---
name: descriptive-analysis
description: >
  Produces a correct, complete and honest descriptive picture of a quantitative
  dataset: frequencies, percentages, means, medians, distributions and spread,
  built on explicitly defined bases. Use for "run the frequencies", "what do the
  numbers say", "give me the toplines", "summarise this dataset", "what
  percentage said yes", "how satisfied were they", "what is the average spend",
  "produce the data tables", "top-box scores", "check these percentages".
category: 05 Quantitative Analysis
ref: 05.01
tier: 0
inherits: [K2, K3, K4, K5]
---

# Descriptive Analysis

## 1. One-line description
Turns a prepared quantitative dataset into an accurate description of what respondents actually said, with every percentage sitting on a stated and correctly chosen base, every summary statistic chosen from the shape of its distribution rather than by habit, and every figure selected because it answers a research question rather than because the software produced it.

## 2. What this skill is used for

**The research problem it solves.** Descriptive analysis is the first thing done to a dataset, the foundation of everything after it, and the most underrated skill in quantitative research. It looks trivial because the arithmetic is trivial, and the arithmetic is not where it goes wrong. It goes wrong in the denominator: a percentage calculated on people who answered a filtered question, then reported as though it described the whole sample. It goes wrong in the summary: a mean reported for a distribution so skewed that no respondent is near it. It goes wrong in the omission: forty rows with no base sizes and no indication that eleven of them rest on fewer than fifty people. And it goes wrong in volume: a descriptive run produces hundreds of numbers, and a report containing all of them has made no analytical decisions at all. Every error made here is inherited by every cross-tab, test, chart and recommendation downstream, and by then it is invisible, because the number has stopped carrying its base.

**Where it sits.** The first analysis step, after preparation and before any comparison. It establishes the figures that later skills compare, test and visualise.

**Typical use cases.**
- Producing toplines and data tables from a fielded survey.
- Establishing the headline figures a report will be built on.
- Describing the profile and behaviour of a customer or population sample.
- Summarising rating scales, satisfaction batteries and frequency measures.
- Checking a set of figures somebody else produced, particularly the bases.
- Preparing verified inputs for cross-tabulation, testing or charting.

**Who uses it.** Quantitative researchers and analysts producing tables; research directors checking numbers before they leave the building; generalists handling a quantitative phase; client-side insight teams reading tables somebody else produced and needing to know whether to trust them.

## 3. When to use it

- You have a prepared respondent-level dataset and need to know what it says before you decide what to do with it.
- The deliverable includes toplines, data tables, a topline summary or a profile section.
- Somebody has asked "what percentage said X" and the honest answer depends on which people were asked.
- The questionnaire contains filters, routing or multi-response questions, so the denominators vary by question and must be established rather than assumed.
- You are about to build cross-tabs, tests or charts and need clean, correctly based figures underneath them.
- You are auditing figures produced elsewhere and need to reconstruct what each percentage is a percentage of.
- A dataset is weighted and the reported figures need to disclose that properly.
- The research question is genuinely descriptive: how many, how often, how much, in what proportion.

