18.2.517-18 · Selection, Evolution, Classification and Conservation
Pearson’s Linear Correlation — Cambridge AS & A Level Biology 9700 Revision Notes & Topical Questions
5 min read 10 parts Lesson 27 of 36 Unit quiz
Lesson summary
18.2.5 Pearson's Linear Correlation — CAMBRIDGE AS & A LEVEL BIOLOGY 9700 — REVISION NOTES notes: Explain correlation and use Pearson's linear correlation coefficient to test for a linear relationship.Correlation — an association or relationship between two variables.Correlation …
- Positive correlation
- Negative correlation
- No correlation
- Perfect correlation
- The correlation coefficient (r)
- Conditions
Section 1 of 10Correlation and causation
Correlation
- Correlation an association or relationship between two variables.
Correlation does not necessarily imply causation.
- Causation occurs when one variable influences, or is influenced by, the other.
Correlation can occur between two species (e.g. always found together) or between a species and an abiotic factor (e.g. a plant and soil pH).
It is analysed with scatter graphs and statistical tests.
Section 2 of 10Types of correlation on scatter graphs
Types of correlation on scatter graphs
Plot both variables on a scatter graph for a broad overview.
Positive correlation
- Positive correlation as variable A increases, variable B increases.
Negative correlation
- Negative correlation as variable A increases, variable B decreases.
No correlation
- No correlation the points show no pattern and r is about 0.
Perfect correlation
- Perfect correlation all points lie on a straight line, r = +1.0 or −1.0.
A cloud of points with a clear straight-line trend suggests the data are suitable for Pearson's test; curved trends are not.
Section 3 of 10The correlation coefficient
The correlation coefficient
The correlation coefficient (r)
- The correlation coefficient (r) indicates the strength and direction of a relationship between variables.
- r lies between −1.0 and +1.0.
- A value near ±1.0 shows strong correlation; a value near 0 shows none.
Pearson's linear correlation
- Pearson's linear correlation a statistical test for whether there is a linear correlation between two variables.
The data must meet these conditions:
- Quantitative, e.g. numbers of individuals counted.
- A linear relationship on visual inspection.
- A normal distribution.
Section 4 of 10Method for Pearson's test
1
Plot a scatter graph of the data and check that a linear correlation exists.
2
State the null hypothesis, e.g. there is no correlation between the abundance of species A and B.
3
Calculate the mean and standard deviation of each variable (x̄, ȳ, sx, sy).
4
Calculate Σxy and n x̄ ȳ.
5
Substitute into r = (Σxy − n x̄ ȳ) ÷ ((n − 1) sx sy).
6
Compare r with ±1 (or the critical value) and state the conclusion.
Section 5 of 10Meaning of the symbols
1
r = correlation coefficient.
2
x and y = the paired values of the two variables, e.g. numbers of species A and B in a quadrat.
3
n = number of paired readings.
4
sx and sy = standard deviations of x and y.
5
x̄ and ȳ = means of x and y.
6
The formula is given in the exam, but you must be able to do the calculation.
Section 6 of 10Interpreting the result
1
If r is close to +1.0 or −1.0 there is a strong linear correlation and the null hypothesis can be rejected.
- A positive r means one variable rises as the other rises.
- A negative r means one variable falls as the other rises.
2
A r value near 0 means no linear relationship and the null hypothesis is retained.
3
Large samples make significance easier to show; very small samples need r close to ±1.
4
Even a strong correlation does not prove one variable causes the other.
- A third variable may influence both.
Section 7 of 10Choosing the correct test
| Situation | Test |
|---|---|
| Quantitative, linear, normally distributed pairs of data | Pearson's linear correlation |
| Ranked, non-linear or non-normal data | Spearman's rank correlation |
| Comparing the means of two samples | t-test |
| Comparing observed with expected counts in categories | Chi-squared |
Section 8 of 10More from the specification
More from the specification
Abiotic factors and niche limits
- Abiotic factors and niche limits evaluating Pearson correlation coefficients quantifies relationships between physical environmental variables and organism niche occupancy.
Percentage cover
- Percentage of a quadrat covered by a species.
Genetic diversity
- The range of alleles within a population.
Species richness
- The number of species in an ecosystem.
Systematic sampling
- Sampling in which positions are chosen by the investigator or at regular intervals.
Lincoln index
- N = n1 × n2 ÷ m2, the estimate of population size from mark-release-recapture.
Ecosystem
- Community plus environment.
Organism
- A living thing, such as a plant or an animal.
Biodiversity
- The number of different species in an area.
Population
- A group of organisms of one species in the same area at the same time.
Complex
- Two or more molecules joined, such as an antibody and antigen.
Habitat
- The place where an organism lives.
Species diversity
- Number of species and the evenness of their abundance.
Random sampling
- Sampling in which positions are decided by chance, avoiding bias.
Conditions
- Pearson's test suits data that show a linear scatter, have no major outliers and are roughly normally distributed.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Correlation | An association or relationship between two variables. |
| Causation | One variable having an influence on another. |
| Correlation coefficient (r) | Measure of the strength and direction of a relationship, from −1 to +1. |
| Pearson's linear correlation | Test for linear correlation between two quantitative, normally distributed variables. |
| Positive correlation | As one variable increases, the other increases. |
| Negative correlation | As one variable increases, the other decreases. |
| Null hypothesis | Statement that there is no correlation between the variables. |
Section 10 of 10Exam technique
1
Saying correlation proves causation — it only shows an association.
2
Using Pearson's test on ranked or non-normal data — use Spearman's rank instead.
3
Using Pearson's test on a curved relationship — the test measures only linear correlation.
4
Forgetting to state a null hypothesis before the test.
5
Taking r = 0 as a perfect relationship — r = 0 means no linear correlation.
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