Calculate population stability index
Enter the counts for each bin in the development sample and a recent sample. See the PSI, which bins shifted and how big the shift is in a minute.
Population stability index
Comparing 10,000 recent cases with 10,000 in development across 10 bins gives a PSI of 0.1886. The <520 bin adds the most.
Development and recent shares by bin
Pale bars show the development share and solid bars show the recent share. The orange bar marks the bin that adds the most.
Bin results
| Bin | Expected count | Actual count | Development share | Recent share | Change | PSI part |
|---|---|---|---|---|---|---|
| <520 | 500 | 1,000 | 5.0% | 10.0% | +5.0 pp | 0.0347 |
| [520,560) | 800 | 1,350 | 8.0% | 13.5% | +5.5 pp | 0.0288 |
| [560,600) | 1,100 | 1,650 | 11.0% | 16.5% | +5.5 pp | 0.0223 |
| [600,640) | 1,400 | 1,700 | 14.0% | 17.0% | +3.0 pp | 0.0058 |
| [640,680) | 1,500 | 1,400 | 15.0% | 14.0% | −1.0 pp | 0.0007 |
| [680,720) | 1,400 | 1,050 | 14.0% | 10.5% | −3.5 pp | 0.0101 |
| [720,760) | 1,200 | 750 | 12.0% | 7.5% | −4.5 pp | 0.0212 |
| [760,800) | 900 | 500 | 9.0% | 5.0% | −4.0 pp | 0.0235 |
| [800,840) | 700 | 350 | 7.0% | 3.5% | −3.5 pp | 0.0243 |
| >=840 | 500 | 250 | 5.0% | 2.5% | −2.5 pp | 0.0173 |
| Total | 10,000 | 10,000 | 100.0% | 100.0% | 0.1886 |
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PSI calculation
Development share = Expected count ÷ All development Recent share = Actual count ÷ All recent PSI part = (Recent share − Development share) × ln(Recent share ÷ Development share) PSI = Σ PSI part A bin with a zero count gets 0.5 added to both its counts before the shares are taken.
PSI shows that the population moved, not that the scorecard ranks worse, which needs outcomes. The bands are a rule of thumb, not a test.
Calculate population stability index
The population stability index compares a score or characteristic across bins in a development sample and a recent sample. It sums each bin’s part to show the size of the shift.
A shift can mean the applicants a scorecard sees have changed. Review which bins contribute most, then consider outcomes because PSI alone does not show whether the scorecard ranks worse.
PSI questions
How do you calculate population stability index?
PSI is the sum of each bin’s part. Each part is the actual share minus the expected share, multiplied by the natural log of the actual share divided by the expected share.
What PSI value means a scorecard needs attention?
As a common rule of thumb, below 0.1 indicates no significant shift. From 0.1 to 0.25 is a moderate shift worth a look, and above 0.25 is a major shift.
What is the difference between PSI and characteristic stability index?
PSI can be calculated for a score or a characteristic. This tool compares development and recent sample counts across bins and reports each bin’s part.
What should I do with a zero count bin in PSI?
The calculator adds 0.5 to both counts in a zero-count bin before calculating shares. This keeps the index finite.
How often should I monitor PSI?
This page does not prescribe a monitoring schedule. It compares the development sample with a recent sample so you can see the size and direction of the shift.