Pearson's Linear Correlation (CIE A Level Biology)

• 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 on, 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 1.0 or -1.0
• 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

Types of Correlation Sketch Graphs

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, e.g. the number of individuals has been counted and a numerical value recorded
  • Show a linear relationship upon visual inspection
  • Show a 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:

• r = correlation coefficient
• x =  number of species A
• y = number of species B
• n = number of readings
• S_x = standard deviation of species A
• S_y = standard deviation of species B
• x̄= mean number of species A
• ȳ= mean number of species B

• If the correlation coefficient r is close to 1.0 or -1.0 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 (these are the 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 strong positive correlation between the abundance of species A and species B