Series ID: EDKS-ADV-VOC-ZH-0041 · Advanced English Vocabulary (Chinese Edition) · Lesson No.041 · C1 → C2 · 简体中文辅助
A relationship can be real without being causal. Correlation tells you that variables move together; it does not tell you why.
关系可以是真实的，但不一定是因果。correlation 告诉你变量如何一起变化，却不会自动告诉你为什么。
Advanced English uses correlation, association, relationship, dependence, independence, covariation, linked, related, corresponding and connected in overlapping but non-identical ways. A strong statistical correlation can coexist with confounding, reverse direction, common cause, selection effects or pure coincidence. The first skill is lexical restraint: describe the relationship you have actually observed before upgrading it to an explanation.
OpenStax repeatedly makes the central boundary explicit: correlation can describe strength and direction of a relationship, but a strong correlation does not by itself establish causation. NIST likewise defines correlation as an association between variables while warning that correlation does not imply cause. This lesson owns the language of relationship before causal interpretation.
Describe the relationship first. Explain the cause only when the evidence supports a causal claim.
先描述关系；只有证据足够时，才解释因果。
Part I — Build the relationship map | 第一部分：建立“关系语言地图”
1. Relationship is the broad parent word | relationship
Relationship is the broadest useful noun: two variables, events or concepts are connected in some describable way. It does not specify whether the relationship is statistical, causal, temporal or logical.
2. Association is broad statistical relationship language | association
Association commonly describes a systematic relationship between variables without committing to causation. “X was associated with Y” is deliberately weaker than “X caused Y.”
3. Correlation is a more specific relationship concept | correlation
In statistics, correlation usually refers to how variables vary together, often measured by a coefficient. The exact coefficient may capture only a particular form of relation, such as linear association.
4. Positive correlation means same directional tendency | positive
When higher X tends to accompany higher Y, a linear correlation can be positive. “Positive” describes direction, not goodness.
5. Negative correlation means opposite directional tendency | negative
When higher X tends to accompany lower Y, the relationship is negative. “Negative” is mathematical direction, not criticism.
6. Zero linear correlation can hide nonlinear dependence | zero correlation
A coefficient near zero may mean no linear relationship while a strong curved relationship exists. “No correlation” should therefore name the coefficient/form if a nonlinear pattern remains possible.
7. Linear relationship follows a straight-line tendency | linear
A linear relation is approximately captured by a straight-line pattern. It is not implied merely because both variables rise over time.
8. Nonlinear relationship needs shape language | nonlinear
U-shaped, threshold and curved relations can be strong while Pearson correlation is small. Describe the form instead of forcing every relation into positive/negative linear language.
9. Pearson r measures linear correlation | Pearson
Pearson’s r is bounded from -1 to +1. Magnitude describes linear association strength; sign describes direction. It does not give the slope of the relationship.
10. Spearman correlation uses rank order | Spearman
Spearman rank correlation captures monotonic rank association. It is not simply a substitute chosen whenever Pearson looks inconvenient; the data structure and analytic job decide.
11. Covariation means variables vary together | covariation
Covariation is useful conceptual language for joint change. It does not specify cause, direction of influence or a particular coefficient.
12. Covariance is not correlation | covariance
Covariance is scale-dependent; correlation standardises joint variation. Technical writing should preserve the exact statistic.
13. Slope is not correlation | slope
Slope expresses expected outcome change per predictor unit in a regression line; correlation expresses standardised linear association. A steep line can have imperfect correlation, and a shallow line can have perfect linear correlation.
14. Regression is not correlation | regression
Regression models an outcome conditional on predictors; correlation summarises association. Regression coefficients can change after adjustment, transformations or interaction terms.
15. Dependence is broader than correlation | dependence
Variables can be dependent even when linear correlation is zero. Dependence is a broader probabilistic relationship than one correlation coefficient.
16. Independence is a strong statistical claim | independence
Statistical independence means the joint probability structure factorises under the formal definition. “No significant correlation” is not proof of independence.
