The standard deviation index calculator answers one question that every external quality assessment report puts in front of a laboratory: how far is our result from the peer group, measured in units of the peer group's own scatter? That is the SDI, and it is the reason a report can compare a sodium result and a troponin result on the same axis despite their having nothing else in common. This page computes it, computes the bias behind it, and computes the mean SDI across a run — and stops there.
Arb Digital builds free tools that respect the boundaries of the systems they touch. Deciding whether an SDI is acceptable is not arithmetic; it is a judgement made under a laboratory's quality system, against the limits its programme and accreditation body publish, by people with the method and the instrument in front of them. This page computes the index. Everything after that belongs to the laboratory.
What This SDI Calculator Does
It subtracts the peer group mean from your result and divides by the peer group standard deviation. Alongside the index it shows the raw bias in the original units, that bias as a percentage of the peer mean, and the peer coefficient of variation, which tells you how tight the peer group itself was. If you paste in previous results from the same peer group, it also reports the mean SDI across the run, which is the figure that reveals a consistent direction.
The sign is kept deliberately. A positive SDI means the result sat above the peer mean and a negative one below, and losing that sign discards most of what makes a run of SDIs informative.
How to Use It
- Take the peer mean and standard deviation from the evaluation report, for the correct peer group. Method-specific and all-method groups can give noticeably different values.
- Enter your reported result in the same units and to the precision the report used.
- Add previous results from the same peer group if you want a mean SDI across the run.
- Read the index, the bias and the peer CV together. An SDI is only as meaningful as the spread it is measured against.
- Compare against your own acceptance limits in your quality system, not against any number on this page.
The Formula and a Worked Example
The definition is SDI = (your result − peer group mean) ÷ peer group standard deviation. It is arithmetically identical to a z-score; what differs is the context. As Westgard QC's page on the calculations puts it, the SDI expresses the difference between your results and the overall average in terms of the number of standard deviations from the overall mean, and while the two use the same arithmetic, the z-score tends to be used in internal quality control and the SDI in external programmes.
Take the defaults. A result of 105 against a peer mean of 100 with a peer SD of 4 gives (105 − 100) ÷ 4 = +1.25. The bias is +5 units, which is 5% of the peer mean, and the peer CV is 4 ÷ 100 = 4%. Adding previous results of 103, 106 and 104 gives SDIs of +0.75, +1.50 and +1.00; with the current result the mean SDI across all four is +1.125. Every one of them is positive, which is exactly the pattern a mean SDI exists to surface.
Who Decides What Is Acceptable
Not this page, and not a rule of thumb from the internet. The College of American Pathologists' proficiency testing and external quality assessment FAQ is explicit that the acceptable limits are the ones printed on your evaluation report, and it warns against confusing those limits with the minimum and maximum values shown in a participant summary, which are simply the lowest and highest results anyone in the peer group reported. It also notes that the SDI is computed from unrounded figures, which is a common reason a hand calculation disagrees slightly with the printed one.
Westgard's guidance is framed as attention rather than adjudication: an SDI of 2.0 or greater deserves special concern whatever the test, and a mean SDI of 1.0 or greater deserves attention because it indicates a systematic difference from the group. Those are prompts to investigate, not verdicts, and they sit underneath whatever your accreditation body and your own quality system require.
Why the Peer Group Choice Changes the Answer
An SDI is a statement about a comparison, so changing the comparison changes the number. A result evaluated against a tight method-specific peer group can produce a large SDI while the same result against a wider all-method group produces a small one, purely because the denominators differ. Neither is wrong; they answer different questions — how does this instrument compare with others like it, versus how does this result compare with everyone measuring the analyte.
Peer group size matters too. A small peer group gives an unstable mean and standard deviation, so an SDI computed against fifteen participants carries far more uncertainty than one computed against six hundred. Some programmes use robust statistics precisely to limit the influence of outliers on the peer mean, which is another reason a hand-recomputed SDI may not match the report exactly.
