Statistical Analysis with AI: reproducible synthetic example
Prepared 19 October 2026. This is constructed educational data, not customer
data, a randomized experiment, or evidence of operational improvement.

START WITHOUT CODE
Open support-workflow-statistics-v1.xlsx or the equivalent CSV.
The Raw observations sheet has 124 data rows, not including its header.
Drop exact repeated records across all six columns (2 repeats). Then exclude
the 2 records with blank avg_handle_minutes, keeping one missing count per
workflow in the audit. Never replace missing outcomes with zero. This leaves
120 operators: current 48, pilot 72. Each operator counts once, regardless of
tickets_resolved. All observations describe the week ending 2026-09-27.

The separately supplied support-workflow-statistics-clean-check-v1.xlsx
contains the 120 included rows split into Current and Pilot sheets. In Current,
avg_handle_minutes is E2:E49; in Pilot, it is E2:E73. COUNT, AVERAGE, MEDIAN and
Excel STDEV.S (Google Sheets STDEV) reproduce the descriptive statistics.
The Summary sheet contains checked static values, not calculated formula cells.

DATA DICTIONARY
operator_id: fictional unique operator identifier; repeated exact records are
intentional input defects. Distinct operators can have equal measurements.
workflow: current or pilot; assignment was constructed, not randomized.
tenure_months: whole months of experience (3 to 25 for the complete observations).
tickets_resolved: fictional count, supplied to make the weighting choice explicit.
avg_handle_minutes: operator's completed-week average handling time, in minutes.
week_ending: ISO date as text (2026-09-27).

EXPECTED BASE RESULTS (rounding only for display)
Current: n 48, missing 1, mean 12.6, median 12.6, sample SD 1.3279323233.
Pilot: n 72, missing 1, mean 10.6, median 10.6, sample SD 2.2838070514.
Welch independent two-sided test: pilot minus current = -2 minutes;
95% CI [-2.6544342233, -1.3455657767]; t=-6.0528600433;
df=116.1481253478; p=1.7896862981e-8. No equal-variance assumption.
Current-group Pearson correlation: n=48, r=-0.5254158125.
Current-group ordinary least squares with intercept:
minutes = 14 - 0.1 * tenure_months; R-squared=0.2760617761.
The zero-tenure intercept lies outside the observed tenure range.

OUTLIER VARIANT
support-workflow-statistics-outlier-v1.csv changes OP001 to 50.0 minutes in
both its original and duplicate record. The same cleaning rule still leaves
48 current and 72 pilot operators. This is a deliberate sensitivity exercise.
Current mean 13.3875, median 12.7, sample SD 5.5576523821.
Pilot minus current=-2.7875; Welch 95% CI [-4.4813986480,-1.0936013520];
two-sided p=0.0016889993. Pearson r=-0.3536893500; slope=-0.2817307692.
Do not discard a valid unusual observation merely to improve a result.

RUN THE INDEPENDENT CHECKS
Dependencies used: R 4.3.3 base stats; Python 3.11+ with NumPy 2.2.6 and SciPy
1.15.3. The included environment record gives the actual Python version.
1. From this folder: Rscript reference.R .
2. From this folder, with uv installed: uv run reference.py
   Alternatively install the pinned NumPy and SciPy versions in an isolated
   Python environment, then run reference.py there.
Each program reads and cleans the raw CSV independently. R writes result,
summary and residual CSVs; Python independently computes the same statistics
and compares them against the R CSVs with relative/absolute tolerance 1e-8.
expected-results.json preserves the checked result and comparison per metric.
R and SciPy agreement checks arithmetic, not whether a study design is valid.
The artificial data do not establish independent sampling from a population;
the intervals and p-values illustrate what these methods compute under their
assumptions. No business rollout or causal conclusion follows from this file.

PROVENANCE
Original synthetic fixture and scripts created for this guide so readers can
follow the example and rerun the checks. No real people or organizations appear.
sha256.json lists the packaged files so another reader can check exact inputs.