17. Uncorrelated is weaker than independent | uncorrelated
Two variables can be uncorrelated yet dependent nonlinearly. Do not paraphrase “uncorrelated” as “unrelated in every way.”
18. Co-occurrence means appearing together | co-occurrence
In corpora, behaviour or event logs, co-occurrence means appearing in the same context/window. Repeated co-occurrence can motivate association analysis but does not prove a mechanism.
19. Linked to can sound causally suggestive | linked to
News summaries often use “linked to.” When the underlying study is observational, associated with is usually clearer about evidential limits.
20. Related to is broad and cautious | related to
“X is related to Y” leaves mechanism unspecified. It is useful when exact relationship type is not established, but too vague when a coefficient is available.
21. Strong does not mean causal | strong association
A correlation near ±1 can still be non-causal. Strength describes pattern regularity, not mechanism.
22. Weak does not mean irrelevant | weak association
A weak individual-level association can matter across large populations, and measurement noise can attenuate observed relationships. Interpret strength in context.
23. Statistical significance is not strength | significance
Large samples can make tiny associations statistically significant. Small samples can make practically important associations uncertain. Significance, strength and importance are separate.
24. No detected association is not proof of no relation | absence of evidence
Sample size, measurement error and model choice affect detection. Prefer “no clear association was detected” over “there is no relationship” when uncertainty remains.
25. Confounding can create a misleading association | confounding preview
A third variable related to both X and Y can produce or distort their observed association. Lesson 042 will own confounding as causal-inference vocabulary.
26. Reverse causation changes direction | reverse causation
If X and Y are associated, Y may influence X instead of X influencing Y. Cross-sectional data often cannot establish directional order.
27. Bidirectional relationships create feedback | feedback
X can influence Y while Y also influences X. Behavioural, social and economic systems often contain feedback loops rather than one-way effects.
28. Common cause can explain co-movement | common cause
A third process can drive both variables, creating association without a direct causal path between them.
29. Coincidence can generate apparent relationships | coincidence
When many variables are examined, some correlations appear by chance. Replication and theory help distinguish persistent association from coincidence.
30. Spurious association is a warning label | spurious
A spurious association is misleading—often due to confounding, common trends, selection or chance. Name the suspected source when known.
31. Time trends can create spurious correlation | common trend
Two unrelated quantities can both rise over decades and therefore correlate strongly. Detrending, differencing or model design may change the relation. Shared time direction is not mechanism.
32. Selection can create association | selection
Who enters the dataset can affect observed relationships. A hospital sample, admitted-student sample or platform-user sample may show associations unlike the source population.
33. Aggregation can reverse association | aggregation
Overall relationships can differ from subgroup relationships because group composition changes. Inspect within-group patterns before generalising from pooled data.
34. Ecological association is group-level | ecological
A relationship between country averages does not automatically describe individual people. Keep the unit of analysis visible.
35. Within-group and between-group relations can differ | levels
Schools can show a positive between-school association while students within each school show little or opposite association. One coefficient can hide level structure.
36. Conditional association depends on subgroup/context | conditional
The X–Y relationship may differ by age, region or baseline level. “Associated overall” can be a poor summary of heterogeneous conditional relations.
37. Interaction can change the relationship | interaction preview
The relation between X and Y can depend on Z. Lesson 042 will distinguish statistical interaction, moderation and causal interaction.
38. Partial correlation is still association | partial correlation
Partial correlation measures association after accounting for specified variables under a model. Adjustment alone does not create causal identification.
39. Correlation matrix is not a causal map | matrix
A correlation matrix summarises pairwise coefficients. It can reveal redundant variables or clusters but not the direction of causal arrows.
40. Multicollinearity is predictor dependence | multicollinearity
Strong relationships among predictors can make regression coefficients unstable or hard to interpret. That is a modelling issue, not proof of causal connection among predictors.
