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18.2.617-18 · Selection, Evolution, Classification and Conservation

Spearman’s Rank Correlation — Cambridge AS & A Level Biology 9700 Revision Notes & Topical Questions

5 min read 10 parts Lesson 28 of 36 Unit quiz

📚 Cambridge AS & A Level Biology 9700 Hub / Topical Revision
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18.2.6 Spearman's Rank Correlation — CAMBRIDGE AS & A LEVEL BIOLOGY 9700 — REVISION NOTES notes: Use Spearman's rank correlation to test for correlation when data are ranked, non-linear or not normally distributed.Spearman's rank correlation — a test for correlation between two v…

  • Critical value
  • Null hypothesis
  • Abundance scale
  • Biodiversity
  • Population
  • Spearman's rank correlation — a test for correlation between two variables

Section 1 of 10When to use Spearman's rank

Spearman's rank correlation
  • Spearman's rank correlation a test for correlation between two variables.
It is used when:
  • The data are not quantitative, e.g. an abundance scale is used rather than counts.
  • A visual inspection suggests a non-linear relationship.
  • The data may not be normally distributed.
It is often used for abiotic-factor investigations, e.g. abundance of limpets against distance from the sea.
It uses ranks, whereas Pearson's test uses the actual values and needs normality.

Section 2 of 10Method

1
Create a scatter graph to look for a possible correlation.
2
State a null hypothesis, e.g. there is no correlation between the abundance of species C and D.
3
Rank each set of data, with rank 1 for the smallest value; tied values take the mean of the ranks they share.
4
Find the difference in rank (D) between each pair of values.
5
Square each difference (D2) and add them to give ΣD2.
6
Substitute into the formula to calculate rs.
7
Compare rs with the critical value for n pairs at the 0.05 probability level.

Section 3 of 10The formula

The formula
rs = 1 − 6ΣD2 ÷ (n3 − n)
  • rs = Spearman's rank coefficient.
  • D = difference in rank.
  • n = number of samples (pairs).
rs lies between −1 and +1, interpreted like Pearson's r.
The formula is given in the exam but the calculation must be done.

Section 4 of 10Using the critical value table

1
The table relates critical values of rs to levels of probability, indexed by the number of pairs n (not by degrees of freedom).
  • At p = 0.05 with n = 10 the critical value is 0.65.
2
If the calculated rs is greater than the critical value at p = 0.05, the null hypothesis is rejected and there is a correlation.
3
If it is smaller, the null hypothesis is accepted and any correlation could be due to chance.
4
Small samples need a very high rs to be significant, so more pairs give the test greater power.

Section 5 of 10Interpreting the result

1
The sign shows direction: positive means both variables rise together, negative means one falls as the other rises.
2
The size shows strength.
3
Write the conclusion in context, e.g. a significant negative correlation between distance from the shore and limpet number.
4
There is less than a 5% probability that a significant correlation arose by chance.
5
Correlation does not mean causation: species C might not cause the presence of species D.
6
Control or measure other variables such as light or soil pH before claiming a cause.

Section 6 of 10Limitations of the test

1
Ranks lose information about the size of differences between values.
2
Tied ranks reduce accuracy.
3
The relationship should be consistently rising or falling (monotonic); it is unsuitable for U-shaped relationships.
4
Draw a scatter graph first to check the pattern.

Section 7 of 10Practical use in transect investigations

1
Place quadrats at regular intervals along a belt transect.
2
Count (or estimate the abundance of) one species in each quadrat.
3
Measure an abiotic factor, e.g. soil moisture, at each quadrat.
4
Rank both sets of values and calculate rs.
5
State whether the null hypothesis is rejected and interpret the result in context.

Section 8 of 10More from the specification

Ecological niche abundance ranking
  • Ecological niche abundance ranking ranking species abundances across environmental gradients provides quantitative correlation analysis for specific ecological niche occupancy.
Spearman's rank correlation test
  • The Spearman's rank correlation coefficient (rs = 1 - (6 * Sigma d2 / (n(n2 - 1))) tests for monotonic relationships between two ranked ecological or biological variables.
Simpson's index of biodiversity
  • Simpson's index (D = 1 - Sigma (n/N)2 quantifies community biodiversity by accounting for both species richness and relative species evenness.
    • (number of species)
Significance testing against critical values
  • Calculated test statistics are compared with statistical critical values at the p = 0.05 probability threshold to reject or retain null hypotheses.
Mark-release-recapture method
  • Mark-release-recapture method estimates mobile animal population sizes by capturing, marking,
    • and releasing individuals to calculate Lincoln index ratios.
Simpson's index of diversity
  • Simpson's index of diversity quantifies ecosystem species richness and evenness, with values closer to 1 indicating higher biodiversity.
Random ecological sampling
  • Random ecological sampling using random coordinates to place sample quadrats ensures unbiased estimation of organism abundance across ecosystems.
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.
Complex
  • Two or more molecules joined, such as an antibody and antigen.
Habitat
  • The place where an organism lives.
Random sampling
  • Sampling in which positions are decided by chance, avoiding bias.
Percentage cover
  • Percentage of a quadrat covered by a species.
Genetic diversity
  • The range of alleles within a population.
Statistical test
  • Test to see if a result is significant or due to chance
Standard deviation
  • Measure of spread around the mean.
Species richness
  • The number of species in an ecosystem.
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.

Section 9 of 10Key terms

TermMeaning
Spearman's rank correlationTest for correlation using ranks, for non-linear or non-normal data.
RankPosition of a value when data are ordered, with 1 for the smallest.
DDifference in rank between paired values.
Critical valueTable value that rs must exceed for significance at p = 0.05.
Null hypothesisStatement that there is no correlation between the variables.
Abundance scaleA scale of estimated abundance used instead of counts.

Section 10 of 10Exam technique

1
Using the table of critical values with degrees of freedom — Spearman's table is indexed by n, the number of pairs.
2
Ranking from the largest value as 1 in one data set and the smallest in the other — rank both the same way.
3
Concluding causation from a significant correlation.
4
Using Spearman's rank without checking the scatter graph for a consistent trend.

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