Worked-example setupScope and assumptions
- The fictional packet's stated frame, randomization, completeness, uniqueness, and variable controls are accepted for the worked calculation.
- Separate one-sample intervals are not used as a two-sample test.
- No policy, customer-mix, open-invoice, forecast, loss, or valuation evidence is supplied.
- Period
- Fictional calendar years 2025 and 2026
- Units
- Calendar days and invoice records
- Rounding
- Full precision in the appendix; two decimal days in reader-facing prose
Accounting-control conclusion
The supplied extract is reproducible as two 16-invoice samples from declared 480- and 520-invoice frames. The packet stipulates unique invoice grain, complete issue and final-application dates, stable eligibility and cutoff, and simple random selection. Before relying on an equivalent real extract, reconcile frame record counts and amounts to the subledger, rerun uniqueness and eligibility tests, trace the 78-day invoice, inspect open and excluded invoices, and preserve the query, parameters, and extraction timestamp.
That note does not promise the data are error-free. It identifies the controls that would support or stop the analysis.
Finance-analysis conclusion
The displayed spread comparison is (13.812434011908739-5.852349955359813=7.960084056548926) days. It is simple subtraction between two sample-standard-deviation labels, not an estimator with its own sampling distribution.
In the selected observations, Year 2 has a mean settlement time 2.50 days below Year 1 and a median 5.00 days below. Its separately computed sample standard deviation is 13.81 days versus 5.85 days for Year 1, an arithmetic label difference of 7.96 days rather than a separate inferential statistic. One source-confirmed 78-day Year 2 invoice creates a long upper tail. Separate 95% supplied-t mean intervals are mechanically
[28.76, 34.99]for Year 1 and[22.01, 36.74]for Year 2, subject to the stated design and condition limitations. The packet does not test a population-mean difference, establish a policy effect, describe unsettled invoices, forecast future collections, quantify credit loss or risk, support valuation, or choose an action.
Next evidence
Request the complete and open-invoice populations, customer and product mix, contract terms, policy dates, repeated-customer concentration, disputes, adjustments, write-offs, subsequent collections, and a prespecified comparison design. Each request discriminates among a named explanation or repairs a named source limitation. “Get more data” does neither.
Verified calculation · descriptive estimation analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- comparisons
- 1 field
Inspect data
{
"year_2_vs_year_1": {
"direction": "right-minus-left",
"left": "year_1",
"right": "year_2"
}
}- series
- 2 fields
Inspect data
{
"year_1": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "simple-random-sample",
"mean_confidence_interval": {
"confidence_level": 0.95,
"critical_value": 2.131449545559323,
"degrees_of_freedom": 15,
"interval_scope": "two-sided-one-sample-mean",
"reference_distribution": "student-t-supplied"
},
"missing_value_policy": "reject",
"observations": [
22,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
38,
40,
44
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
},
"year_2": {
"dispersion_convention": "sample-n-minus-one",
"inference_basis": "simple-random-sample",
"mean_confidence_interval": {
"confidence_level": 0.95,
"critical_value": 2.131449545559323,
"degrees_of_freedom": 15,
"interval_scope": "two-sided-one-sample-mean",
"reference_distribution": "student-t-supplied"
},
"missing_value_policy": "reject",
"observations": [
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
33,
35,
78
],
"outlier_policy": "retain-and-flag",
"population_role": "sample",
"quartile_method": "median-of-halves-exclusive"
}
}Recomputed result
| Measure | Value |
|---|---|
| potential outlier count | 1 |
| vs year 1 right minus left mean | -2.5 |
| vs year 1 right minus left median | -5 |
| vs year 1 right minus left standard deviation | 7.9601 |