meta-statistics

Meta Statistics

Overview

Use this meta-skill to apply statistical discipline to business-plan evidence. It helps choose the right method, summary, chart, or inference so numbers support decision-making rather than decorative credibility.

Use When

• Use when market sizing, survey results, forecasts, or comparative metrics need statistical rigour.
• Use when a chart, rate, trend, or average could be misleading if calculated badly.
• Use when the plan needs defensible quantitative presentation.

Do Not Use When

• Do not use to create false precision from weak data.
• Do not apply advanced methods when the data does not support them.
• Do not use statistics to decorate claims that remain strategically weak.

• For meta-statistics, route to the relevant plan-section skill instead when the request is section drafting rather than cross-section analysis.

Required Inputs

Input	Source / provider	Required?	If absent
Statistics brief and decision audience	Client, plan owner, or approved project files	Yes	Stop before making a recommendation; state the missing decision context.
Claims, assumptions, and supporting evidence	Source register, model, research notes, interviews, or operating records	Yes	Separate known facts from assumptions and return a qualified gap list.
Authority and delivery constraints	Requesting owner and repository instructions	Yes	Remain read-only and produce a draft or review only.

• The dataset, figures, or claim being analysed
• The decision or message the numbers need to support
• Data quality, sample size, and sourcing context
• Any adjacent sections that rely on the same metrics

Workflow

1. Identify what decision or claim the numbers must support.
2. Check whether the data quality and structure fit the intended method.
3. Apply the simplest sound statistical treatment that answers the question.
4. Present the result using the right summary or chart.
5. Reconcile the statistic with the surrounding commercial narrative.
6. Flag weak data, weak sampling, or over-interpretation risks.

Decision, stop, and recovery controls

• Decision point: confirm that the requested output is the statistical review record and that the decision concerns which inference, comparison, or chart the evidence supports.
• Stop condition: halt the affected conclusion if required evidence is missing (dataset, sampling method, metric definitions, and calculation files) or if the work could lead to this identified risk: turning a biased sample or unstable average into a business claim.
• Recovery: obtain the missing record or reviewer, repeat the affected check, and update the exception record before release.

Quality Bar

• The chosen method fits the data and question.
• Results are interpretable by the intended audience.
• Charts and metrics clarify rather than distort.
• Any uncertainty or estimate basis is explicit.

Anti-Patterns

• Using averages where distributions matter more.

• Plotting charts that make the wrong comparison easy.

• Presenting regression or inference without adequate data.

• Treating estimated data as measured fact.

• Treating a generic statistics template as a conclusion. Correction: tie each choice to the named audience, evidence, and operating constraint.

• Applying the wrong neighbouring route to meta statistics. Correction: confirm the decision and route to the named neighbour before analysis.

• Treating an assumption as verified evidence. Correction: label it, cite its source or owner, and assign a verification action.

• Recommending action without a decision threshold. Correction: state the measurable acceptance condition and review trigger.

• Recording an unavailable check as passed. Correction: mark it not assessed and state the consequence for the decision.

• Mutating or publishing during an analysis-only task. Correction: remain read-only until the owner gives explicit authority.

Outputs

Artefact	Consumer	Observable acceptance condition
Statistics deliverable	Named decision-maker or plan author	The recommended choice, assumptions, countercase, and next action are explicit.
Evidence and exception register	Reviewer, funder, board, or implementation owner	Every load-bearing claim is sourced or labelled as an assumption; missing checks are not shown as passes.

• Statistically sound summaries, methods, or visualisation guidance
• Corrected metrics or interpretation notes
• Any data-quality caveats affecting confidence

Overview

This skill transforms raw numbers into credible, decision-quality evidence. Every figure in a business plan must be:

1. Correctly computed right method for the data type
2. Properly presented chart/table chosen for the message, not decoration
3. Verifiably sourced primary source cited, or flagged as estimate with basis

Source books: Anderson et al. Essentials of Statistics for Business and Economics (7th ed., Cengage 2013); Keller Statistics for Management and Economics (9th abbrev. ed., Cengage 2011).

