Two operators. Five items. Three readings each. Separate the item from the way it is measured.
The evidence
Repeat the reading. Keep the item fixed.
30 readings per study
● A: circles■ B: squaresReference values hidden
Before repairsOriginal measurement systemAfter repairsNo repairs selected
Both plots share one scale. Each mark is one reading; its small vertical offset identifies repeat 1, 2, or 3. The items themselves never change.
Read the pattern and check your diagnosis
Small study, uncertain estimates: random noise can create apparent bias or an operator gap. A near-zero overall bias can also hide equal and opposite operator errors. These are descriptive indicators, not pass/fail criteria.
See every reading
The data behind the picture.
Calculations use unrounded readings. Display: 3 decimal places.
Before repairs: three readings per item and operator, in millimeters.
Item
Operator
Repeat 1
Repeat 2
Repeat 3
Mean
Reference
CSV contains both studies. References are included only when revealed. Work stays in this tab; download the data before leaving. No accounts, uploads, or saved student responses.
15-minute team activity
A diagnosis you can defend.
3 minutes: inspect the readings without references. Write one claim you can support and one you cannot.
4 minutes: reveal the references. Distinguish bias, repeatability, and operator disagreement.
5 minutes: predict which repair will help, try it, then test the other repairs. Explain why a metric may move even when it was not the target.
3 minutes: plan a check for your own process: operational definition, instrument, operators, repeated measurements, and a trusted reference.
Before collecting project data
Improve the measurement first.
Bias: the average difference from an accepted reference. Repeated agreement alone cannot establish accuracy.
Repeatability: variation when one operator measures the same item repeatedly under the same conditions.
Reproducibility: variation when measurement conditions change, such as the operator. This lab uses the mean B-minus-A difference as a simple indicator of systematic operator disagreement.
Different item, different question: the spread across all items mixes real item differences with measurement error. It is not a repeatability estimate.
How the simulation and calculations work
Model: reading = item reference + common bias + operator offset + random error. Operator A has offset −gap/2; B has +gap/2. Random errors are independent normal draws with mean zero and the stated model standard deviation. The five item references are exact in this simulation; real reference uncertainty must be considered.
Estimated average bias: average of all 30 (reading − reference) differences. Operator-specific biases use each operator's 15 differences.
Pooled repeatability: subtract each item/operator cell mean from its three readings, sum the 30 squared residuals, divide by 5 × 2 × (3 − 1) = 20 degrees of freedom, then take the square root. This excludes between-item and systematic between-operator mean differences.
Mean operator gap: average of the five (operator B mean − operator A mean) differences. It is signed, in millimeters, and is not a reproducibility standard deviation or a variance component.
Controlled comparison: repairs reuse the same underlying random draws, so a repair can be isolated. New sample changes the seed and creates a fresh paired comparison. Reset restores the case's original seed and clears repairs and reference reveal. A repaired study is a model comparison, not an independent validation study.
Limits: no full gage R&R ANOVA, percent GRR, acceptance thresholds, specification limits, process capability, long-term drift, operator-by-item interaction, instrument-to-instrument variation, or instrument resolution model. The controlled cases are illustrations, not a measurement-system certification. Real studies need a representative sample, randomized/blinded measurement order, appropriate repeats, and a method matched to their design.