41. Autocorrelation is relation across ordered observations | autocorrelation
A time series can correlate with its own past values. This is different from cross-sectional association between two variables.
42. Local relation can differ from global relation | local
X and Y may rise together at low values and fall together at high values. A single global coefficient can average these regimes into a misleading near-zero relation.
43. Measurement error can weaken observed correlation | attenuation
Noisy measurements can reduce apparent association. Weak observed correlation may reflect measurement limitations rather than a weak underlying relation.
44. Restricted range can weaken correlation | range restriction
If a sample includes only high performers, the X–Y relationship can look weaker than in the full population because variability has been restricted.
45. Outliers can inflate or reverse correlation | outliers
One extreme point can strongly influence Pearson correlation. Inspect scatterplots and influence before trusting the coefficient alone.
46. Sample correlation is not population certainty | sample
A sample correlation estimates or describes the observed sample relationship. Generalising to the population requires uncertainty and sampling considerations.
47. Replication strengthens confidence in association | replication
A relationship repeatedly observed across independent samples and measures is more credible than a one-off coefficient, though replication still does not by itself prove causation.
48. Robust association survives reasonable analysis choices | robustness
If a relationship disappears under small legitimate modelling changes, confidence should weaken. “Robust association” should describe sensitivity evidence, not rhetorical confidence.
49. Relationship language should match the design | design
Observational cross-sectional data usually support relationship/association language. Experimental or well-identified causal designs may justify stronger causal wording. Method controls verb strength.
50. Part I checkpoint: relationship first, explanation later | 第一部分检查点
Ask what variables, unit of analysis, form, direction, strength, uncertainty and subgroup context are actually observed. Then stop. Causal explanation belongs to the next lesson unless the design supports it.
Part II — Relationship language across domains | 第二部分：跨领域的关系词汇
51. Education: attendance and scores can be associated without simple causation | 教育
Students with higher attendance may also have higher scores, but motivation, health, prior attainment and family support can affect both. “Associated with” is safer than “attendance caused the score” without a causal design.
52. Education: prior attainment can confound later associations | prior attainment
A tutoring programme may appear associated with higher exam scores because stronger students select into it. Adjustment may change the association; selection and baseline differences matter.
53. Business: advertising and sales can co-move with season | business
Advertising and sales may rise together during holidays because both respond to seasonal demand. Correlation alone does not isolate the advertising effect.
54. Finance: assets can correlate because of common market exposure | finance
Two stocks can show high correlation because both respond to the same market factor. Pairwise correlation does not imply one stock drives the other.
55. Portfolio diversification depends on dependence structure | dependence
Low pairwise correlation can support diversification, but tail dependence and regime changes can matter. “Uncorrelated” is not the same as independent under all market conditions.
56. Medicine: biomarker association is not treatment effect | health
A biomarker can be associated with disease outcome without being a causal target. It may be a consequence, common-cause marker or correlate of severity.
57. Public policy: neighbourhood associations are often ecological | policy
A neighbourhood with higher income may have better outcomes, but this group-level association cannot automatically be applied to every resident.
58. Computing: request volume and latency can be nonlinear | computing
Latency may remain flat at low load and rise sharply after capacity thresholds. A single linear correlation can understate threshold behaviour.
59. Machine learning: feature correlation can indicate redundancy | features
Highly correlated predictors may carry overlapping information. This can affect model stability or interpretation, but feature correlation is not a causal graph.
60. Language corpora: co-occurrence is evidence of association, not meaning identity | corpus
Two words often appearing together can signal collocation or topic association. It does not mean they are synonyms or causally linked.
61. Search trends: simultaneous growth may reflect one external event | trends
Two search terms can spike together because a news event drives both. Co-movement is real; direct relationship may be absent.
62. Geography: spatial correlation can arise from location | spatial
Nearby areas can have similar values because of shared geography, infrastructure or spatial processes. Observations are not always independent across space.
63. Time series: common trend can dominate correlation | time series
Population and GDP may both rise over time and correlate strongly. Relationship in levels can be driven by shared trend rather than direct mechanism.
