Standard Deviation Index Calculator
Standard Deviation Index Calculator
Place an external quality assessment result against its peer group in standard deviations. The SDI measures bias against your peers — which is not the same thing as bias against the truth.
Standard Deviation Index
Result, peer mean, peer SD → SDIEQA return 5.60 mmol/L; peer group mean 5.20 mmol/L, peer group SD 0.26 mmol/L
Formula
|SDI| ≤ 1.0 good · 1.0–2.0 acceptable · 2.0–3.0 questionable · >3.0 unacceptable
- your result
- the value your laboratory returned for the EQA sample, in the scheme’s units
- peer group mean
- the mean of laboratories using the same method and usually the same instrument. Comparing against all participants instead mixes methods with genuinely different calibrations and generates SDIs that reflect method choice rather than performance
- peer group SD
- the spread of that group. It is a divisor, so a tight peer group produces large SDIs from small analytical differences and a wide one hides real bias. Always check how many laboratories are in the group
- the sign
- half the information. The direction, repeated across rounds, is what identifies a calibration bias; the size alone cannot
- what it is not
- a measure of accuracy. The SDI is the distance from your peers, and where a whole method group is biased against the reference method — which happens, and is one of the things EQA schemes exist to detect — every laboratory in it can score an excellent SDI while all of them are wrong together
Worked example
EQA return 5.60 mmol/L; peer group mean 5.20 mmol/L, peer group SD 0.26 mmol/L
5.60 − 5.20 = 0.40 mmol/L above the peer mean
0.40 ÷ 0.26 = +1.54 SDI
Between 1 and 2: acceptable for this round, and no action is required on this result alone
But look at the sign against the last five rounds. Five returns at +1.2, +1.6, +1.4, +1.5 and +1.54 are a consistent positive bias of about 1.5 SD, and worth a calibration check
Five returns at +1.5, −0.8, +0.3, −1.6 and +1.54 are imprecision, not bias, and the response is quite different: look at the CV, not the calibration
Reading the SDI
| |SDI| | Verdict | What to do |
|---|---|---|
| ≤ 1.0 | Good | Nothing. Note the sign for the trend |
| 1.0–2.0 | Acceptable | Nothing on this round alone. Watch the direction across rounds |
| 2.0–3.0 | Questionable | Investigate before the next round: calibration, reagent lot, internal QC on the day |
| > 3.0 | Unacceptable | Investigate as an error. Check whether other analytes on the instrument moved together |
One excursion or a consistent lean?
| Pattern across five rounds | Reading | Response |
|---|---|---|
| +1.2, +1.6, +1.4, +1.5, +1.5 | A consistent positive bias of about 1.5 SD | Check calibration and traceability, even though no single round failed |
| +0.2, −0.4, +3.2, −0.1, +0.3 | One excursion on a background of good agreement | Investigate that round specifically — sample handling, a transcription error, a bad reagent lot |
| +1.5, −0.8, +0.3, −1.6, +1.5 | Scatter, not bias | Look at imprecision: the CV and the sigma metric, not the calibration |
| +0.3, +0.6, +1.1, +1.7, +2.3 | A drift | Something is changing over time — calibrator lot, electrode, lamp, temperature. Act before it fails |
Distance from your peers, not distance from the truth
External quality assessment sends every participating laboratory the same sample and compares the answers. The standard deviation index expresses your answer’s distance from the comparison group in standard deviations of that group: subtract the peer mean from your result and divide by the peer SD. A result of 5.60 against a peer mean of 5.20 with an SD of 0.26 gives an SDI of +1.54 — one and a half standard deviations high. Conventionally, an SDI within ±1 is good, up to ±2 acceptable, ±2 to ±3 questionable and beyond ±3 unacceptable.
The comparison group is the part most worth scrutinising. Most schemes report against your own method and instrument, because different methods genuinely measure slightly different things and comparing across them produces indices that reflect method choice rather than laboratory performance. The peer SD is a divisor, so its size matters too: a very tight group turns small analytical differences into large indices, and a wide one can hide a real bias. Look at how many laboratories are in your group before reacting strongly to any single number.
The limitation that gives the SDI its name and its blind spot is that it measures agreement with peers, not accuracy. A whole method group can share a calibration bias against the reference method, and when it does, every laboratory in it returns a comfortable SDI while all of them are equally wrong. Detecting that is a job for schemes using commutable samples with values assigned by a reference method, which is why the choice of EQA scheme matters and why an excellent SDI is reassurance about consistency rather than proof of correctness.
The most useful way to read the index is over time. One SDI of +2.5 on a background of scattered small values is probably that sample, that day: check for a transcription error, a handling problem or a bad reagent lot. Five consecutive returns at +1.5, none of which fails on its own, are a consistent bias of about one and a half standard deviations and a much stronger signal — that is a calibration question. And indices that swing widely in both directions are not a bias problem at all but an imprecision one, answered by looking at the CV and the sigma metric rather than at the calibration. The sign, repeated, carries more information than the size in any single round.
Frequently asked questions
How is the standard deviation index calculated?
Subtract the peer group mean from your result and divide by the peer group standard deviation. A result of 5.60 against a peer mean of 5.20 and an SD of 0.26 gives an SDI of +1.54, meaning your result sits one and a half peer standard deviations above the group.
What is an acceptable SDI?
Conventionally an SDI within ±1.0 is good, between 1.0 and 2.0 acceptable, between 2.0 and 3.0 questionable and above 3.0 unacceptable. Individual EQA schemes set their own criteria, so read your scheme’s limits alongside these general bands.
Does a good SDI mean my results are accurate?
No. It means they agree with laboratories using the same method. If that whole method group carries a calibration bias against the reference method, every laboratory in it can score well while all are wrong together. Only schemes using reference-method target values can answer the accuracy question.
Should I worry about a small SDI that is always in the same direction?
Yes, more than about one larger excursion. Five consecutive returns at +1.5 pass every individual criterion but describe a consistent bias worth investigating through calibration and traceability, whereas one isolated result at +2.5 among scattered small values usually points to that particular sample or day.
Why compare against the peer group rather than all participants?
Because different methods measure slightly different things and are calibrated differently, so an all-participant mean mixes real method differences into your index. Comparing within your own method and instrument group isolates how your laboratory is performing rather than which analyser you bought.
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References
- Miller WG, Jones GRD, Horowitz GL, Weykamp C. Proficiency testing/external quality assessment: current challenges and future directions. Clin Chem. 2011;57(12):1670–1680.
- Westgard JO. Basic QC Practices. 4th ed. Westgard QC; 2016 — external quality assessment and the standard deviation index.
- ISO 13528:2022. Statistical methods for use in proficiency testing by interlaboratory comparison. International Organization for Standardization; 2022.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.