Correlation and Causation | 相关性与因果关系辨析

📚 Correlation and Causation | 相关性与因果关系辨析

In CIE A-Level Biology, students are frequently asked to interpret experimental data, draw conclusions from graphs and tables, and evaluate whether an observed relationship supports a hypothesis. One of the most common conceptual pitfalls is confusing correlation with causation. Two variables may change together in a predictable pattern (correlation), but this does not necessarily mean that one variable causes the other to change (causation). Mastering this distinction is essential for Paper 3 (practical skills) and Paper 5 (planning, analysis and evaluation) of the CIE A-Level Biology syllabus.

在 CIE A-Level 生物考试中，学生经常需要解读实验数据、从图表中得出结论，并评估所观察到的关系是否支持某一假设。最常见的概念陷阱之一就是将相关性与因果关系混为一谈。两个变量可能以可预测的模式共同变化（相关性），但这并不一定意味着一个变量导致了另一个变量的变化（因果关系）。掌握这一区别对于 CIE A-Level 生物 Paper 3（实验技能）和 Paper 5（实验设计、分析与评估）至关重要。

1. Core Definitions | 核心定义

Correlation is a statistical association between two variables. It describes the extent to which changes in one variable are accompanied by changes in another. For example, as light intensity increases, the rate of photosynthesis in a plant also increases — up to a point. This is a positive correlation between the two variables.

相关性是两个变量之间的统计关联。它描述了一个变量的变化在多大程度上伴随着另一个变量的变化。例如，随着光照强度增大，植物的光合速率也增大——在某一范围之内。这就是两个变量之间的正相关。

Causation, by contrast, is the claim that a change in one variable directly produces a change in another through a biological mechanism. For example, raising the temperature of an enzyme-substrate mixture from 10 °C to 30 °C causes an increase in the rate of reaction because more substrate molecules gain sufficient kinetic energy to form enzyme-substrate complexes.

相比之下，因果关系是指一个变量的变化通过生物学机制直接导致另一个变量的变化。例如，将酶-底物混合物的温度从 10 °C 升至 30 °C 会导致反应速率升高，因为更多底物分子获得足够动能以形成酶-底物复合物。

2. The Correlation Coefficient (r) | 相关系数 r 及其解读

The Pearson product-moment correlation coefficient (r) is a numerical measure of the strength and direction of a linear relationship between two variables. Its value always lies between −1 and +1.

皮尔逊积矩相关系数（r）是衡量两个变量之间线性关系强度和方向的数值指标，其取值始终介于 −1 和 +1 之间。

r = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]

In the CIE A-Level Biology examination, it is unlikely that you will be required to calculate r by hand; instead, you will be expected to interpret the value from a calculator display, a spreadsheet, or experimental data. A value close to +1 indicates a strong positive correlation, a value close to −1 indicates a strong negative correlation, and a value close to 0 indicates no linear relationship.

在 CIE A-Level 生物考试中，你不太可能需要手工计算 r；相反，你需要能够解读计算器、电子表格或实验数据给出的结果。接近 +1 的值表示强正相关，接近 −1 的值表示强负相关，接近 0 的值表示无线性关系。