64. Lagged correlation describes timing, not cause | lag
X today can correlate with Y next week. Temporal ordering is useful evidence but does not eliminate confounding or common trends.
65. Lead–lag language needs care | leads/lags
“X leads Y by two months” can mean its peak/movement occurs earlier, not that X causes Y. If causation is intended, add evidence/design.
66. Cross-correlation is a time-lag tool | cross-correlation
Cross-correlation compares series at different lags. It can reveal timing alignment, but strong lagged correlation remains associational.
67. Association can disappear after stratification | stratification
An overall relation may be explained by age, region or baseline status. Stratified analysis helps reveal whether association is consistent across groups.
68. Association can appear after stratification | suppression
A relationship hidden in aggregate data can appear within relevant strata. Aggregation can mask as well as create patterns.
69. Correlation is symmetric; regression is directional | symmetry
Correlation between X and Y equals correlation between Y and X. Regression of Y on X is not the same model as X on Y. This grammatical/statistical distinction matters for interpretation.
70. Associated with is not affected by | verb strength
Associated with is relational. Affected by, driven by, leads to, results in are causal or mechanism-suggestive. Match verbs to design.
71. Predictive relationship is not causal relationship | prediction
A variable can predict an outcome accurately without causing it. Predictive usefulness and causal manipulability are different.
72. Proxy variables can correlate strongly with the target | proxy
A proxy stands in for a harder-to-measure construct. Strong proxy correlation does not make the proxy identical to the construct.
73. Surrogate endpoint is not the final outcome | surrogate
In research, surrogate measures can track outcomes while remaining imperfect substitutes. Correlation between surrogate and outcome does not guarantee intervention effects transfer.
74. Concordance is agreement, not correlation | concordance
Two measurement methods can correlate highly yet disagree systematically in level. Agreement/concordance asks whether measurements are close, not merely ordered together.
75. Agreement and association answer different questions | agreement
If one thermometer always reads 5°C higher than another, readings can correlate perfectly while failing agreement. Lesson 044 will deepen accuracy/precision.
76. Similarity is not correlation | similarity
Two profiles can be numerically similar without showing a relationship across observations. Similarity compares objects; correlation relates variable patterns.
77. Correspondence can be structural rather than statistical | correspondence
“There is a correspondence between categories” may describe mapping, not measured correlation. Avoid statistical overreading of ordinary relation words.
78. Coupling suggests connected dynamics | coupling
Engineering and systems science use coupled for components that interact. It can imply mechanism more strongly than correlation, so use only when system connection is established.
79. Decoupling means relationship weakens/breaks | decoupling
Economic or engineering prose may say two variables have decoupled when their historical co-movement weakens. This is descriptive unless a mechanism is established.
80. Part II checkpoint: ask what kind of relation the domain means | 第二部分检查点
Correlation, association, agreement, similarity, co-occurrence, predictive value and coupling all describe different relation jobs. Do not flatten them into “connected.”
Part III — Mandarin-to-English relationship control | 第三部分：中文母语学习者的关系词汇转换
81. 相关 = correlated / related / relevant, depending meaning | 相关
“两个变量相关” → the variables are correlated/associated. “相关资料” → relevant information. “相关部门” → relevant authorities/departments. Chinese 相关 spans statistical relation and relevance; English separates them.
82. 相关性 = correlation / association / relevance | 相关性
Statistical 相关性 may be correlation/association; topic 相关性 may be relevance. Do not translate relevance as correlation.
83. 正相关 = positive correlation | 正相关
Use positive correlation/positive association. Positive means same direction, not beneficial.
84. 负相关 = negative correlation | 负相关
Use negative/inverse correlation depending context. Negative means opposite direction, not harmful.
85. 无相关 = no correlation / no clear association | 无相关
If a formal test only fails to detect a relation, write no clear/statistically significant association was detected rather than absolute “no relationship.”
