Statistics 1

Vocabulary Precision List

#FORGE Vocabulary Precision List — WST01 (Statistics 1)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md in full (re-read end to end, then grepped for command words, mark-type language, and every named misconception/conflation in Sections 2–6 and the per-lesson coverage audits). Cross-checked against the live lesson files in content/veridian/curriculum/wst01/ and every existing document in content/veridian/technique-hub/wst01/ (forge-exam-technique-guide.md, forge-battle-card.md, codex-formula-and-method-bank.md, signal-frequency-and-boundaries.md, and all 13 codex-deep-dive-*/signal-topic-brief-* files) so this list does not restate what any of them already cover — each entry below either cites material none of them centre, or reframes material they do cover into a different, cross-cutting pairing they don't state. No new PDF fetches were made; every claim traces to the facts bank, named inline, and every quotation is reproduced under ~15 words with attribution, per this course's standing no-verbatim-reproduction rule. Where the facts bank itself flags a claim as unconfirmed or single-series, that flag is carried over here rather than smoothed away.

#Scope — what this is, and what it deliberately doesn't repeat

This is a glossary, not an essay: short, alphabetisable-by-topic entries a student can look up in under a minute before a paper, each stating the exact two things that get blurred and what the mark scheme actually rewards. It is not a replacement for:

forge-battle-card.md / forge-exam-technique-guide.md — the mark-scheme abbreviation table (cao, awrt, isw, oe, bod, cso, ft, SC) is already built there in full; it is not reproduced here.
codex-deep-dive-show-that-answer-discipline.md — the full mechanism of "show that" marking is derived there; this document only cites the one fact that essay doesn't centre (see §1).
codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md — the independent-vs-mutually-exclusive proof and every worked angle live there; this list gives it one compact entry and points there for depth.
Every signal-topic-brief-* — frequency and mark-tariff evidence per topic; not repeated here.

What's new here: entries assembled from facts that exist in the bank but were never centred as their own named vocabulary item (§2's expectation-vs-probability pair, §2's coding-squaring pair stated across its two separate syllabus contexts together, §1's write-down/state contrast), plus one cross-cutting observation that doesn't appear written down anywhere else in this repo — that the single word "independent" carries three unrelated technical meanings on this one paper (§3).

#1. Command words — what method they actually buy you

"Write down" / "state" vs "calculate" / "find" / "determine" vs "show that." These are not interchangeable politeness variants — they map onto different mark types with different real consequences:

"Write down"/"state" signals a B mark — Pearson's own definition: an "independent accuracy mark... where there is no method" (General Instructions for Marking, all 14 schemes reviewed). Real instance: Jan 2025 Q1(c) prints "Write down the value of (i) E(R) (ii) E(B)" and the mark scheme awards two independent B1s with no method line at all — a student who writes derivation working here isn't penalised, but isn't credited for it either; the number alone earns the mark.
"Calculate"/"find"/"determine" signals M + A marks — a method mark for a correct or attempted-correct approach, then an accuracy mark dependent on that method being seen. The same numeric target scored via "find" typically credits a bare correct answer in full (verified: Jan 2021 Q3(a), a plain "find," scores full marks with no working shown).
"Show that" is the odd one out precisely because it looks like "find" but scores differently: the identical standardise-and-subtract calculation that scores full marks bare under "find" (Jan 2021 Q3(a)) requires evidence of both method steps under "show that" wording, with no bare-answer route at all (Oct 2021 Q6(a), scored M1 M1 A1cso). Same skill, same mark tariff, structurally different scheme, purely because of the command word — a finding already assembled in signal-topic-brief-normal-distribution-standardisation-and-conditional-probability.md §3, cited here because it belongs in a command-word glossary as much as a topic brief. The general discipline this implies — full intermediate working shown, not just the printed target repeated — is the whole subject of codex-deep-dive-show-that-answer-discipline.md and isn't re-derived here.

