Claimed and rebuilt intervals pass through separate audit gatesUpdates with every input
Math & Statistics
Confidence Interval Verification Calculator
Verify a reported one-sample t confidence interval by independently rebuilding its standard error, margin, center, symmetry, width, and endpoint residuals against an entered tolerance.
Verification verdict -
Expected interval -
Lower residual -
Upper residual -
Center residual -
Width residual -
Rebuilt standard error -
Rebuilt t critical -
INTERVAL FORENSICS
Claimed and rebuilt intervals pass through separate audit gates
Two rails expose endpoint displacement while four gates distinguish center, width, lower, and upper failures.
AUDIT LEDGER
Independent checks behind the final verdict
A reported interval can have the right center but wrong width, or matching width but shifted endpoints; the ledger keeps those defects separate.
| Check | Claimed | Expected | Residual | Tolerance | Status |
|---|
AUDIT INPUTS
Transcribe the report without repairing it first
- Enter the reported mean, SD, sample size, and confidence level exactly.
- Enter both published endpoints with their displayed precision.
- Choose a tolerance that reflects rounding rather than the desired verdict.
- Inspect signed endpoint residuals before the overall pass or fail.
- Trace any failure to the report's critical value, SE, center, or arithmetic.
FAILURE DIAGNOSIS
One pass/fail badge is not enough for interval quality control
Equal endpoint residuals indicate a center shift; opposite residuals often indicate a width problem. Checking only total width can miss a translated interval.
Rounding tolerance should be small and declared. A wide tolerance can make an incorrect interval appear verified.
RECONSTRUCTION AUDIT
Rebuild first, compare second
The expected interval is generated solely from mean, SD, n, and confidence. Claimed endpoints are then tested for endpoint, center, and width consistency.
Detailed calculation process and general formulas
SE = s / sqrt(n)ME = t* x SEL_exp = mean - MEU_exp = mean + MEr_L = L_claim - L_exp; r_U = U_claim - U_expSymbols, meanings, and units
- L_exp, U_exp
- independently rebuilt endpointsoutcome units
- L_claim, U_claim
- reported endpoints under auditoutcome units
- r_L, r_U
- signed endpoint residualsoutcome units
- tau
- entered absolute toleranceoutcome units
- ME
- rebuilt margin of erroroutcome units
ERROR SIGNATURES
Recognize the geometry of common reporting errors
Residual patterns point toward different upstream mistakes.
Shifted center
-Both endpoints move in the same direction by a similar amount.
Wrong width
-Endpoints move in opposite directions around the correct center.
Single endpoint typo
Only one endpoint breaches tolerance while the other aligns.
Decision takeaway: Preserve signed residuals so a failed audit explains where the report diverged.
Applied decisions
Confidence interval quality-control cases
Rounded publication
A report rounds endpoints to two decimals while retaining an unrounded mean.
What the result clarifies: A documented tolerance can distinguish harmless display rounding from an arithmetic error.
Wrong standard error
The analyst divides by n rather than sqrt(n).
What the result clarifies: Both endpoints fail mainly through an incorrect width.
Worked current scenario
Substitution, intermediate values, and reconciliation
Method references
Sources for this calculator's specific method
Scope and limitations
Passing this arithmetic audit verifies consistency with the entered one-sample t formula only. It does not validate the sampling design, data cleaning, SD calculation, distributional assumptions, or interpretation.
Confidence Interval Verification Calculator | Endpoint and Center Audit FAQ
Why test center and width if endpoints are tested?
They reveal the structure of the error and make correction faster.
What tolerance should I use?
Use the smallest tolerance justified by published rounding and units.
Can a symmetric interval still fail?
Yes. It can be symmetric around the wrong center or have the wrong margin.