📚 Spearman's Rank Correlation | 斯皮尔曼等级相关系数
Correlation analysis is used in biology to test whether two variables are associated. Spearman's rank correlation coefficient, rₛ, is a non-parametric test that measures the strength and direction of a monotonic relationship between two ranked variables without assuming normal distribution.
在生物学中，相关性分析用于检验两个变量之间是否存在关联。斯皮尔曼等级相关系数 rₛ 是一种非参数检验，用于衡量两个等级变量之间单调关系的强度和方向，无需假设数据呈正态分布。
1. What is Spearman's Rank Correlation? | 什么是斯皮尔曼等级相关？
Spearman's rank correlation coefficient, denoted rₛ or ρ, is a non-parametric test that measures the strength and direction of association between two variables. Instead of using the original measurements, the test ranks each variable separately and then compares the ranks. This makes it useful when data are ordinal, skewed, or contain outliers.
斯皮尔曼等级相关系数记作 rₛ 或 ρ，是一种非参数检验，用于衡量两个变量之间关联的强度和方向。该检验不对原始测量值进行分析，而是分别对每个变量排序，再比较秩次，因此特别适用于顺序数据、偏态数据或含异常值的数据。
2. When to Use Spearman's Rank in Biology | 在生物学中何时使用斯皮尔曼等级相关
In biology, many data sets are not normally distributed. Examples include percentage cover, abundance counts, behavioural scores, and subjective indices. Spearman's rank is appropriate when the relationship is monotonic, meaning that as one variable increases, the other tends to increase or decrease consistently, but not necessarily at a constant rate.
在生物学中，许多数据集并不呈正态分布，例如盖度百分比、多度计数、行为评分和主观指数。当变量之间存在单调关系（即一个变量增大时，另一个变量总体趋势是持续增大或减小，但不必以恒定速率变化）时，斯皮尔曼等级相关是合适的方法。
3. Null and Alternative Hypotheses | 零假设与备择假设
. The alternative hypothesis H₁ can be directional: rₛ > 0 for positive correlation or rₛ < 0 for negative correlation; or non-directional: rₛ ≠ 0. The choice of one-tailed or two-tailed test changes the critical value used.
对于相关性检验，零假设 H₀ 指出总体中两个变量之间不存在显著相关，即 rₛ = 0。备择假设 H₁ 可以是方向性的：rₛ > 0 表示正相关，rₛ < 0 表示负相关；也可以是非方向性的：rₛ ≠ 0。选择单尾还是双尾检验会改变所使用的临界值。
4. Formula and Notation | 公式与符号
The Spearman rank correlation coefficient is calculated using the formula:
rₛ = 1 − (6 Σ d²) / [n(n² − 1)]
where d is the difference between the ranks of each paired observation, Σ d² is the sum of the squared rank differences, and n is the number of paired observations. If tied ranks occur, assign the average of the tied ranks.
斯皮尔曼等级相关系数使用以下公式计算：
rₛ = 1 − (6 Σ d²) / [n(n² − 1)]
其中 d 是每对观测值秩次之差，Σ d² 是秩差平方之和，n 是配对观测值的数量。如果出现并列秩次，应分配并列秩次的平均值。
5. Step-by-Step Calculation | 逐步计算Published by TutorHao | A-Level Biology Revision Series | aleveler.com
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