.1 expects you to analyze data types and scales: identify them in scenarios and select appropriate methods.

Continuous (Variables) Data

Continuous data (also called variables data) come from measurements that can take any value within a continuum, limited only by instrument resolution.

Examples: length (mm), weight (g), time (seconds), temperature (°C), pressure, voltage, financial amount, cycle time.

Properties useful to Green Belts:

• Support mean, median, variance, standard deviation, histograms, box plots
• Enable I-MR, X-bar/R, X-bar/S charts and capability indices when process and measurement systems cooperate
• Carry more information per observation than pass/fail, so sample sizes for a given precision are often smaller
• Still require MSA: bias, linearity, stability, and Gage R&R matter because continuous CTQs drive customer specs

Worked contrast: Measuring shaft diameter to 0.001 mm tells you how close you are to the limit. Calling each shaft “in” or “out” only says whether you crossed the limit—you lose information about margin and drift.

Discrete (Attributes) Data

Discrete data take countable values. In quality work, two attribute flavors dominate:

1. Classification (defectives) — each unit is good/bad, pass/fail, conforming/nonconforming.
2. Count (defects) — number of nonconformities on a unit or in an area (scratches, missing fields, dents).

Other discrete examples: number of calls per hour, number of changeovers per week, defect code categories, days late (if recorded as whole days only).

Properties:

• Often cheaper and faster to collect (go/no-go gage, visual inspection)
• Require larger samples to detect shifts of the same practical size compared with continuous data
• Drive p, np, c, u charts rather than X-bar charts
• Still need operational definitions: what counts as a “scratch”? when is a claim “late”?

Defect vs defective (repeat until automatic):

One defective board can carry multiple defects. Your data type choice and chart family follow that distinction.

Measurement Scales (Stevens)

Independent of continuous vs discrete, each measurement lives on a scale of measurement. Scale determines allowed statistics.

Nominal scale

• Definition: Names or labels only; no order.
• Examples: machine ID, shift color code, defect type (scratch / dent / stain), department, yes/no coded as labels.
• Valid ops: count, mode, contingency tables, chi-square tests of association, Pareto by category.
• Invalid: mean of “Machine 1, 2, 3” if numbers are only names; “average defect type” is meaningless.

Ordinal scale

• Definition: Ordered categories; gaps between ranks are not necessarily equal.
• Examples: severity rankings (low/medium/high), satisfaction 1–5 Likert items, inspection grades A > B > C, priority scores.
• Valid ops: median, percentiles, rank-based methods, ordered bar charts; mode.
• Caution: Treating ordinal averages as precise interval means is common but theoretically shaky—acceptable as a rough KPI only with care and consistent interpretation.

Interval scale

• Definition: Equal intervals between values; no true zero (zero is arbitrary).
• Classic example: temperature in °C or °F (0 °C is not “no temperature”); calendar year.
• Valid ops: mean, standard deviation, many parametric methods; differences are meaningful (“5 °C warmer”).
• Invalid: ratios (“20 °C is twice as hot as 10 °C” is false on Celsius).

Ratio scale

• Definition: Equal intervals and a true zero meaning absence of the quantity.
• Examples: length, mass, time duration, counts, Kelvin temperature, money, defect counts, cycle time from start to finish.
• Valid ops: all interval ops plus ratios (“twice as long,” “half the scrap cost”).
• Green Belt default: most engineering CTQs and cost metrics are ratio-scale continuous or ratio-scale counts.

Putting Type and Scale Together

Practical Green Belt Rules

1. Prefer continuous ratio data for CTYs when measurement cost is acceptable—more sensitivity per sample.
2. Write operational definitions before collection so “late,” “dent,” and “rework” do not morph mid-project.
3. Do not average nominal codes. Summarize with counts and percentages.
4. Match chart to type: variables charts for continuous measurements; attribute charts for defectives/defects.
5. Stratify nominal factors (machine, shift, supplier) even when the Y is continuous—multi-vari and ANOVA thinking start with correct factor typing.
6. In surveys, treat single Likert items as ordinal; multi-item scales sometimes behave more interval-like—know your organization’s standard and exam expectations (usually: ordinal caution).

Common Exam and Project Traps

• Recording “% defective” and forgetting it is still attribute-derived—control chart and sample-size logic differ from measuring the underlying continuous CTQ.
• Coding Yes = 1, No = 0 and computing a “mean” (which is a proportion)—valid as a proportion, but you are not working with continuous variables data for capability in the usual Cp/Cpk sense without a continuous Y.
• Calling all numeric-looking fields “continuous”—zip codes and priority ranks are not ratio engineering data.
• Using parametric mean tests on pure ranks without acknowledging ordinal limitations.

Link Forward in Measure

Once type and scale are clear, the next BoK topics—sampling plans, descriptive statistics, graphics, and MSA—fit naturally. You cannot design a check sheet, choose a sample size, or interpret a standard deviation until you know whether each field is a continuous CTQ, a count of defects, or a category label. Classify first; analyze second.