86. 关联 = association / link / connection | 关联
Statistical relation → association; general connection → link/connection; database linkage → link/relate. Domain decides.
87. 联系 = relationship / connection / contact | 联系
“两变量之间的联系” → relationship between the variables. “联系我们” → contact us. Surface translation is unsafe.
88. 关系 = relationship / relation | 关系
Use broad relationship unless a more specific statistical relation is known. “因果关系” is causal relationship, not correlation.
89. 共同变化 = covariation / co-movement | 共同变化
Statistical prose may use covariation; finance/economic prose often uses co-movement. Both avoid claiming why the variables move together.
90. 同步变化 = move together / co-move | 同步变化
“两指标同步上升” → the two indicators rose together. That is a descriptive temporal relation, not necessarily correlation calculated across observations.
91. 独立 = independent | 独立
In statistics, independent has a strong formal meaning. “独立变量” can mean independent/explanatory variable in experimental language, which is different from variables being statistically independent.
92. 不相关 ≠ independent automatically | 不相关
“Uncorrelated” does not guarantee independence except under special conditions. Translate the exact mathematical relation.
93. 强相关 = strong correlation, but define metric/context | 强相关
Do not convert “strongly correlated” into “closely caused.” Keep strength and causality separate.
94. 弱相关 = weak correlation | 弱相关
Weak correlation can still be stable, significant or practically relevant. Do not add “unimportant” unless evidence supports it.
95. 线性关系 = linear relationship | 线性关系
Use linear relationship/association when the relation is approximately straight-line. “Linear” is a shape property.
96. 非线性关系 = nonlinear relationship | 非线性
Curved, threshold or U-shaped patterns are nonlinear. Do not call them uncorrelated simply because Pearson r is near zero.
97. 假相关 / 伪相关 = spurious correlation/association | 伪相关
Use spurious when the observed relationship is misleading due to confounding, trend, selection or chance. Explain which mechanism is suspected.
98. 反向因果 = reverse causation | 反向因果
Use when the apparent exposure→outcome direction may actually run outcome→exposure. It is a causal alternative explanation, not a correlation statistic.
99. 混杂 = confounding | 混杂
Confounding is the standard causal-inference term. Do not translate it as ordinary “confusion.” Lesson 042 will own its causal logic.
100. Part III checkpoint: 相关 is not always correlation | 第三部分检查点
Chinese 相关 can mean statistical correlation, general relation or simple relevance. English requires you to decide which relation job is active before choosing correlation, association, related, relevant or another term.
Part IV — Relationship failure laboratory and mastery | 第四部分：关系失误实验室与掌握系统
101. Strong correlation, zero causal evidence | 强相关不等于因果
Two variables move almost perfectly together because both are driven by time. The coefficient is strong; the causal claim is unsupported. This is the central discipline of Lesson 041.
102. Weak observed correlation from noisy measurement | 测量噪声
The underlying constructs are strongly related, but both are measured poorly. Observed correlation shrinks. “Weak correlation” can reflect measurement attenuation rather than weak substantive relation.
103. Zero Pearson r, perfect U-shape | 非线性陷阱
Y is lowest at middle X and high at both ends. A linear coefficient can be near zero despite a deterministic nonlinear relation. Plot before concluding “no relationship.”
104. One outlier creates the correlation | 离群值驱动
Most observations show no relation, but one extreme point produces a large coefficient. Remove or investigate only with a principled data-quality/influence rule, not because the point is inconvenient.
105. Removing one valid outlier destroys the real relation | 真极端值
An extreme observation is genuine and reveals the upper range where the relationship appears. Automatic outlier deletion can erase real structure.
106. Overall positive, within-group negative | aggregation reversal
Pooled data show positive association because high-X groups also have high baseline Y. Within each group, X and Y slope downward. “X is positively associated with Y” needs the level of analysis.
107. Between-school relation is not student-level relation | ecological trap
Schools with higher average homework time have higher average scores. This does not establish that individual students who do more homework score higher within each school.