## 4. When NOT to use it

- **You want to know whether a difference is real. This skill does not test differences.** It describes them. Reporting that 44% of one group and 37% of another gave an answer is a description; saying the groups differ, or that one is higher in any sense stronger than arithmetic, is a claim that needs **05.02 Statistical Testing** behind it. Per K4 §3.1, ordinary comparative language is permitted for observed differences provided both bases are shown and no reliability is claimed. **Describing a difference is not claiming one, and the output must not let a reader mistake the first for the second.** Where a difference will be used to support a decision, stop and hand to 05.02.
- **The structure of a relationship between two variables is the question.** A description of one variable at a time cannot answer "does this vary by segment". That is **05.03 Cross-Tabulation**, and running it as a series of separate filtered descriptives instead invites exactly the base error this skill exists to prevent.
- **The dataset has not been prepared.** Descriptive analysis on uncleaned data produces authoritative-looking figures on duplicated records, straight-liners, out-of-range values and unconverted codes. Run **04.01 Data Validation** and **04.02 Data Cleaning** first. If figures are needed before cleaning is complete, label them provisional and say what remains outstanding.
- **Missing data is extensive and its pattern is unexamined.** Where a question has substantial non-response, a descriptive figure describes the people who answered, which may not be the people you think. Above roughly 10% missing on a key variable, go to **04.03 Missing Data Handling** before reporting, not after.
- **The base is too small to describe proportionally.** Below n=30 no percentages are reported at all, per K4 §7. Report counts, or report nothing, and say why. This is not a presentational preference: a percentage on a base of 18 moves 5.6 points per respondent and communicates a precision that does not exist.
- **The sample cannot support the description being asked for.** A non-probability sample describes itself, not a population, per K4 §3.3. If the request is for population estimates from a sample that cannot carry them, say so before producing the figures, because once the figures exist they will be used.
- **You are being asked for the numbers that support a conclusion already written.** Selecting which descriptives to report is a legitimate and necessary analytical act, done against the research objectives. Selecting them against a predetermined answer is cherry-picking, per K4 §4.2. The difference is whether the selection rule was written before or after the figures were seen.
- **The variables mean something other than their labels suggest and nobody can confirm what.** Per K4 §6.2, do not infer scale direction, scale length or code meaning from a variable name. A reverse-coded satisfaction item described as a satisfaction score will produce a confident, precise and exactly inverted finding. Ask, or state the assumption and flag it as unverified.

## 5. Required inputs

**Required.** Without these the skill cannot run. If absent, ask. If no answer is available and work must proceed, state the assumption at the point where it bites, per K5 §5.

- **A prepared respondent-level dataset**, one row per respondent, with the cleaning already done or its status known.
- **The questionnaire as fielded**, including question wording, response lists, scale labels and their order. Wording changes what a figure means: "have you ever" and "in the last month" produce different numbers about different things.
- **The routing and filter logic.** This is what defines the base of every filtered question. Without it, denominators are guesses. If routing is not documented, reconstruct it from the data and state that it was reconstructed.
- **A data dictionary or codebook**: variable names, value labels, scale direction, and the codes used for missing, don't know, refused and not asked. Where these are absent, they must be established before any figure is calculated.
- **The research objectives**, or the questions the study exists to answer. Descriptive analysis without objectives produces a data dump, not an analysis.

**Optional, and what each one adds.**

- **Weighting variables and the weighting specification**: allow weighted figures to be produced and the effective base to be calculated, and make the required disclosure possible. Without them, report unweighted and say so. Detail belongs to **04.05 Weighting and Base Management**.
- **Sample and fieldwork documentation** (source, method, quotas, fieldwork dates, response rate): determines what the description can be said to describe, and supplies the disclosures in K4 §7.
- **A previous wave's tables and conventions**: allow the same base definitions, scale collapses and rounding rules to be reused, which is the only way a comparison across waves means anything.
- **The cleaning log**: says which cases were excluded and why, so the base of the analysis can be reconciled to the base of the fieldwork.
- **A prior table specification or client tabulation plan**: says which breaks and figures the client expects, and often reveals base definitions that have become house conventions.
- **The intended output medium**: a chart, a table, a topline slide and an appendix have different tolerances for volume and different rounding conventions.

## 6. Questions to ask before starting

1. **Which questions were asked of everybody, and which were filtered?** This determines the denominator of every figure and is the single most consequential piece of information in the whole task. *Default if unanswered:* reconstruct the base of each question from the pattern of valid responses in the data, state that bases were reconstructed rather than documented, and flag any question where the reconstruction is ambiguous.
2. **Are don't know, refused and not answered inside or outside the base?** A four to six point swing on a headline figure commonly turns on nothing else. *Default:* keep don't know inside the base where it is a substantive answer (as it usually is for awareness, opinion and knowledge questions), exclude item non-response from the base, show both bases where the choice materially changes the figure, and state the rule once.
3. **Is the dataset weighted, and should reported figures be weighted?** Determines the figures themselves and the disclosure required. *Default:* if weights exist, report weighted percentages with unweighted counts and effective base shown; never mix weighted and unweighted figures in one table without labelling.
4. **What decision does this research inform?** Determines which of the several hundred available figures are reported and which are held in the appendix. *Default:* report against the stated objectives, list what was produced but not reported, and flag that the selection is an analytical judgement.
5. **What scale conventions does this audience or tracker already use?** Top-two-box, top-three-box, mean score, net score: all are defensible and they are not comparable to each other. *Default:* follow the existing tracker convention where one exists; otherwise report the full distribution plus one declared summary, and state the convention.
6. **What is the smallest subgroup that will be reported?** Determines whether the analysis can carry the reporting the client wants, and surfaces the small base problem before the chart is built rather than after. *Default:* apply the K4 §7 thresholds, and say up front which requested breaks the sample cannot support.
7. **Is this a single wave or part of a series?** Determines whether conventions can be chosen freely or must match a previous definition even where a better one exists. *Default:* match the previous definition, report the alternative alongside where the old convention is materially misleading, and say what the difference is.

