# 18.2.5 Pearson's Linear Correlation

### Pearson's Linear Correlation

• When recording the abundance and distribution of species in an area different trends may be observed
• Sometimes correlation between two variables can appear in the data
• Correlation is an association or relationship between variables
• There is a clear distinction between correlation and causation: a correlation does not necessarily imply a causative relationship
• Causation occurs when one variable has an influence or is influenced by, another
• There may be a correlation between species; for example, two species always occurring together
• There may be a correlation between a species and an abiotic factor, for example, a particular plant species and the soil pH
• The apparent correlation between variables can be analysed using scatter graphs and different statistical tests

#### Correlation between variables

• In order to get a broad overview of the correlation between two variables the data points for both variables can be plotted on a scatter graph
• The correlation coefficient (r) indicates the strength of the relationship between variables
• Perfect correlation occurs when all of the data points lie on a straight line with a correlation coefficient of 1 or -1
• Correlation can be positive or negative
• Positive correlation: as variable A increases, variable B increases
• Negative correlation: as variable A increases, variable B decreases
• If there is no correlation between variables the correlation coefficient will be 0
• The correlation coefficient (r) can be calculated to determine whether a linear relationship exists between variables and how strong that relationship is

#### Pearson linear correlation

• Pearson’s linear correlation is a statistical test that determines whether there is linear correlation between two variables
• The data must:
• Be quantitative
• Show normal distribution
•  Method:
• Step 1:  Create a scatter graph of data gathered and identify if a linear correlation exists
• Step 2:  State a null hypothesis
• Step 3:  Use the following equation to work out Pearson’s correlation coefficient r

• If the correlation coefficient r is close to 1 or -1 then it can be stated that there is a strong linear correlation between the two variables and the null hypothesis can be rejected

#### Exam Tip

You will be provided with the formula for Pearson’s linear correlation in the exam. You need to be able to carry out the calculation to test for correlation, as you could be asked to do this in the exam. You should understand when it is appropriate to use the different statistical tests that crop up in this topic, and the conditions in which each is valid.

### Author: Lára

Lára graduated from Oxford University in Biological Sciences and has now been a science tutor working in the UK for several years. Lára has a particular interest in the area of infectious disease and epidemiology, and enjoys creating original educational materials that develop confidence and facilitate learning.
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