108. Selection into hospital reverses association | collider-like selection
Among admitted patients, two risk factors can appear negatively related because either one can trigger admission. The selected sample creates an association not present in the source population.
109. Range restriction hides a real relation | 限制范围
Among only elite students, prior score and final score correlate weakly. In the full population, the relation is stronger. Selection compressed the predictor range.
110. Same correlation, different slope | r ≠ slope
Two datasets can have the same correlation but different units/scales and therefore different regression slopes. Correlation strength is standardised; slope is not.
111. Same slope, different correlation | noise changes tightness
Two datasets can share a regression slope while one has much greater scatter. The slope describes expected change; correlation describes how tightly points align linearly.
112. High agreement impossible despite high correlation | method comparison
Instrument B always reads twice Instrument A. Correlation can be perfect, yet the instruments do not agree numerically. Lesson 044 will own agreement/accuracy.
113. Predictor is useful but non-causal | prediction vs intervention
Umbrella sales predict rain because both respond to weather. Buying umbrellas will not cause rainfall. Predictive association is not an intervention effect.
114. Correlation caused by a shared calendar cycle | seasonality
Electricity demand and ice-cream sales peak in summer. Their correlation partly reflects season. Adjusting for season can alter the relation.
115. Correlation changes across eras | regime dependence
Two financial variables correlate positively before a policy change and negatively after. One full-period coefficient hides regime-specific relations.
116. Association differs by age group | heterogeneity
An exposure relates to outcome among younger participants but not older ones. One average coefficient may be an incomplete summary.
117. Multiple testing finds accidental correlations | chance
Search thousands of variable pairs and some will look impressive by chance. Pre-specification, correction and replication matter.
118. A beautiful chart is not a relationship test | visual seduction
Scaled axes, smoothed curves and dual-axis charts can make unrelated trends look aligned. Visual co-movement motivates analysis; it does not replace it.
119. Correlation of percentages can inherit denominator effects | ratio variables
Two ratios sharing a denominator can correlate mechanically. Lesson 037’s denominator logic remains relevant when interpreting associations among rates and proportions.
120. Part-whole correlation can be structural | compositional data
Shares that sum to 100% are constrained: one share rising forces others to fall. Negative correlations can arise from the composition itself, not direct competition.
121. Repeated measures violate naive independence | clustered observations
Ten measurements from one student are not equivalent to ten independent students. Within-person observations share context, creating dependence.
122. Family members are not independent observations | clustered data
Siblings share genes and environment. Treating family observations as independent can understate uncertainty.
123. Spatial neighbours can be correlated | spatial autocorrelation
Nearby areas often share infrastructure, climate or population composition. Standard methods assuming independent locations may misstate uncertainty.
124. Correlation is symmetric; causal language is asymmetric | symmetry reminder
Correlation(X,Y) = correlation(Y,X), but “X causes Y” is not equivalent to “Y causes X.” This is why correlation alone cannot provide causal direction.
125. Build the relationship FENCE | 关系 FENCE
| Fence | Question | Job |
|---|---|---|
| F0 Variables | What two things? | name X/Y |
| F1 Unit | Person, school, day, country? | unit of analysis |
| F2 Form | Linear, monotonic, nonlinear? | shape |
| F3 Direction | Positive/negative? | sign |
| F4 Strength | How strong? | coefficient/context |
| F5 Stability | Across groups/time? | heterogeneity |
| F6 Alternatives | Confounding, selection, chance? | non-causal explanations |
| F7 Uncertainty | How precise/stable? | sampling/model limits |
| F8 Claim | What verb is justified? | associated vs caused |
126. Practice A — choose the relationship noun | 练习 A
- Two variables rise together linearly.
- Two categorical features occur together more often than expected.
- One variable predicts another but mechanism unknown.
- Two instruments produce close values.
- Two concepts are topically relevant.
Choose among correlation, association, co-occurrence, predictive relationship, agreement, relevance.