## 7. Step-by-step methodology

**1. Write the output plan before running anything.** List the research objectives, and against each write the specific figures that would answer it. A questionnaire of 40 questions yields several hundred descriptive statistics, and running them all first and selecting afterwards is how a report ends up describing the questionnaire rather than answering the brief. *Correct result:* a plan naming, per objective, the questions, the bases and the summary form expected, so that selection is a decision rather than a default.

**2. Build the base register before calculating a single percentage.** For every question record four things: the base description in words ("all adults", "those aware of the service", "those who used it in the past month and gave a rating"), the base size, the routing rule that produced it, and the cases excluded from the total sample to reach it. Reconcile: total sample, minus those routed out, minus item non-response, equals the base. If it does not reconcile, the routing is not what you think it is. *Correct result:* a table a colleague could use to reconstruct any denominator without opening the data. Everything downstream inherits it.

**3. Classify every variable by measurement level and response structure.** Nominal, ordinal, interval or ratio; single-response, multi-response, numeric entry or open text. Measurement level constrains which summaries are legitimate; response structure determines what the denominator means. Record scale length, scale direction and the exact endpoint labels, because "very satisfied" at position 5 and at position 1 produce identical arithmetic and opposite findings. *Correct result:* a variable inventory with no unknowns. Per K4 §6.2, an unverified scale assumption is flagged, not absorbed.

**4. Decide the treatment of don't know, refused and not asked before any figure exists.** These are three different things and merging them is a consequential error. *Not asked* means the respondent was routed away: outside the base, never entering it. *Don't know* is usually a substantive answer and usually belongs inside the base, because excluding it silently converts "of those who had a view" into "of everyone", the base error in a different costume. *Refused* is item non-response and normally sits outside. Where the choice moves a headline by more than two points, show it both ways once, choose one, state the choice. *Correct result:* one written rule, applied everywhere, disclosed once.

**5. Look at the whole distribution before choosing any summary of it.** This step separates description from reflex. Examine the frequency distribution of every variable you intend to summarise, then read what the shape says. A long right tail on spend or tenure means the mean sits above most respondents. **Bimodality means the sample contains two populations and any single summary describes neither**, frequently the most useful thing the variable has to say. Clustering at scale endpoints suggests polarisation, or a question people could not answer moderately. A pile-up at the top of a satisfaction scale means the scale has no room left to detect improvement, a finding about the instrument that the summary hides. A spike at a round number means estimation, not measurement. *Correct result:* a one-line written reading of every distribution you summarise, produced before the summary is chosen.

**6. Choose the summary statistic from the distribution, not from the variable type.** The mean is the default and frequently the wrong statistic: where a distribution is skewed, which is normal for income, spend, transaction counts, tenure, durations and visit frequency, a few very high values pull it away from the typical respondent. Report the median in these cases, and add the mean only where the total matters (revenue, volume, aggregate demand), because the mean and the total are the same information. **On ordinal scales the mean is a convention, not a measurement**: treating a five-point scale as interval assumes the gap from "strongly disagree" to "disagree" equals the gap from "neutral" to "agree", which nobody has tested. Ordinal means are permitted, are useful for tracking movement, and must carry the distribution and the label. Where a distribution is bimodal, no measure of central tendency is honest. *Correct result:* every summary has a stated reason for being the one chosen, and no mean appears without spread or a distribution beside it.