Bias, Imprecision and What SDI Does Not See
SDI describes bias — a systematic offset between your laboratory and its peers. It says nothing about imprecision, the run-to-run scatter of your own method, which is measured with your internal quality control data and expressed as a coefficient of variation. A laboratory can post an excellent SDI while being badly imprecise, if a scattered set of results happens to average near the peer mean; and it can post a poor SDI while being extremely precise, if a well-controlled method is consistently offset by a calibration difference.
The other blind spot is that the peer mean is a consensus, not a reference value. It reflects what a group of laboratories using similar methods obtained, and a group can be collectively offset from a definitive or reference measurement procedure. Comparing well with peers is a statement about agreement, not about accuracy in an absolute sense.
How This Differs From a Plain Z-Score
Arithmetically it does not. Our z-score calculator computes the same quantity in a general statistical setting, and adds percentiles and one- and two-tailed p-values, which is what you want when you are working with a distribution and asking how extreme a value is. This page is the laboratory framing: peer mean and peer SD as the inputs, bias and peer CV as the supporting figures, a mean SDI across a run, and the explicit statement that acceptance is set elsewhere. Use the z-score page for general statistics, and this one when the numbers came off an evaluation report.
Arb Digital builds tools and content for specialist audiences, where a cited convention and a stated limitation matter more than a keyword. Tell us what you are publishing and we will show you how we would frame it.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the wrong peer group's statistics. Method-specific and all-method groups give different means and standard deviations, and therefore different SDIs.
- Discarding the sign. A run of positive SDIs and a run of alternating ones mean very different things.
- Treating a threshold as a rule. Published attention levels are prompts to investigate; acceptance limits come from your own quality system and programme.
- Comparing SDIs computed against very different peer group sizes. A small group gives an unstable mean and standard deviation.
- Reading a good SDI as good precision. SDI describes bias against peers; imprecision is a separate measurement from your own internal QC.
Related Free Tools From Arb Digital
For the general statistical form, use the z-score calculator. To derive a standard deviation from raw data, the standard deviation calculator and the pooled standard deviation calculator do the work, while the coefficient of variation calculator expresses scatter relative to the mean. The mean median mode calculator and the confidence interval calculator cover the surrounding basics, and the percentage calculator the bias percentage on its own. The free online tools hub lists everything else.
Frequently Asked Questions
It is the difference between a laboratory's result and its peer group mean, divided by the peer group standard deviation. It expresses bias in units of the peer group's own scatter, which lets results for very different analytes be compared on a single scale.
Subtract the peer group mean from your result, then divide by the peer group standard deviation. A result of 105 against a peer mean of 100 with a peer standard deviation of 4 gives an SDI of plus 1.25.
The arithmetic is identical. The difference is convention and context: z-scores are generally used in internal quality control and general statistics, while SDI is the term used in external quality assessment and proficiency testing programmes, computed against a peer group.
That is set by your laboratory's quality system and by the programme and peer group you participate in, and the acceptable limits appear on your evaluation report. Published attention levels, such as taking an SDI of 2.0 or greater seriously, are prompts to investigate rather than acceptance criteria.
Programmes compute the index from unrounded figures, while the values printed for readability are rounded. Some programmes also use robust statistics for the peer mean and standard deviation, which will not match a plain calculation from the same published summary.
It reveals direction. A single index can move for many reasons, but several results in a row on the same side of the peer mean point to a systematic difference rather than to scatter, which is why the mean across a run is reported separately here.
It means you agree with your peers. A peer group is a consensus of laboratories using similar methods and can itself be offset from a reference measurement procedure, so agreement with peers is not the same as accuracy in an absolute sense.
This tool computes a published index from figures you supply. It does not evaluate a quality control run, does not pass or fail any result, and is not a substitute for your laboratory's quality system, its accreditation requirements, or the evaluation reports issued by your external quality assessment programme.