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Section-by-Section Application Guide

Plan Section	Primary Statistic	Method	Reference
04 Market Analysis	TAM/SAM/SOM sizing	Frequency tables + totals from sourced data	See statistics-for-business-plans.md Market Sizing
04 Market Analysis	Market growth trend	Geometric mean (not arithmetic)	Growth Rates
05 Target Market	Customer segment profiles	Descriptive stats + bar/stacked bar charts	Descriptive Stats
06 Competitive Analysis	Competitor positioning	Scatter diagram (2 axes: price quality)	Chart Selection
07 Marketing/Sales	Customer survey results	Confidence intervals + sample design	Sampling & CIs
10 Financial Projections	Revenue forecasting	Regression (if 3+ years historical data exist)	Regression
10 Financial Projections	Risk comparison across markets	Coefficient of variation	Variability
10 Financial Projections	Multi-year growth rate	Geometric mean (CAGR)	Growth Rates

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1. Growth Rates Always Use Geometric Mean

Rule: Any multi-period growth rate (revenue CAGR, population growth, market expansion) must use the geometric mean never the arithmetic mean.

Why it matters: Arithmetic mean of annual returns overstates true compounded growth.

• Year 1: +100%, Year 2: 50% Arithmetic mean = +25% (misleading: you broke even)
• Geometric mean = 0% (correct: $100 $200 $100)

Formula:

CAGR = (End Value / Start Value)^(1/n)  1
Geometric Mean = n(x1  x2  ...  xn)

When to cite: "Revenue grew at a CAGR of 18.4% over 5 years (geometric mean of annual growth rates, 20192024)."

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2. Variability and Risk Comparison

Use standard deviation to describe spread within one variable. Use coefficient of variation (CV) to compare variability across variables with different scales or units.

CV formula: CV = (s x) 100%

Business plan application:

• Compare revenue stability of two product lines: Line A (mean UGX 45M/month, CV = 8%) is more predictable than Line B (mean UGX 120M/month, CV = 31%)
• Compare supply-chain risk across sourcing geographies
• Compare customer cohort reliability (repeat purchase rate CV)

When to cite: "Supply from Supplier X shows a coefficient of variation of 12% vs. Supplier Y at 34%, indicating greater supply reliability from X (Anderson et al., 2013)."

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3. Chart and Table Selection

Read references/statistics-for-business-plans.md Chart Selection for the full decision table. Summary:

Message / Data Type	Chart
Market share or fund allocation	Pie chart (max 5 slices) or bar chart
Revenue trend over time	Line chart
Revenue mix by period	Stacked bar chart
Competitor comparison (2 attributes)	Scatter diagram
Distribution of customers by revenue size	Histogram
Multiple KPIs on one screen	Dashboard (bar + line + KPI card)

Hard rules from Anderson et al. (2013):

• Never use 3D charts adds visual noise, distorts magnitudes
• Axis must start at zero when comparing absolute values
• Label axes with units (UGX millions, % market share)
• Maximum 56 pie slices; use "Other" for remainder
• Use direct labels (percentages on slices) not a separate legend

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4. Data Visualisation Best Practices (Section 2.5, Anderson et al.)

1. Give the chart a clear, concise title that states the conclusion or key fact
2. Keep displays simple remove all decoration that carries no information
3. Label every axis with the variable name and unit of measure
4. Use colours that are clearly distinguishable (not red/orange/brown together)
5. Scale axis from zero unless explicitly noting a truncated axis
6. For dashboards: group related charts, use borders, minimise scrolling
7. Strategic vs. tactical layers: operational dashboard (granular, real-time); executive dashboard (aggregate KPIs)

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5. Sampling Design for Primary Research

When the plan includes a primary customer survey or field research, document the sampling method.

Population Type	Method	Minimum Sample
Homogeneous (single industry/area)	Simple random sampling	n 30
Heterogeneous (multiple segments)	Stratified random sampling	n 30 per stratum
Geographically dispersed, cost-sensitive	Cluster sampling	Varies; see Sampling

Sample size for confidence interval: n = (z2 2) / E2 where E = desired margin of error, z = 1.96 for 95% CI

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6. Confidence Intervals for Market Research Claims

When the plan cites a survey finding ("70% of customers prefer X"), always attach a confidence interval.

Formula (proportion): p 1.96 [p(1p)/n]

Example (n=150, 70% preference): CI = 0.70 1.96 (0.700.30/150) = 0.70 0.073 = [62.7%, 77.3%]

Write-up: "70% of surveyed customers (n=150) reported preference for X [95% CI: 6377%] (primary survey, March 2026)."

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7. Regression for Forecasting

Use simple or multiple linear regression when 3+ years of historical data exist.

Decision rules:

• One driver (e.g., population sales): simple regression y = b0 + b1x
• Multiple drivers (population + income + competition): multiple regression
• Use adjusted R2 (not R2) to decide whether additional variables improve the model
• Only predict within the observed range of x (no extrapolation beyond data)

Reporting standard: "A simple linear regression of monthly revenue on customer base (R2 = 0.87, p < 0.001, n=36 months) projects revenue of UGX 82M at a customer base of 2,400."

See references/statistics-for-business-plans.md Regression for worked examples.

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8. Verifiability Standards

Every statistic in the plan must pass this three-question test:

Question	Standard
Source?	Named source (UBOS, World Bank, primary survey) with date
Method?	State if geometric mean, CV, regression, or raw secondary data
Reproducible?	A reader with the same data could arrive at the same figure

Flagging estimates:

• Sourced fact: "(UBOS, 2024)"
• Derived calculation: "(calculated from UBOS 2024 data; geometric mean 20192024)"
• Acknowledged estimate: "(author estimate based on industry benchmarks; see assumptions)"

Never acceptable: Unsourced percentages, rounded numbers without basis, growth rates without stating the method.

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References

• references/analytics-ladder-and-kpi-standard.md Analytics ladder, data-quality gate, method selection, market/financial/demand analytics, AI analytics controls, and KPI dashboard standards
• references/statistics-for-business-plans.md Full decision tables, formulas, worked Uganda/EA examples, chart selection guide, data type definitions
• Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. & Cochran, J.J. (2013). Essentials of Statistics for Business and Economics (7th ed.). Cengage Learning.
• Keller, G. (2011). Statistics for Management and Economics, Abbreviated (9th ed.). Cengage Learning.

Evidence Produced

Evidence	Format	Acceptance condition
Statistical review record decision trace	Sources, calculations, assumptions, countercase, and selected action	A reviewer can trace the selected action and rejected alternatives to the cited inputs.
Exception record	Failed and not-assessed checks with owner and due action	The register exposes every unresolved exception that could lead to turning a biased sample or unstable average into a business claim.

Capability and Permission Boundaries

Default to read-only inspection while producing the statistical review record. Read supplied records and run non-mutating checks; running reproducible analysis without altering source data is permitted only when requested. Do not publish, contact third parties, alter live systems, commit funds, or claim legal, tax, audit, valuation, ESG, or investment assurance without the owner's explicit authorisation and the appropriate reviewer.

Degraded Mode

If dataset, sampling method, metric definitions, and calculation files cannot be obtained, return a qualified statistical review record covering only the checks that remain supportable. Leave this decision unresolved: which inference, comparison, or chart the evidence supports. Record the evidence owner and next check; an inaccessible source, tool, or reviewer is never a pass.

Decision Rules

Decision condition	Action	Failure or risk avoided
Evidence is sufficient to decide: which inference, comparison, or chart the evidence supports	Record the conclusion, source trail, owner, and review trigger in the statistical review record.	Risk of turning a biased sample or unstable average into a business claim
Material evidence conflicts or remains uncertain	Run the appropriate sensitivity, robustness, or alternative specification and report how the business conclusion changes.	Selecting an option without resolving the decision-relevant uncertainty
Required evidence is missing: dataset, sampling method, metric definitions, and calculation files	Mark the decision on which inference, comparison, or chart the evidence supports not assessed in the statistical review record, and send it to the analyst and decision owner.	Otherwise, the work risks turning a biased sample or unstable average into a business claim

Quality Standards

Accept the statistical review record only when evidence is sufficient for this decision: which inference, comparison, or chart the evidence supports. Assumptions and countercases remain visible, calculations and cross-references reconcile, and the reviewer can see how the recommendation addresses the risk of turning a biased sample or unstable average into a business claim.

Worked Example

A survey average hides opposite results between new and repeat customers. Report the segment estimates and uncertainty, then revise the recommendation instead of relying on the blended mean.