127. Practice B — safe versus causal verbs | 练习 B
- associated with
- linked to
- predicts
- increases
- causes
- drives
Rank them by how much causal/mechanistic commitment they usually carry, then match them to study designs.
128. Practice C — find alternative explanations | 练习 C
For each observed association, generate at least four alternatives: X→Y, Y→X, common cause Z, selection/chance. This trains causal restraint before Lesson 042.
129. Practice D — Mandarin repair | 练习 D
- 两个变量高度相关，但不能因此推出因果。
- 这个关系在不同年龄组中并不一致。
- 整体呈正相关，但组内关系相反。
- 没有发现显著线性相关，不代表变量完全独立。
- 这个相关可能由共同趋势造成。
130. A 15-minute relationship session | 15 分钟训练
| Time | Task |
|---|---|
| 0–3 | Choose one scatterplot/data pair. |
| 3–6 | Describe form/direction/strength. |
| 6–9 | Check groups/outliers/range. |
| 9–12 | List causal alternatives. |
| 12–15 | Write one claim with appropriate verb strength. |
131. Seven-day mastery route | 七天路线
| Day | Focus |
|---|---|
| 1 | relationship / association / correlation |
| 2 | positive / negative / zero / nonlinear |
| 3 | dependence / independence |
| 4 | confounding / reverse / selection / chance |
| 5 | group vs individual / aggregation |
| 6 | Mandarin transfer |
| 7 | full FENCE audit |
132. First weak-link diagnostic | 弱点诊断
| Symptom | Weakness | Repair |
|---|---|---|
| I say “causes” after seeing correlation. | claim strength | association verb ladder |
| I think r=0 means unrelated. | nonlinearity | U-shape cases |
| I think uncorrelated means independent. | probability logic | dependence examples |
| I ignore groups. | aggregation | stratification cases |
| I trust one coefficient. | diagnostic blindness | plot/outlier/range audit |
| I translate 相关 as correlation everywhere. | bilingual polysemy | relevance/association contrasts |
133. Reading harvest | 阅读提取
Collect bundles such as positively associated with, strongly correlated with, no clear linear association, relationship attenuated after adjustment, association varied by subgroup, substantial overlap. Store the full claim, not just the noun.
134. Writing activation | 写作激活
Use: variables + unit + relationship form + direction + magnitude + uncertainty + caveat. Example: “Within schools, attendance showed a modest positive association with score; this observational pattern does not establish a causal effect.”
135. Speaking activation | 口语激活
Describe one relationship in 45 seconds without using cause, effect, drives, leads to. This forces association vocabulary to become active rather than merely understood.
136. Paraphrase test | 改述测试
Original: “X was associated with Y after adjustment.” Unsafe: “X independently caused Y.” Safe: “The association remained after accounting for the measured covariates included in the model.”
137. Canonical ownership boundary | 本课所有权边界
Lesson 041 owns relation language: correlation, association, covariation, dependence, independence, linear/nonlinear form, spurious association, aggregation and non-causal alternatives. Lesson 042 owns causal claims, mechanisms, confounding control, mediation and moderation.
138. Recommended reference floor | 推荐参考资源
- NIST — Correlation — association without implied cause.
- OpenStax — Correlation Coefficient — strength, direction and linear limits.
- OpenStax — Regression Equation — correlation does not imply causation and correlation is not slope.
- OpenStax — Correlation and Third Variables.
139. SEO language map | 本课关键词范围
correlation vs causation, association vs correlation, positive negative correlation, zero correlation nonlinear relationship, independence vs uncorrelated, spurious correlation, confounding correlation, reverse causation, correlation coefficient meaning, C1 C2 data English, 相关英语, 关联英语, 正相关负相关, 伪相关, 独立性英语, 相关不等于因果.
140. Final rules | 最后的规则
A relationship can be real without being causal.
关系可以是真实的，但不一定是因果。
Correlation tells you how variables move together. Causal evidence tells you why an intervention would change an outcome.
