18.2.5 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

Different types of correlation in scatter graphs

• 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

• • Where:

• 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

Null hypothesis: There is no correlation between the abundance of species A and species B.

Steps to calculate the correlation coefficient:

Step 1: Calculate xy

Step 2: Calculate  x̅ and y̅ (means of x and y)

Step 3: Calculate nx̅y̅

Step 4: Find ∑xy

Step 5: Calculate standard deviation for each set of data S_x  and S_y

Step 6: Substitute the appropriate numbers into the equation

• • n = 10 as there are 10 quadrat samples.
  • The sum of x x y (∑xy) = 2114
  • n x mean of x x mean of y = nx̅y̅ = 2060
  • S_x = 2.16 and S_y = 3.02
  • Substitute values into the equation above:

• • As the value of r lies close to 1, the null hypothesis can be rejected. There is a positive correlation between the abundance of species A and species B