Pearson Linear Correlation Analysis | 皮爾遜線性相關分析

📚 Pearson Linear Correlation Analysis | 皮爾遜線性相關分析

A-Level Biology requires handling data from experiments, and often we need to know whether two variables are related. Pearson’s correlation coefficient (r) is a statistical tool used to measure the strength and direction of a linear relationship between two continuous variables. In this article, we will explore how to calculate and interpret r, test its significance, and avoid common errors.

在A-Level生物學中，我們經常需要處理實驗數據，並判斷兩個變量之間是否存在關係。皮爾遜相關係數（r）是用來衡量兩個連續變量之間線性關係強度和方向的統計工具。本文將探討如何計算和解釋 r、檢驗其顯著性，以及避免常見錯誤。

1. Why Correlation in Biology? | 生物學中為何需要相關分析？

Biologists frequently collect paired measurements to investigate whether a change in one variable is associated with a change in another. For example, an ecologist might measure the feeding time and body mass of birds, or a biochemist might record enzyme activity at different substrate concentrations. Correlation analysis transforms a scatter graph into a single number that summarises the relationship.

生物學家經常收集成對的測量數據，以考察一個變量的變化是否與另一個變量的變化相關。例如，生態學家可能測量鳥類的進食時間與體重，或者生物化學家記錄不同基質濃度下的酶活性。相關分析將散點圖轉化為一個數字，用於概括這種關係。

• Is plant height correlated with root length?

  植物高度是否與根長度相關？

• Is the heart rate of Daphnia correlated with water temperature?

  水蚤的心率是否與水溫相關？

2. Visualising Relationships: Scatter Plots | 可視化關係：散點圖

Before calculating Pearson’s r, always draw a scatter plot. On the x-axis place the explanatory or independent variable and on the y-axis the response variable. The pattern of points reveals whether the relationship is linear, curved, or absent.

在計算皮爾遜 r 之前，請先繪製散點圖。將自變量（解釋變量）放在 x 軸上，因變量（響應變量）放在 y 軸上。點的分布模式可以顯示關係是線性、曲線還是不存在。

If the points rise from left to right, the correlation is positive; if they fall, it is negative. A horizontal cloud of points suggests no linear correlation. One distant point (an outlier) can strongly inflate or deflate r, so it must be checked for measurement errors.

如果點從左向右上升，則呈正相關；如果下降，則是負相關。水平分布的點表明沒有線性相關。一個遠離主群的異常點（離群值）可能極大地增大或減小 r，因此需要檢查是否為測量錯誤。

3. Pearson’s Correlation Coefficient: Definition | 皮爾遜相關係數：定義

Pearson’s correlation coefficient, written as r, measures the strength and direction of the linear relationship between two continuous variables. It has no units and always lies between -1 and +1.

皮爾遜相關係數（記為 r）衡量兩個連續變量

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