# Analyze and verify

> Run established statistical libraries, bound numerical error, check that each claim follows from the result, and keep design, data, analysis, and claim connected.

## From calculation to a supported claim.

Run an eligible analysis on approved inputs, check covered numerical and logical conditions, and return the claim the evidence supports. Assumptions, unresolved checks and unsupported requests stay visible.

## Three questions behind the answer.

| Question | What is checked | What comes back |
| --- | --- | --- |
| Is this the intended analysis? | Design, comparison and approved source inputs refer to the same research target. | The identified method, inputs and version. |
| Are the covered numbers established? | Numerical error bounds and decision conditions are checked. | An established check, a failed condition or an unresolved boundary. |
| Does the claim follow? | Direction, uncertainty and stated assumptions support the interpretation. | The supported claim and its recorded scope. |

Numerical error bounds, statistical uncertainty and external research assumptions are different. A verified calculation does not establish biological truth.

## A useful answer includes the next step.

1. **Established.** Use the result within its stated target, conditions and checked scope.

2. **Condition not met.** Inspect the specific mismatch and any permitted correction.

3. **Unresolved.** Keep the uncertainty visible; review what information or precision is missing.

Unsupported requests and operational errors are reported separately. These are explanatory outcomes, not a live verification response.

## Calculation, claim and stability checks.

### Trusted libraries. Independent checks.

Standard methods run on established scientific libraries such as SciPy and NumPy, with versions and settings recorded for every run. An independent checker then re-verifies the covered results.

### Numbers with error bounds.

Key numbers are computed with guaranteed error bounds using high-precision tools such as FLINT/Arb, a library for arithmetic with guaranteed error bounds. If a p-value is too close to its threshold to call, SciGround says so instead of rounding it into a verdict.

### Claims that fit the evidence.

Each result comes with the claim it supports. SciGround rejects the classic leaps: reading non-significance as no effect, a mean difference as causation, a reversed group direction, or a quietly changed target.

### Design to claim, one chain.

Design, data, analysis, and claim are checked as one connected chain with formal logical checks. A correct calculation on the wrong samples, or for a different comparison than the one planned, does not pass.

### When it stops, it shows the way forward.

Every diagnosis comes in four parts: what was confirmed, what could not be and why, what you can still use and save, and the next safe step—or why it is right to stop. Where a fix is possible, SciGround suggests it with reasons, runs it within the permitted steps, rechecks, and returns a new version with a diff.

### Would the conclusion survive losing a sample?

For small two-group t-test comparisons (Student or Welch), SciGround can prove that removing up to two samples does not change the decision, show a concrete removal that does change it, or explain why neither can be established.

## The result and the conditions it carries

- The result with method, library version, and settings
- The supported claim and the assumptions it depends on
- A clear check outcome: established, condition not met, or unresolved—with unsupported requests and operational errors reported separately
- Optional sample-removal stability evidence for small two-group t-test comparisons

## Limits and conditions

Verification is precise about what it covers. See the conditions every result carries. [Read the limits](https://www.licklider.ai/sciground/analysis/limits/) ([Markdown](https://www.licklider.ai/sciground/analysis/limits.md)).

## Related

- [The mathematics behind it](https://www.licklider.ai/math/)
- [Supported analyses](https://www.licklider.ai/sciground/analyses/)
- [How verification works](https://www.licklider.ai/docs/sciground-verification/)