**7. Handle multi-response explicitly, and label it so a reader cannot be misled.** Where respondents could select more than one option, percentages are calculated on respondents, not responses, and therefore sum to more than 100. Report the base as respondents, state the convention in the table title ("percentages sum to more than 100, respondents could select multiple options"), and report the mean number of selections per respondent, because a list averaging 4.1 selections and one averaging 1.3 behave completely differently and the percentages alone do not reveal it. Percentaging on total mentions is legitimate for share-of-mentions questions and gives entirely different numbers, so never do it silently. Define every "any of" net explicitly: a net of overlapping options is not the sum of its parts. Watch for the second meaning of the word net (a difference between two groups on a scale), and never let both appear unlabelled in one output. *Correct result:* no multi-response figure a reader could mistake for a single-response one.

**8. Treat top-box and net scores as conventions, and declare them.** Collapsing a scale into a top-box, a top-two-box or a net of top minus bottom groups makes movement visible and destroys information: the distribution cannot be recovered from a net, and two quite different distributions produce the same one. State the convention in the same place as the number ("top-two-box, positions 4 and 5 of 5"). Never compare a top-two-box figure to a top-three-box figure or to a mean score. Keep the distribution in the deliverable even where the summary carries the headline, and check what a net is hiding, because a net stable across waves can conceal both ends growing at once. *Correct result:* a stated convention travelling with every collapsed figure.

**9. Apply the weighting decision and calculate the effective base.** Weighted figures are labelled weighted, the scheme is named, and the effective base is shown alongside the unweighted count, per K4 §7. A weighted count is not a number of interviews and must never be presented as one. Where weights vary substantially the effective base can be materially smaller than the achieved sample, and it is the effective base, not the raw n, that governs small-base thresholds and everything downstream. Weighted and unweighted figures never share a table unlabelled. Scheme design and diagnostics belong to **04.05 Weighting and Base Management**.

**10. Apply the small-base rules, honestly and without negotiation.** Per K4 §7: below n=100, show n, flag the small base, interpret directionally only; below n=30, no percentages, report counts or verbatim. Two working rules follow. **The value of one respondent is 100/n percentage points**: on a base of 80 one respondent moves the figure 1.25 points, so even whole percentages overstate precision. And when a subgroup is too small to report, name it, give its base, and say what would be needed to report it. Silently dropping it looks like the subgroup was uninteresting; "n=19, too small to report as a proportion" is honest, and is often informative about who the sample reached.

**11. Set precision to what the method supports, then reconcile the totals.** Whole percentages by default: a decimal claims a precision sampling does not provide, per K3 §4.4, and on any base under 1,000 it is finer than a single respondent. Where percentages do not sum to 100, diagnose rather than force. Rounding across a handful of categories moves a total by a point, occasionally two; a single-response column summing to 96 or 104 has a base error, a missing category, an overlapping code frame or a multi-response question mislabelled as single. Never adjust a category to make a column add up, and never round a percentage into a word in a document that does not also carry the figure, per K2 §7. *Correct result:* every total sums correctly or has a diagnosed and stated reason for not doing so.

**12. Select against the objectives, and record what you left out.** Return to the output plan. Report the figures that answer a research question, anything genuinely surprising the plan did not anticipate, and the profile figures a reader needs in order to know who was surveyed. Everything else goes to an appendix or nowhere. This is not economy for its own sake: a reader given 300 numbers will find their own story in them, and it will not be the one the evidence supports. **Every reported figure needs an answer to "which question does this help answer".** *Correct result:* a reported set an order of magnitude smaller than the run, plus a list of what was produced and not reported.

**13. Verify before presenting.** Recalculate at least three headline figures independently from the raw data, including one filtered percentage. Reconcile each base against the routing. Check every scale direction against the questionnaire, not the variable name. Check that figures quoted in prose match the tables they came from. *Correct result:* a verification note recording what was re-checked and any discrepancy resolved.

