Run this study#
Your question: what sigma value do your allowable total error, bias and imprecision give at one concentration?
Bring: an allowable total error (TEa), a signed bias and an imprecision estimate at one concentration. Sigma uses estimates you already have, so you collect no new measurements. Each concentration entry gives one sigma value, up to 20 entries per study.
- Choose the concentration and TEa. Use a concentration where your laboratory makes decisions. Set the TEa before looking at results. A different TEa gives a different sigma.
- Gather the bias evidence. Use a saved bias check or method-comparison estimate at that concentration, or enter an estimate you already have.
- Gather the imprecision evidence. Prefer a within-laboratory SD or CV that covers routine variation. Enter multi-day precision estimates by hand. A single-run repeatability estimate can overstate sigma.
- Enter the values. Open Data and choose Add concentration entry. Use Copy bias from a saved calculation and Copy precision from a saved calculation where they are offered. Check the concentration, and whether each value is a percentage or an absolute value in the study unit.
- Calculate and check the entries. Choose Calculate results. Results opens. Read the flags beside each entry, for example evidence that changed after copying. On Report, choose Download PDF.
You get: sigma = (TEa − |bias|) / SD at the stated concentration, with its inputs. Sigma has no pass or fail. Review the bias and multi-day precision studies behind it before relying on it.
Purpose#
Sigma counts the SDs that fit between your bias and the allowable total error at one concentration. See sigma metric and TEa. No 1.5 SD shift is applied.
When to use it#
Use it when you already have bias and imprecision estimates for an analyte, from studies in this project or from documents, and a TEa.
For a pass/fail verdict on bias, use Bias against an assigned value. For imprecision, use Multi-day precision or Repeatability.
Study setup#
Choose New study. Enter Analyte and Unit exactly as in the studies you want to copy from, select Sigma metric under Summaries, and choose Create study. The study opens on Set up, where the Values to gather card lists what to bring. Choose Add entries to go to Data.
Under Calculation settings, Measurement scale is Ratio scale · CV usable by default. Choose Interval scale · no CV when the analyte has no true zero.
Entering data#
In Data, choose Add concentration entry for each concentration. Enter numbers with a decimal point. Each entry needs all four values to be calculated:
| Field | What to enter |
|---|---|
| Concentration | Above zero, in the study unit |
| TEa and TEa is entered as | Above zero, as Percent of the concentration or Absolute · {unit} |
| Bias (signed) and Bias is entered as | Test minus reference or target, as a percent or an absolute value |
| Imprecision and Imprecision is entered as | 0 or above, as CV · % or SD · {unit} |
Copying from saved studies. Copy bias from a saved calculation and Copy precision from a saved calculation list estimates from the other studies in this project that have exactly the same analyte and unit and a saved calculation (a study's signed-off calculation, otherwise its latest). Choose an estimate and Copy selected estimate. It fills in the value, links it, and fills in the concentration if that is blank. Refresh evidence reloads the lists. You can copy:
- bias from a Bias check level, or a Method comparison medical decision level inside the measured range. It is copied as an absolute value.
- imprecision from Repeatability or Descriptive summary. It is copied as a CV on the ratio scale, otherwise as an SD.
Editing a copied value by hand removes its link. When a sigma study in this project with the same analyte and unit already has a TEa, Use last TEa appears under Allowable total error and copies the most recent one.
Each entry is calculated separately:
- Not computed when the concentration, TEa, bias or imprecision is missing, or a percent input is used on an interval scale (enter TEa, bias and SD in the study unit instead). The entry lists the reason.
- Undefined when the imprecision is 0.
- A sigma of zero or below is flagged. The bias uses up the whole TEa.
Statistics#
Units are aligned through the stated concentration C: TEa% = 100 × TEa / C, |bias|% = 100 × |bias| / C, CV% = 100 × SD / C, and back again.
On a ratio scale, sigma = (TEa% − |bias|%) / CV% at full precision, the same as (TEa − |bias|) / SD at C. On an interval scale only the absolute form is calculated. The sign of the bias is ignored.
Source: Westgard S, Bayat H, Westgard JO (2019), Biochemia Medica 29(1):010903, Eq. 5. Another view: Coskun A, Serteser M, Ünsal I (2019), Biochemia Medica 29(1):010902. See Methods and sources.
Worked example#
The study Glucose · derived sigma at 100 mg/dL in the example project copies its values from two other studies in that project:
- a bias of 0.17 mg/dL from Glucose · assigned-target bias check, level 1, assigned 100 mg/dL
- a CV of 0.935 % from Glucose · single-run repeatability, level 1, mean 100.17 mg/dL
Entry 1 has concentration 100 mg/dL, and TEa 8 % as Percent of the concentration. The results table shows:
| Column | Displayed value |
|---|---|
| Concentration | 100 mg/dL |
| TEa | 8.000% (8.000 mg/dL) |
| |Bias| | 0.170% (0.170 mg/dL) |
| CV | 0.935% (SD 0.935 mg/dL) |
| Sigma | 8.38 |
The report's Key results table shows the same 8.38.
Other entries:
| Entry | Result shown |
|---|---|
| TEa 10 %, bias 1 %, CV 2 % at 100 mg/dL | 4.50 |
| The same with imprecision 0 | Undefined |
| TEa 10 %, bias 12 %, CV 2 % (bias larger than TEa) | −1.00, flagged |
| TEa 6 mg/dL, bias −0.5 mg/dL, SD 1.5 mg/dL at 50 mg/dL (absolute inputs) | 3.67 |
Reading the results#
Derived sigma by concentration lists each entry with its inputs, sigma, and any reasons and flags. Percentages show the study-unit value beneath.
If a linked study changes after copying, Data warns under the entry and the next calculation flags it. Copy the value again and recalculate to use the new one. Signing off is refused while a linked value is out of date.
If nothing is offered to copy, check that the other study has exactly the same analyte and unit text and has been calculated.
The report opens with a decision chart of |bias| against imprecision with lines for 2σ to 6σ, then Key results, the inputs in the study unit and, for copied values, the linked studies.