Cost of blurring it: treating "write down" as licence to skip a check (fine — no method is credited either way) is harmless; treating "show that" as equivalent to "find" and writing only the final line is not — it is the single most repeated meta-level complaint in every examiner report reviewed for this paper (paraphrased from Oct 2021, Jan 2023 and Jun 2024 general comments).

#2. Term pairs the mark scheme is precise about, and candidates blur

Independent events vs mutually exclusive events (spec 3.3 vs 3.2). The canonical pair: Pearson's own examiner report names this "the usual confusion" (Oct 2021 Q1(b)), quoting a candidate's reasoning that overlap alone disproves independence. The exact distinction: mutual exclusivity is a statement about whether two sets intersect at all ( $P(A\cap B)=0$ ); independence is a statement about whether one event's probability changes given the other has occurred ( $P(A\cap B)=P(A)P(B)$ ) — sets that overlap can still be independent (a King of Hearts is both a King and a Heart, and the two properties are independent), and sets that don't overlap can never be independent once both have positive probability. Full proof and worked angles: codex-deep-dive-conditional-probability-independence-vs-mutually-exclusive.md.

"Assumed independent" vs a calculated conditional probability. A related but distinct pair, worth separating from the one above: independence is a property that must be established, not a default. Pearson's own stated general diagnosis one series: candidates "often assume independence" where a genuine conditional probability was required (Jun 2022, general comment). The cost is structural, not just conceptual — assuming independence skips the calculation the mark scheme is actually paying for.

E(X) vs P(a single favourable outcome). A clean, quoted conflation: a real question has a fictional character reason "because E(X) > 0 he will play the game," and the mark scheme instead requires citing P(win) < 0.5 as the deciding quantity (Jun 2019 Q5(e)). Pearson's examiner report states plainly that most attempts focused on E(X) rather than the real deciding quantity, P(win) (paraphrased, Jun 2019 Q5 report). The exact distinction: E(X) is a long-run weighted average across every possible outcome; P(win) is the chance of one single outcome on one single play. A positive long-run average does not imply a better-than-even chance on any one attempt — a rare large payoff can carry the average positive while most individual plays still lose. Full worked treatment: the discrete-random-variables-probability-function.ts lesson's Jun-2019 worked chain (added 2026-09-25).

E(X²) vs Var(X). Quoted directly: "some still think E(X²) = Var(X)" (Jan 2021 Q4, paraphrased from the examiner report). They are related — $\text{Var}(X)=E(X^2)-\mu^2$ — but E(X²) is one term inside that formula, not the answer itself; treating them as synonyms skips the $-\mu^2$ step entirely.

Var(aX+b) — the coefficient must be squared, and this trap recurs in two unrelated syllabus contexts under two different names. Confirmed independently in three separate series with the identical mechanism: candidates compute $a\times\text{Var}(X)$ instead of $a^2\times\text{Var}(X)$ (Jan 2021 Q4, Jun 2024 Q2(c), Jun 2024 Q3(d) — the second restating the identical error three years later in the same paper's own series). The same squaring requirement resurfaces, unnamed as the "same trap," under spec 2.2's coding guidance: decoding a variance under $y=(x-b)/a$ requires dividing by $a^2$ , not $a$ , and the confirmed real error is "not decoding," using $a$ instead of $a^2$ , or using $a^2$ but multiplying instead of dividing (Jun 2022 Q3(e), paraphrased). Spec 5.3 (E/Var of a linear transformation of a random variable) and spec 2.2 (coding a data set) are taught as separate lessons in this course and tested as separate question types on the real paper — but the exact mathematical distinction that costs marks in both is the same one: a linear scaling constant multiplies a mean, but its square multiplies a variance.

Mean vs median as "the average." Both are measures of location; neither is a more accurate version of the other. Confirmed, quoted misconception: candidates asserted "the mean is more accurate than the median" with no supporting reasoning (Jun 2022 Q1(e), paraphrased). This exact item is already given full treatment in codex-deep-dive-outliers-boxplots-comparing-distributions.md §synthesis table and forge-exam-technique-guide.md's comparing-distributions checklist; listed here only because a vocabulary glossary would be visibly incomplete without the paper's single most-quoted term-precision misconception.

Describing correlation vs interpreting the gradient. Two different tasks that sound like one: "describe the correlation" wants a direction (positive/negative, weak/strong); "interpret the gradient in context" wants a rate — a stated real-world quantity changing by a stated amount per unit increase, with correct units. Confirmed real failure: candidates gave direction-only answers ("as x increases then y increases") when a rate-in-context sentence was required, and separately mixed up the two variables' units (Jan 2023 Q6(a), paraphrased). Already centred in codex-formula-and-method-bank.md and forge-exam-technique-guide.md; listed here as a term pair because "correlation" and "gradient" are genuinely different objects (a coefficient describing scatter-strength vs a rate of change) that this paper tests as separate, separately-worded skills.

"Unreliable" (a bare adjective) vs a reliability judgement that names a value and a range. A judgement of "unreliable" alone, unsupported, is confirmed to earn nothing: candidates who stated an estimate was unreliable without naming which value fell outside which range, or who stated the wrong verdict despite correct working, both lost the mark (Jun 2022 Q2(e); Jan 2023 Q6(c), paraphrased). The credited form names the specific value and states it lies outside the explanatory variable's data range — a bare verdict word is not the same claim as a justified one, even when the word itself is correct.

A calculated outlier fence vs an actual data value (box-plot whiskers). The general rule this paper rewards is that a whisker is drawn to a real data point, not to the calculated boundary used to identify outliers — confirmed via a repeatedly-quoted error of drawing to 98 (the fence) rather than 97 (the true highest non-outlier value) (Jan 2021 Q2, paraphrased). One genuine asymmetry is worth flagging honestly rather than smoothing into an absolute rule: the same question's own mark scheme credits the lower whisker at either the true data value (54) or the fence itself (50), while crediting the upper whisker only at the true value (97), never its fence (98) — verified directly against the mark scheme, not just the examiner report's summary (codex-deep-dive-outliers-boxplots-comparing-distributions.md carries the full correction history). The safe default remains "draw to the real value," precisely because the fence-credit only worked once, for one whisker, on one series.

Explanatory (independent) variable vs response (dependent) variable — and why the word "independent" is dangerous vocabulary on this exact paper. Spec 4.2 names these "explanatory (independent)" and "response (dependent)" variables — parenthetical synonyms a student is expected to recognise interchangeably with "explanatory"/"response." The real hazard: "independent" carries three unrelated technical meanings on this one paper, and nothing in the spec or any mark scheme warns a student the same word is being reused:

Independent events (spec 3.3) — a probability relationship, $P(A\cap B)=P(A)P(B)$ .
Independent (explanatory) variable (spec 4.2) — the variable a regression treats as the input, plotted on the x-axis, used to predict the other.
"Independent" as a mark-type word (General Instructions for Marking, every scheme reviewed) — a B mark is called an "independent accuracy mark" because it doesn't depend on a prior method mark having been earned, which is a statement about how the mark is awarded, unconnected to either meaning above. A student who reads "independent" in a regression question and starts checking a probability product rule, or who reads "independent mark" and thinks of independent events, is applying the wrong one of three genuinely distinct technical definitions that happen to share an English word. This observation doesn't appear centred anywhere else in this course's WST01 material; it is assembled here directly from the spec's own wording (§1, S1.3 items 3.3 and 4.2) and the mark-scheme boilerplate (§4 of the facts bank), not from an examiner-report quote of the confusion itself — flagged honestly as a structural-precision point, not a confirmed candidate error, since no examiner report in the reviewed archive documents a candidate making exactly this cross-meaning slip.

#3. Notation and convention precision (the paper is exact here, even without a quoted "confusion")

These entries are grounded in the spec, formula booklet, or mark scheme directly rather than in a quoted candidate error — flagged as such, per this document's own honesty standard, rather than dressed up as confirmed misconceptions they aren't yet evidenced to be.

$S_{xx}/S_{xy}$ vs $S_{pp}/S_{qq}$ (or any other letter pair). The S-notation is generic — the subscript letters simply name whatever two variables are in play that question. The mean-squared-standing-in-for-sum-squared-over-n error is structurally identical wherever it strikes, but the facts bank is explicit that only the $S_{pp}$ case (Oct 2021 Q2(b)) has direct evidence — the $S_{xx}$ version of the identical error was never actually observed in the reviewed record, because that particular question happened to give $S_{xx}$ directly rather than require its calculation. Treat the trap as real and general; treat " $S_{xx}$ specifically" as unconfirmed.
$n$ vs $n+1$ in linear interpolation for quartiles. Both conventions are tolerated by the mark scheme, but one series found the $n$ -based convention empirically more successful for candidates than $n+1$ (Jan 2023 Q1(e), paraphrased) — not a rule that one is "correct," only real empirical evidence about which route students more often complete accurately.
Population standard deviation ( $\div n$ ) vs "sample standard deviation" ( $\div(n-1)$ ). Confirmed jointly credited for the same 2 marks on exactly one reviewed series (Jan 2023 Q1(d)) — both the $\div n$ form and the $\div(n-1)$ form scored full marks there. A parallel check of the June 2023 scheme found no equivalent dual credit. This is a one-series-confirmed alternative, not a general WST01 marking convention — the $\div n$ form remains the safe default.
Exclusive events vs complementary events. The spec's own 3.2 heading lists these as two related but separate ideas ("Exclusive and complementary events") rather than one. Complementary events ( $A$ and $A'$ ) are necessarily mutually exclusive and exhaustive — together, they cover the whole sample space, so $P(A)+P(A')=1$ exactly; two merely mutually exclusive events need not cover everything, and their probabilities need not sum to 1. No examiner-report quote in the reviewed archive documents a candidate confusing these two terms specifically — flagged as a spec-precise distinction worth knowing, not a confirmed exam trap.

#Open flags — where this document stops rather than reaches for more

No likelihood percentage or grade-boundary figure appears anywhere above, consistent with this course's standing rule and the facts bank's own confirmed absence of grade-boundary data (signal-frequency-and-boundaries.md §2).
Every "confirmed in N series" statement above uses the same honest denominator the rest of this course's WST01 material uses: 6 of 14 mark-scheme series have a located, fully-read examiner report (Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024); 8 series remain unread. A pairing absent from this list is not confirmed absent from the paper — only not yet found stated as a term-precision point in the material reviewed.
§3's three entries and §2's "independent" triple-meaning point are explicitly flagged as spec/mark-scheme-grounded rather than examiner-report-confirmed misconceptions, because that is what the evidence actually supports — they are real and checkable, just not yet evidenced as things candidates have been shown to blur in practice.
This document does not include a "causation vs correlation" entry: the facts bank was grepped directly for "causation" and returns no match anywhere in the six reviewed examiner reports, the spec, or the formula booklet. Rather than invent one because it's a conventional statistics-course topic, it is left out.

#Sources

research/veridian/WST01-verified-facts.md — §1 (spec transcription, items 2.2/3.2/3.3/4.2), §2a/§4 (formula booklet and mark-scheme boilerplate, mark-type definitions), §5 (all per-section examiner-report quotes cited above, Sections 2–6), §7 (frequency context), and the per-lesson coverage audits for discrete-random-variables-probability-function.ts (Jan 2025 and Jun 2019 anchors), expectation-and-variance-of-linear-transformations.ts (Jun 2024/Jan 2021 anchors), and outliers-boxplots-comparing-distributions.ts (Jan 2021 Q2 whisker-asymmetry correction). Cross-checked against every existing file in content/veridian/technique-hub/wst01/ (listed in the Scope section above) to confirm non-duplication, and against content/veridian/question-bank/wst01.ts (checked; no overlapping vocabulary-glossary item exists there). No new PDF fetches, web searches, or primary-source downloads were performed for this document.