**14. Write the conventions and disclosure block once, and attach it.** Base definitions, don't know treatment, weighting status and scheme, effective bases, scale collapse conventions, rounding rule, small-base thresholds, exclusions and their count, fieldwork dates. It travels with the figures into every downstream deliverable, because per K2 §7 a caveat left behind in the analysis is a caveat that does not exist. *Correct result:* a reader who receives only the tables can still tell what every number is a number of.

## 8. Analytical framework

The chain for every reported figure:

    Variable → Base definition → Distribution → Summary choice → Qualification → Selection

**Variable.** What was actually asked, in the words it was asked in.
**Base definition.** Who is in the denominator, described in words and counted. Established before the arithmetic, never inferred from it.
**Distribution.** The full shape, read before it is reduced.
**Summary choice.** The statistic chosen from that shape, with the reason stated.
**Qualification.** Base size, weighting status, small-base flag, convention used, precision limit.
**Selection.** Whether this figure answers a research question, or is being reported because it exists.

A figure that skips the third link is a habit, not an analysis. A figure that skips the fifth link is a data dump.

Against the K2 evidence chain, **descriptive analysis stops at Finding.** It produces analysis and findings, and it hands them onward. Interpretation of why the numbers look as they do belongs to **08.01**. The most common way this skill fails is the sentence that runs the finding into its explanation without a signal word between them, per K2 §3.2.

## 9. Output format

**1. Conventions and disclosure block.** One block, at the front, covering: total sample and how it was achieved; fieldwork dates; weighting status, scheme and effective base; don't know and missing treatment; scale collapse conventions; rounding rule; small-base thresholds; cases excluded and why; and whether AI performed any calculation step and whether a human verified it, per K4 §7.

**2. Base register.**

| Question | Base description (words) | Base n | Effective base | Routing rule | Excluded from total, and why |
|---|---|---|---|---|---|

**3. Frequency table**, one per reported variable.

| Response option | % | n | Base description | Base n |
|---|---|---|---|---|

Multi-response tables carry the sum-exceeds-100 statement in the title, plus mean selections per respondent. Single-response tables that do not sum to 100 carry the diagnosed reason, not a silent adjustment.

**4. Summary statistic table**, for numeric and scale variables.

| Variable | Distribution shape (one line) | Chosen summary | Value | Spread | Mean (where reported) | Base n | Reason for choice |
|---|---|---|---|---|---|---|---|

**5. Small-base register.** Every subgroup requested and not reported, with its base and the reason, so suppression is visible.

**6. Findings summary.** Short, ordered by research objective, each figure carrying its base description and base size inline, in K2 §4.1 format. No interpretation, no causal language, no comparative claim beyond arithmetic.

**7. What was produced and not reported**, with the selection rule stated.

**8. What could not be established**, per K3 §5.2: questions the objectives asked that the data cannot answer, subgroups the sample could not support, and variables whose meaning could not be verified.

**Where the evidence is thin**, the format does not get filled anyway. A base too small for a percentage gets a count and a flag, not a percentage in smaller type. A variable whose scale direction could not be confirmed is reported as unverified or held back. A question the objectives asked and the questionnaire did not ask gets a line in section 8 saying so. Per K4 §1, a slot in a table is not evidence that a number belongs in it.

## 10. Quality checks

Run before anything is presented. These sit on top of K4 §8, which runs anyway.

1. Does every percentage in the output have a base description in words and a base size next to it, not in a footnote?
2. For every filtered question, has the base been checked against the routing rather than assumed from the count of valid responses?
3. Has any percentage on a filtered base been described anywhere in language that implies the total sample?
4. Is every multi-response table labelled as such, with the mean number of selections reported?
5. Was the distribution examined before the summary statistic was chosen, for every summary reported?
6. Is there a mean anywhere on a skewed distribution without a median beside it?
7. Is there a mean on an ordinal scale without the distribution and the convention statement?
8. Does every collapsed score (top-box, top-two-box, net) state its convention in the same place as the number?
9. Are any two collapsed scores compared that use different conventions?
10. Do all single-response columns sum to 100, or carry a diagnosed reason for not doing so?
11. Is any percentage reported on a base under 30, or any decimal place on a base under 1,000?
12. Are weighted figures labelled, with effective base and unweighted n shown?
13. Is every suppressed subgroup listed with its base and reason, rather than silently absent?
14. Has any comparative or evaluative language been used ("significantly", "notably", "clearly", "much higher") that this skill has not tested and cannot support?
15. Can every reported figure be attached to a research objective, and has the list of unreported figures been written down?

