📚 Correlation in Biology: Testing Relationships Between Variables | 生物中的相关性：检验变量之间的关系
In A-Level Biology investigations, correlation is a statistical method used to describe the direction and strength of a relationship between two measured variables. It does not prove that one variable causes another; instead, it asks whether the variables tend to change together in a predictable pattern. Cambridge International AS and A Level Biology papers, especially Paper 5, often expect students to draw scatter graphs, calculate a correlation coefficient such as Spearman’s rank correlation, and interpret the result against a critical value.
在 A-Level 生物实验中，相关性是一种统计方法，用来描述两个测量变量之间关系的方向和强度。它并不证明一个变量导致另一个变量变化，而是考察这些变量是否倾向于以可预测的模式共同变化。剑桥国际 AS 和 A Level 生物试卷，尤其是 Paper 5，通常要求学生绘制散点图、计算如斯皮尔曼等级相关系数，并将结果与临界值进行比较和解释。
1. What Is Correlation? | 什么是相关性？
Correlation is a measure of the linear association between two continuous or ordinal variables. For example, a biologist might measure light intensity and the rate of photosynthesis in Elodea, or temperature and the heart rate of Daphnia. A correlation coefficient tells us how closely the two variables follow a straight-line trend.
相关性是衡量两个连续或有序变量之间线性关联程度的指标。例如，生物学家可能测量黑藻的光照强度和光合作用速率，或者温度和水蚤的心率。相关系数告诉我们两个变量在多大程度上遵循直线趋势。
In biology, correlation is often used in preliminary investigations and in ecological surveys where controlled experiments are difficult. It helps identify relationships that may deserve further experimental testing. However, correlation alone is never enough to establish a biological mechanism.
在生物学中，相关性常用于难以进行受控实验的初步研究和生态调查。它有助于识别值得进一步实验检验的关系。然而，仅凭相关性永远不足以确定生物学机制。
2. Direction and Types of Correlation | 相关的方向与类型
A positive correlation means that as one variable increases, the other variable also tends to increase. For example, increasing light intensity up to the light-saturation point generally increases the rate of photosynthesis. A negative correlation means that as one variable increases, the other tends to decrease, such as the relationship between water temperature and dissolved oxygen concentration.
正相关意味着当一个变量增加时，另一个变量也倾向于增加。例如，在达到光饱和点之前，增加光照强度通常会提高光合作用速率。负相关意味着当一个变量增加时，另一个变量倾向于减少，例如水温和溶解氧浓度之间的关系。
Zero correlation means there is no apparent linear relationship between the two variables. The points on a scatter diagram appear randomly scattered. It is important to note that zero correlation only means no linear relationship; there may still be a strong curved or non-linear relationship.
零相关意味着两个变量之间没有明显的线性关系。散点图上的点看起来随机分布。重要的是要注意，零相关仅表示没有线性关系；仍可能存在很强的曲线或非线性关系。
- Positive correlation: r > 0 | 正相关：r > 0
- Negative correlation: r < 0 | 负相关：r < 0
- No linear correlation: r ≈ 0 | 无线性相关：r ≈ 0
3. Strength of Correlation and Scatter Plots | 相关强度与散点图
The strength of a correlation is shown by how close the data points lie to a straight line. A coefficient of +1 indicates a perfect positive correlation; all points lie exactly on an upward straight line. A coefficient of −1 indicates a perfect negative correlation; all points lie exactly on a downward straight line. Values close to 0 indicate weak or no linear correlation.
相关强度通过数据点靠近直线的程度来体现。系数 +1 表示完全正相关；所有点都恰好落在向上的直线上。系数 −1 表示完全负相关；所有点都恰好落在向下的直线上。接近 0 的值表示弱相关或无线性相关。
On a scatter diagram, the independent variable is plotted on the x-axis and the dependent variable on the y-axis. A line of best fit should only be drawn when the relationship appears linear. The spread of points around this line gives a visual impression of the strength of correlation before any calculation is performed.
