What Is Standard Deviation Index?
The standard deviation index, or SDI, says how many group standard deviations a result lies from the group mean. It is a z-score where the reference is a peer group, and it is widely used for laboratory comparisons.
Enter one result or several, the peer group mean and the group SD. You get the SDI, the difference, the percent bias, a reading of how far out the result is and, for several results, the mean SDI and how many fall beyond two SDI.
Below are the formulas, a worked example and answers on acceptable limits.
How to Use the Standard Deviation Index Calculator
- Enter your result.
- Enter the peer group mean and SD.
- Read the SDI and the reading.
- Enter several results to review bias.
Standard Deviation Index Formula
Standard deviation index
Percent bias
Standard Deviation Index Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| SDI | Standard deviation index | |
| x | Your result | |
| x̄ group | Peer group mean | |
| s group | Peer group SD |
Standard Deviation Index Worked Example
A laboratory reports 104.2 and the peer group mean is 100 with SD 2.5. Then SDI = (104.2 − 100) ÷ 2.5 = 1.68, and the bias is 4.2 %. The result is between 1 and 2 SDI above the group, which many programs flag for attention.
With the example values loaded in the calculator above, the steps are:
- SDI = (result − group mean) ÷ group SD.
- For the first result: (104.2 − 100) ÷ 2.5 = 1.68.
- |SDI| = 1.68, which is between 1 and 2 sdi.
Result: Standard deviation index (SDI) = 1.68; Reading = Between 1 and 2 SDI.
How to Read a Standard Deviation Index
The SDI is a z-score of your result against a peer group: (result − group mean) ÷ group SD. A laboratory reporting 104.2 against a group mean of 100 with SD 2.5 has SDI = 1.68, which is a bias of 4.2% above the group.
Many programs treat values near 0 as in line with peers, and values beyond about ±2 as a flag for review. The exact limits differ by program, so use the criteria set by yours. The percentile shown assumes the group is roughly normal.
Where Standard Deviation Index Is Used
Proficiency testing
Compare a laboratory result with the peer-group mean and SD.
Several results
Enter more than one result to see an SDI for each.
Bias estimate
See the difference from the group mean as a percentage.
Quality review
Spot results that sit far from the group.
Common Standard Deviation Index Mistakes to Avoid
- Use the peer group’s mean and SD, not your own.
- The sign shows the direction. Positive means above the group mean.
- The index is a z-score, so it assumes the peer data are roughly normal.
- Acceptance limits are set by the program. Check yours.
Standard Deviation Index Terms and Definitions
- Peer group
- Laboratories or instruments measuring the same sample.
Standard Deviation Index FAQs
What is the standard deviation index?
It is the difference between your result and the peer-group mean, divided by the peer-group standard deviation. It says how many standard deviations you are from the group.
How do I calculate SDI?
SDI = (your result − group mean) ÷ group SD. For 104.2, a mean of 100 and an SD of 2.5, SDI = 4.2 ÷ 2.5 = 1.68.
What is an acceptable SDI?
It depends on the program. A value near 0 is closest to the group, and many programs flag larger absolute values. Use the limits set by your own program.
How is SDI different from a z-score?
The calculation is the same. "SDI" is the name used in laboratory proficiency testing, where the reference is a peer group.