## 11. Common failure modes

| Failure | How to recognise it | How to prevent it |
|---|---|---|
| **Filtered base reported as total** | A figure described as "of customers" that was asked only of a routed subgroup. Commonest error in commercial research and usually introduced in the write-up, not the tables | Base description in words on every figure, and rebase arithmetic shown wherever a filtered figure is converted to a total-sample statement |
| **Base separated from its number** | The table says n=612 and the slide says "of our 1,500 customers"; or a small-base figure quoted three documents later with no n at all | Base description and base size travel with the number into every document; the small-base flag is part of the number, not a formatting choice; verify prose against tables at step 13 |
| **Multi-response read as single-response** | Column sums to 214% and a reader concludes the data is wrong, or worse, does not notice | Statement in the table title, mean selections reported, never presented as a share |
| **Mean on a skewed distribution** | Reported average spend that almost no respondent is near; mean far above median | Look at the distribution first; report median for bounded-below open-ended variables; report the mean only where the total is the point |
| **Mean of an ordinal scale presented as measurement** | "Average satisfaction is 3.7" with no distribution and no scale labels | Report the distribution alongside; state the convention; use for tracking movement, not for describing a level |
| **False precision** | 62.4% on a base of 480, where one respondent is worth 0.21 points | Whole percentages by default; no precision finer than one respondent |
| **Forced totals** | A category quietly adjusted so a column sums to 100 | Diagnose the shortfall; a four-point gap is never rounding |
| **Silent don't know exclusion** | A satisfaction figure four points higher than expected, with no note | One written rule, applied everywhere, disclosed once; show both bases where the choice moves the headline |
| **Description that argues** | "Notably higher among younger customers" in a descriptive output; or a table that arrives already explaining itself | Arithmetic comparison only, with both bases shown; hand to 05.02 for reliability and 08.01 for interpretation, per K4 §3.1 and K2 §3.2 |
| **Exhaustive dumping** | Every question in the questionnaire reported, in questionnaire order | Output plan written before the run; selection against objectives; unreported figures listed rather than hidden |
| **AI: plausible arithmetic** | A percentage that is consistent with the surrounding numbers and was not calculated from the data | Recalculate headline figures independently from raw data; per K4 §2.1, never fill a cell with a plausible value |
| **AI: inferring meaning from a variable name** | Scale direction, scale length or code meaning taken from a label | Verify against the questionnaire; flag unverified assumptions per K4 §6.2 |

## 12. AI guardrails

Skill-specific only. K4 applies in full and is not repeated here.

1. **Never report a percentage without its base description and base size in the same place.** Not as a footnote, not in an appendix, not "available on request".
2. **Never calculate a percentage on a base you have not verified against the routing.** A count of valid responses is not a base definition; it is a symptom of one. Where routing is undocumented, state that the base was reconstructed.
3. **Never restate a filtered percentage in total-sample language**, and never let one pass through unchallenged in supplied text. If a total-sample figure is wanted, do the rebase arithmetic explicitly and show both figures.
4. **Never choose a summary statistic before examining the distribution.** If the distribution cannot be examined, say so and report the frequency table rather than a summary of it.
5. **Never report a collapsed score without its convention**, and never compare two collapsed scores built on different conventions, including across waves.
6. **Never report a percentage on a base below 30**, and never report a decimal place on a base below 1,000, whatever the requester's preference. Per K4 §9, offer the strongest honest alternative instead.
7. **Never adjust a figure to make a total sum to 100.** Diagnose and disclose.
8. **Never use evaluative or comparative language that implies a tested difference.** No "significantly", "notably", "clearly", "sharply", "meaningfully" in a descriptive output. Per K4 §3.1, plain arithmetic comparison with both bases shown is the ceiling.
9. **Never present a weighted count as a number of interviews**, and never let a weighted figure travel without its effective base.
10. **Never produce an exhaustive descriptive dump in place of a selection.** If the objectives are unknown, ask; if they cannot be obtained, report the profile and the planned measures, and say explicitly that selection against objectives has not been possible.