在散点图上，自变量绘制在 x 轴，因变量绘制在 y 轴。只有当关系看起来呈线性时，才应绘制最佳拟合线。点围绕这条线的分散程度可以在计算之前直观地显示相关强度。
4. Pearson and Spearman Coefficients | 皮尔逊与斯皮尔曼系数
Pearson’s product-moment correlation coefficient, denoted r, uses the actual measured values. It assumes that both variables are continuous, approximately normally distributed, and have a linear relationship. Pearson’s r is sensitive to outliers because raw values are used in the calculation.
皮尔逊积矩相关系数，记作 r，使用实际测量值。它假设两个变量都是连续的、近似正态分布的，并且具有线性关系。由于计算中使用原始值，皮尔逊 r 对异常值很敏感。
Spearman’s rank correlation coefficient, denoted rₛ, uses the ranks of the data rather than the raw values. It is a non-parametric test, meaning it does not require normally distributed data. Spearman’s rank is more suitable for small biological samples, data with outliers, or a monotonic but not strictly linear relationship.
斯皮尔曼等级相关系数，记作 rₛ，使用数据的等级而不是原始值。它是一种非参数检验，意味着不要求数据呈正态分布。斯皮尔曼等级相关更适合小样本生物数据、含有异常值的数据，或单调但并非严格线性的关系。
For most Cambridge A-Level Biology practical tasks, Spearman’s rank is the preferred choice because biological data are often not normally distributed and the sample size is small.
对于大多数剑桥 A-Level 生物实验任务，斯皮尔曼等级相关是首选，因为生物数据往往不呈正态分布，且样本量较小。
5. Spearman Rank Calculation | 斯皮尔曼等级相关计算
The calculation of Spearman’s rank correlation coefficient follows a clear sequence of steps. First, state the null hypothesis H₀: there is no significant correlation between the two variables. The alternative hypothesis H₁ states that a positive or negative correlation exists.
斯皮尔曼等级相关系数的计算遵循清晰的步骤。首先，陈述零假设 H₀：两个变量之间没有显著相关性。备择假设 H₁ 表明存在正相关或负相关。
- Rank each variable separately, giving rank 1 to the smallest value, rank 2 to the next smallest, and so on. | 分别对每个变量进行排序，最小值给等级 1，次小值给等级 2，依此类推。
- For tied values, assign the average of the ranks they would have occupied. | 对于并列值，分配它们本应占据的等级的平均值。
- Calculate d = rank of x − rank of y for each pair. | 计算每对数据的 d = x 的等级 − y 的等级。
- Square each d to obtain d², then sum to find Σd². | 将每个 d 平方得到 d²，然后求和得到 Σd²。
- Substitute into the formula. | 代入公式。
rₛ = 1 − (6 × Σd²) ÷ [n(n² − 1)]
Here, n is the number of paired observations. The coefficient rₛ always lies between −1 and +1. After calculating rₛ, compare it with a critical value for the chosen significance level, usually p = 0.05.
这里 n 是配对观测值的数量。系数 rₛ 始终在 −1 和 +1 之间。计算 rₛ 后，将其与所选显著性水平（通常 p = 0.05）的临界值进行比较。
6. Worked Example: Light Intensity and Photosynthesis | 实例：光强度与光合作用
A student investigated the relationship between light intensity and the rate of oxygen production in a submerged aquatic plant. The data are shown in Table 1. The light intensity values are already arranged from smallest to largest, so their ranks are 1 to 8. The oxygen production values are ranked separately.
一名学生研究了光照强度与沉水植物产氧速率之间的关系。数据见表 1。光照强度值已按从小到大排列，因此其等级为 1 到 8。产氧速率值单独进行排序。
Table 1. Raw data, ranks, differences and squared differences | 表 1. 原始数据、等级、差值及差值平方
| Light intensity / lux | 光照强度 / lux | O₂ production / cm³ min⁻¹ | 产氧速率 / cm³ min⁻¹ | Rank x | x 等级 | Rank y | y 等级 | d = Rank x − Rank y | d = x 等级 − y 等级 | d² |
|---|---|---|---|---|---|
| 100 | 2.0 | 1 | 1 | 0 | 0 |
| 200 | 3.8 | 2 | 2 | 0 | 0 |
| 300 | 5.5 | 3 | 3 | 0 | 0 |
| 400 | 7.2 | 4 | 5 | 更多咨询请联系16621398022（同微信）
CommentsMore posts |
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply