Run this study#
Your question: how much variation will this method show across days and runs?
Bring: two stable materials near low and high decision concentrations. Suggested starting plan: 5 days × 1 run per day × 5 replicates = 25 results per level, 50 for two levels. This follows CLSI's public precision implementation guide.
- Set your limits first. Choose New study, enter the Analyte and Unit, pick Multi-day precision under Precision and choose Create study. On Set up, under Acceptance limits, choose Enter your own limit and enter the acceptable Within-laboratory SD or CV, and a Repeatability SD or CV limit if needed. An SD usually changes with concentration, so set one SD limit per level or one CV limit for all levels.
- Collect each day. Use routine conditions and acceptable QC. Measure five replicates of each material in the day's run.
- Enter the results. Record material ID, level, day, run, replicate and result. On Data, choose Import a file and choose your file (start from Blank template (CSV), or replace the example results in precision.csv and add the second level). Answer any question the dialog asks, then choose Import into this study. To type the results instead, use Apply a design on the empty study; to number rows that came without day, run and replicate values, use Renumber day, run and replicate (see Entering data).
- Check the design and calculate. Choose Calculate results; Results opens. Every day needs the same number of runs, and every run the same number of replicates. An excluded result leaves its run short and stops the calculation.
- Review and report. Check the counts, then compare repeatability and within-laboratory SD and CV with your limits. On Report, choose Download PDF.
Need separate run and day effects? Plan two runs a day: 20 days × 2 runs × 2 replicates = 80 results per level, 160 for two. With one run a day, run and day effects are combined. Calculation minimum: 2 days × 1 run × 2 replicates.
Purpose#
For each level, a balanced random-effects analysis of variance splits imprecision into within-run, between-run and between-day parts:
- Repeatability SD and CV: within-run imprecision.
- Between-run SD (within days): needs two or more runs per day.
- Between-day SD, or Between-day/run SD with one run per day.
- Within-laboratory SD and CV: the total imprecision. See within-laboratory precision.
- The grand mean, with a confidence interval from the day means.
When to use it#
Use it when replicates span days and runs and you need the variation split into parts. Use Repeatability when all replicates come from one run, and Descriptive summary for unstructured results.
Repeatability SDs can feed the Deming λ of a method comparison.
Study setup#
The design must be balanced:
- One material per level.
- At least two days, with the same number of runs each day. One run a day is fine.
- At least two replicates per run, the same number in every run.
- A day, run and replicate on every included row, with each replicate ID used once per run.
Entering data#
On Data, choose Import a file or Add row. See Importing a file.
| Column | Required? | What to enter |
|---|---|---|
| Material ID | Yes | The control or pool ID, one per level |
| Level | No | The concentration level. Default 1 |
| Day | Yes | For example 1 to 5 |
| Run | Yes | Run within the day, for example 1 or 2 |
| Replicate | Yes | Unique within day and run |
| Result | Yes | The measured value |
The Precision design panel at the top of Data numbers the days, runs and replicates for you. Pick 5 days × 1 run × 5 replicates or 20 days × 2 runs × 2 replicates, then:
- With no rows yet, choose Materials (levels) (1, 2 or 3) and then Apply a design. It adds a blank row for every result the design needs, with level, day, run and replicate filled in. Enter the material ID and result on each row.
- With rows, for example imported with empty Day, Run and Replicate columns (the file still needs those three columns), choose Renumber day, run and replicate. Each level needs exactly 25 or 80 included rows. A confirmation, Renumber day, run and replicate?, says that the day, run and replicate of all included rows are replaced in table order. Choose Renumber rows, or Cancel to keep them.
Correct or exclude a censored value such as <5. See Missing and censored values.
The calculation stops, naming the level, if the design is unbalanced, a level has two materials, a row has no day, run or replicate, or a replicate ID repeats within a run.
Statistics#
Balanced random-effects ANOVA: days, runs nested in days, replicate error. D days, R runs per day, n replicates per run:
| Component | How it is calculated |
|---|---|
| Grand mean | Mean of the day means |
| Repeatability SD | √(MS within runs) |
| Between-run SD (within days) | √([MS(runs within days) − MS(within runs)] / n), with 2 or more runs per day |
| Between-day SD (or Between-day/run SD) | √([MS(days) − MS(runs within days)] / (R × n)). With one run per day, √([MS(days) − MS(within runs)] / n) |
| Within-laboratory SD | Square root of the sum of the non-negative components |
| Within-laboratory CV | 100 × within-laboratory SD / grand mean, on a ratio scale |
| CI for grand mean | Student t with D − 1 degrees of freedom and SD(day means) / √D |
A component comes out negative when day-to-day variation is too small to detect against within-run scatter. It is then reported as 0, with a note.
Acceptance limits for this study#
- CV limits need a ratio scale (Measurement scale under Calculation settings, the default). On an interval scale they are Undecided.
- With one run per day, a Between-run SD (within days) limit is Undecided. A Between-day SD limit then uses the combined between-day/run SD.
One unmet limit fails the whole study. See Acceptance limits, including More statistics, and Limit outcomes.
Worked example#
precision.csv has one control material (QC1), level 1, on 5 days with 1 run per day and 5 replicates per run (25 rows). The results are 5.4 or 5.5.
Setup: analyte Example analyte, unit mmol/L, 95% confidence. Limits:
- Within-laboratory CV at most
2%. - Repeatability CV at most
1%.
What the saved result shows#
| Estimate | Displayed value |
|---|---|
| Grand mean | 5.49 mmol/L |
| Repeatability SD / CV | 0.032 mmol/L / 0.58% |
| Between-run SD (within days) | Not estimated |
| Between-day/run SD | 0.011 mmol/L |
| Within-laboratory SD / CV | 0.033 mmol/L / 0.61% |
| 95% CI for grand mean (independent days) | 5.47–5.51 mmol/L |
| Day and run structure | 5 days, 1 run per day, 5 replicates per run |
| Variance analysis, degrees of freedom | Between days/runs 4; Within runs 20 |
| Criterion | Observed | Acceptance limit | Outcome |
|---|---|---|---|
| Within-laboratory CV | 0.61% | ≤ 2% | Met |
| Repeatability CV | 0.58% | ≤ 1% | Met |
The study status is Criteria met. A note says that with one run per day the between-day/run SD combines day and run effects. The day means are 5.5, 5.46, 5.48, 5.5 and 5.5 mmol/L.
Reading the results#
Results and acceptance gives N, mean, repeatability SD and CV, and within-laboratory SD and CV for each level. Compare Within-laboratory SD with a total imprecision goal. Repeatability SD is the within-run part. The SDs and CVs are point estimates: the true imprecision can be higher, so look twice at a within-laboratory CV close to your limit.
Also watch for one day's mean far from the others, or a between-day component larger than repeatability.
Additional statistics and calculation history shows the Day and run structure found, the Variance analysis table (in the unit squared) and each run's count, mean and SD under Run summaries. Raise Display decimal places under Calculation settings for more digits.
When a limit is not met#
- Recheck day, run and replicate IDs, decimals and the decimal convention. The design message names the unbalanced level.
- Find the largest component. Between-day: look for calibration, reagent lot, operator or temperature changes. Repeatability: look at pipetting, mixing or the control material.
Common mistakes#
- Two control lots in one level: give each material its own level.
- Day numbers restart for each level: that's fine. Days are matched within a level.
Statistical detail#
SD and CV decisions use the entered decimal results before display rounding; equality meets an inclusive limit.
Sources: NIST/SEMATECH e-Handbook, nested designs. Numerical examples from Chakravarthy et al. (2019). See Methods and sources.