## 13. Best-practice principles

- **The denominator is the analysis.** Most descriptive errors are base errors wearing the clothes of arithmetic errors. An experienced analyst reads a table by looking at the base line first and the numbers second.
- **The base description in words matters more than the base size.** "n=612" tells a reader how much to trust the figure. "Those who used the service in the past month" tells them what it is about. Both are required and the second is more often missing.
- **Look before you summarise.** A summary statistic is a decision about what to discard. Making that decision without seeing the distribution means discarding without knowing what.
- **A distribution is a finding about the question as well as about the answer.** Ceilings, floors, bimodality, spikes at round numbers and pile-ups at endpoints all say something about whether the instrument worked. Read them; they are frequently more useful than the mean.
- **Two summaries can be right and incompatible.** Median spend among purchasers and mean spend per head answer different questions. Neither is more honest. Naming which question you are answering is what makes the choice defensible.
- **Every collapse is a loss, and the loss must be recoverable.** Top-box scores are good communication and bad archaeology. Keep the distribution in the deliverable so somebody can go back.
- **Precision is a claim.** Every decimal place asserts something about measurement. Report to the precision the method supports and no further.
- **The percentage that does not sum to 100 is a diagnostic tool.** Analysts who force the total lose their best early warning of a base error, an overlapping code frame or a mislabelled question.
- **Small bases are reported, not hidden.** A suppressed subgroup with its reason stated is more informative than a subgroup that silently never appears, and it protects the reader from concluding that nothing was found.
- **Selection is analysis, and its rule must predate the figures.** Choosing what to report is the analyst's job. Choosing it after seeing which numbers help is a different activity with the same appearance.
- **A descriptive figure is a floor, not a conclusion.** It says what the sample said. What it means, whether the difference is real, and what should be done about it are three further skills, and running them together is where descriptive analysis stops being honest.

## 14. Worked example

**INPUT.** A fictional regional transport authority surveys residents to inform a service investment decision. Achieved sample 1,500 adults, weighted to the population profile on age, gender and district. Objectives: how widely the service is used, how satisfied users are, and what stops non-users using it.

**PROCESS.**

*Steps 1 to 2.* The output plan names five figures against the three objectives. The base register is built from the routing. Q4 (used the service in the past month) was asked of all: base 1,500. Q7 (satisfaction) was asked only of past-month users: base 612. Q9 (reasons for not using) was asked only of non-users: base 888. Reconciliation checks: 612 + 888 = 1,500, so nobody was lost between the routes. Percentages are weighted, counts unweighted, effective base 1,340, and the block says so.

*Step 4.* Q7 attracted 41 don't know responses. Rule adopted: don't know stays in the base for opinion questions. Top-two-box on the base of 612 including don't know is 58%; on the 571 who gave a rating it is 62%. The four-point gap is exactly the kind of difference that later travels as a headline, so both are shown once, the convention goes in the disclosure block, and 58% is used throughout.

*Steps 5 and 6.* Q12 asks users how many journeys they made in the past week. The distribution is heavily right-skewed: a long tail of commuters, with 8% reporting 20 or more. Mean 6.4, median 3, mode 2. The mean describes almost nobody. **Judgement call:** the finance team wants an average for capacity modelling, and for that purpose the mean is correct, because total journeys is what they model. Resolution: report median 3 as the headline description of a typical user, report mean 6.4 explicitly labelled as the input to volume estimates, and show the distribution beside both. Reporting only one would have been wrong for one of the two readers.

*Step 7.* Q9 is multi-response. Percentages sum to 231%, mean 2.3 reasons per non-user, and the table title states both. The top reason is selected by 44% of non-users, which is 26% of all residents. Both are shown, because the second is what the investment case needs.

*The base error, caught.* A draft summary line reads "58% of residents are satisfied with the service". It is wrong. 58% is of past-month users, who are 41% of residents. The rebase is 0.41 × 0.58, so 24% of residents are past-month users who are satisfied. The corrected line reads: "58% of past-month users are satisfied (top-two-box, n=612). Past-month users are 41% of residents, so this represents 24% of all residents."

