Standard Deviation Index Calculator | Free SDI Tool

What is a standard deviation index?

The standard deviation index (SDI) is a number that shows how far a test result is from a control mean, measured in standard deviations. Laboratories use it to check whether a test result is close to the expected value or far enough away to be a problem.

Standard deviation index formula

In proficiency testing reports, the SDI is the result minus the peer group mean, divided by the standard deviation. The SDI formula is:

$$\text{SDI} = \frac{\text{Test Result} - \text{Control Mean}}{\text{Standard Deviation}}$$

• Test result: the value from the sample being checked.
• Control mean: the average result from a control sample, usually built up over many past runs.
• Standard deviation: how spread out the control results normally are. It measures the usual amount of variation in the control data.

The standard deviation must be greater than zero. If it is zero or negative, the SDI cannot be calculated, because dividing by zero or by a negative spread has no meaningful result.

How to calculate the standard deviation index

1. Find the test result from the sample being evaluated.
2. Find the control mean, the average of past control results.
3. Find the standard deviation of those control results.
4. Subtract the control mean from the test result.
5. Divide that difference by the standard deviation.

Worked example

Suppose a lab has these values:

• Control mean = 50
• Test result = 55
• Standard deviation = 5

$$\text{SDI} = \frac{55 - 50}{5} = \frac{5}{5} = 1.0000$$

The SDI is 1.0000. The test result sits exactly one standard deviation above the control mean.

How to interpret standard deviation index results

Cut-off values differ between quality-control programs. A proficiency-testing job aid from the SLMTA laboratory training program, which is supported by PEPFAR through the US CDC, groups SDI values like this:

External quality assessment schemes can use wider limits for the same kind of score. A score below 2 in absolute value is acceptable, 2 to 3 is questionable, and above 3 is unsatisfactory. If results follow a normal distribution, about 4.6% of scores fall beyond ±2 and 0.27% beyond ±3 by chance alone.

The calculator reports the SDI itself and does not apply any of these cut-offs.

An SDI of 0 means the test result equals the control mean exactly. A positive SDI means the result is above the mean; a negative SDI means it is below the mean. The sign shows direction, and the size shows how far off the result is.

Where the standard deviation index is used

The SDI is common in clinical laboratory quality control. Labs compare their own results against a control mean, or against results from other labs running the same test, to check whether their instruments and methods are producing consistent, accurate results. A high SDI can point to a calibration problem, a faulty reagent, an instrument fault, or an error in how the test was run.

The same idea applies outside medical labs. Manufacturers use it to check whether a measured product value has drifted from its target. Researchers use it to spot a result that differs unusually from expected values.

SDI is closely related to the z-score, which measures how many standard deviations a single value is from a population mean. The main difference is context: SDI is normally used to compare one test result against a control or peer-group mean in a quality-control setting.

Limitations of the standard deviation index

The SDI assumes the control data follows a roughly normal (bell-shaped) distribution. If the control data is skewed, the SDI may not describe performance well. A few extreme outliers in the control data can distort the mean and the standard deviation, which then distorts the SDI. A small number of control runs also gives a less reliable standard deviation, which makes the SDI less trustworthy.

Frequently asked questions

What does the standard deviation index measure?

It measures how many standard deviations a test result is from a control mean. It shows both direction (above or below the mean) and size (how far away).

How do you calculate the standard deviation index?

Subtract the control mean from the test result, then divide by the standard deviation of the control data: SDI = (Test Result − Control Mean) / Standard Deviation.

What is a good SDI value?

It depends on the program. In peer-comparison reports, an SDI between −1 and +1 is usually acceptable, and values from 1 to 2 in either direction call for a look at bias. External quality assessment schemes may accept scores below 2 in absolute value and treat scores above 3 as unsatisfactory.

Can the standard deviation index be negative?

Yes. A negative SDI means the test result is below the control mean. The standard deviation itself, however, must always be a positive number, since it measures spread and cannot be negative or zero.

Is the standard deviation index the same as a z-score?

They use the same kind of formula, and SDI is also called a z-score. SDI is the term used in laboratory quality control, comparing a single test result to a control or peer-group mean. Z-score is the more general statistical term for the same kind of calculation.

What causes a high standard deviation index?

A high SDI, meaning a large positive or negative value, can come from an instrument out of calibration, a bad reagent lot, operator error, or an actual shift in the sample being tested. It is a signal to check the testing process, not proof of any one specific cause.

References

1. College of American Pathologists. Proficiency Testing/External Quality Assessment FAQ. CAP PT/EQA frequently asked questions — the SDI is obtained by subtracting the peer group mean from the result and dividing by the standard deviation.
2. SLMTA (Strengthening Laboratory Management Toward Accreditation). Job Aid 2: Interpreting PT Reports. Interpreting PT reports (PDF) — SDI (a.k.a. z-score) bands: ±1.0 acceptable, 1.0 to 1.9 investigate bias, 2.0 or greater among the poorest performance.
3. Coucke W, Soumali MR. Demystifying EQA statistics and reports. Biochemia Medica, 2017. PMC5382862 — z-score below 2 acceptable, 2 to 3 questionable, above 3 unsatisfactory; 4.6% and 0.27% beyond 2 and 3 under a normal distribution.