• 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 ?x? and y? (means of?x?and?y)

Step 3:?Calculate nx?y?

Step 4:?Find?∑xy

Step 5:?Calculate?standard?deviation?for each set of data Sx??and Sy

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?= nx?y? = 2060
  • Sx?= 2.16 and Sy?= 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