*Step 10.* Residents using a wheelchair or mobility aid: n=24. No percentages. Reported as counts with the base shown, and entered in the small-base register with a note that a boosted sample would be needed to report the group proportionally. Disclosed rather than dropped, because an accessibility question the study cannot answer is itself relevant to the decision.

*Steps 12 to 14.* Around 340 descriptive figures were produced and 22 are reported, the rest going to the appendix with the selection rule stated. **Researcher review recommended:** whether the 24-person mobility group warrants a supplementary study is a materiality judgement about the investment decision, not an analytical one, per K5 §2.1.

**OUTPUT.** A disclosure block; a base register reconciling every denominator; 22 figures each carrying its base in words and in count; a median-plus-mean treatment of journey frequency with the reason for each stated; a multi-response table labelled and rebased to residents where the decision needs it; a small-base register; and a statement that satisfaction among mobility-aid users could not be established at this sample size.

## 15. Advanced usage

**Tracking and wave-on-wave work.** Conventions outrank preferences. If a tracker has reported top-three-box for six waves, a better convention introduced now breaks the series. Report both for one wave, show the difference, and let the client decide when to switch. Hand to **05.05 Trend and Tracker Analysis**.

**Rebasing between audiences.** Senior stakeholders usually want total-population figures; operational teams usually want figures based on the relevant user group. Produce both from the same register rather than converting on the fly, and label each. A figure converted in a meeting is a figure that will be wrong in the minutes.

**Diagnosing a questionnaire from its distributions.** A descriptive run is the best available audit of the instrument. Endpoint pile-ups, high don't know rates, straight-lined batteries, spikes at round numbers and a code frame where "other" runs above 15% all point at question problems that will recur next wave. Report them as a methodological note; they are worth more than several of the figures.

**Bimodality as a segmentation signal.** Where a key variable is genuinely two-peaked, the mean is not merely imprecise, it is describing a population that does not exist. Flag it for **09.01 Audience Segmentation** rather than papering over it with a summary.

**Descriptives on derived variables.** Indices, composites, recodes and banded variables inherit every assumption made when they were built. Report the derivation rule alongside the figure, and never let a derived variable be described in language implying it was asked. Construction belongs to **04.04**.

**When the standard approach does not fit.** Continuous behavioural or transactional data with heavy tails may need trimmed means or explicit percentile reporting rather than a single centre; say which trimming rule was applied and how many cases it touched. Very short questionnaires with high routing complexity may have no meaningful total-sample base at all, in which case say so rather than manufacturing one.

## 16. Skill chain

**Recommended previous skills:**
- **04.02 Data Cleaning.** Hands over a dataset where duplicates, out-of-range values, straight-liners and speeders have been resolved and logged, so that descriptive figures describe respondents rather than defects.
- **04.04 Data Transformation and Dataset Preparation.** Hands over recodes, bands, nets, composites and derived variables with their construction rules documented, so that a description of a derived variable can state what it is a description of.
- **04.05 Weighting and Base Management.** Hands over the weighting scheme, the weight variable and the effective base, which this skill discloses on every weighted figure.

**Recommended next skills:**
- **05.03 Cross-Tabulation.** Takes verified figures and correct base definitions and extends them to two or more variables at once, inheriting the base register directly.
- **05.02 Statistical Testing.** Takes described differences and establishes whether they are reliable, which this skill deliberately does not do.
- **11.04 Data Visualisation and Chart Selection.** Takes the selected figures with their bases and conventions attached, so that the chart carries the qualification the number arrived with.
- **08.01 Finding to Insight Development.** Takes findings that stop at the K2 Finding boundary and does the interpretation work this skill leaves undone.

**Runs well alongside:**
- **04.03 Missing Data Handling**, wherever non-response is extensive enough to change what a base describes.
- **13.03 AI Output Verification**, run against the tables and the prose before figures leave the analysis.
- **K2**, for the source-reference format every figure carries, and **K3 §4.4**, for the precision rules.

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A Yazi Supplied Skill and resource.