Statistical analysis in ecology (t-test, Spearman, Pearson, Simpson index, mark-release-recapture)

Biology· Unit 19: Biodiversity, Classification, Conservation and Genetic Technology· 12 min read

1. Test Selection for Ecological Datasets★★☆☆☆⏱ 10 min

CIE exam questions frequently require you to justify your choice of statistical test for a given scenario, rather than just performing calculations. The first step is to identify if you are comparing two groups, testing for correlation, measuring diversity, or estimating population size.

Scenario	Appropriate Test
Compare mean plant height in shaded vs sunlit sites	Unpaired t-test
Test if soil pH correlates with lichen coverage	Spearman's Rank
Test if temperature correlates with metabolic rate	Pearson Correlation
Quantify diversity of insect species in a meadow	Simpson's Index
Estimate total rabbit population in a woodland	Mark-Release-Recapture

📐 Worked Example

A student collects data on number of earthworms in 10 quadrats from a pasture and 10 quadrats from an arable field. Select the correct statistical test and justify your choice.

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Step 1: Identify the two independent groups: pasture and arable field earthworm counts
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Step 2: Confirm you are comparing the mean of two unrelated datasets
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Step 3: Select unpaired t-test, as it is designed to test for significant difference between two independent sample means

✓ Quick check

Test your understanding of test selection

Which test is most appropriate for measuring correlation between percentage vegetation cover and distance from a river?
- A) Unpaired t-test
- B) Spearman's Rank
- C) Simpson's Index
- D) Mark-Release-Recapture
Reveal answer
B —
Spearman's rank is ideal for non-linear transect data that is not normally distributed.

Exam tip:

Always state your justification for test selection explicitly in exams, even if not asked directly, to earn full method marks.

2. Unpaired t-test for Habitat Comparison★★★☆☆⏱ 12 min

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📘 Definition

Unpaired t-test

t = \frac{|\bar{x_1} - \bar{x_2}|}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}

Calculates the difference between two sample means relative to the spread of the data

Example:

Comparing mean species richness of two different woodland sites

📐 Worked Example

Sample 1 mean = 12, variance = 3, n=10; Sample 2 mean = 8, variance = 2, n=10. Calculate the t statistic.

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Step 1: Calculate absolute difference between means: |12 - 8| = 4
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Step 2: Calculate denominator: sqrt((3/10)+(2/10)) = sqrt(0.5) ≈ 0.707
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Step 3: Divide difference by denominator: t = 4 / 0.707 ≈ 5.66
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Step 4: Compare to critical t value for 18 degrees of freedom at p=0.05: critical t ≈ 2.10, so result is significant

3. Correlation Tests: Pearson vs Spearman's Rank★★★☆☆⏱ 15 min

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Methods compared

These two correlation tests are often confused, but they have very different use cases in ecology

Pearson Correlation

Requires normally distributed continuous data, measures linear correlation only

+ Pros: Higher sensitivity for linear relationships

− Cons: Gives misleading results for non-linear or skewed data

Spearman's Rank

Non-parametric, ranks data points before calculation, works for ordinal or non-linear data

+ Pros: Robust to outliers, suitable for most field ecology data

− Cons: Less sensitive for perfectly linear normally distributed data

📐 Worked Example

Calculate Spearman's rank for 5 paired data points where sum of squared difference between ranks = 6

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Step 1: Use formula r_s = 1 - \frac{6\sum d^2}{n(n^2 -1)}
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$r_s = 1 - \frac{6 * 6}{5*(25 -1)} = 1 - \frac{36}{120} = 0.7$
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Step 3: Interpret result: strong positive correlation between the two variables

4. Simpson's Diversity Index★★★☆☆⏱ 10 min

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📘 Definition

Simpson's Diversity Index

D = 1 - \frac{\sum n(n-1)}{N(N-1)}

n = number of individuals of each species, N = total number of individuals of all species

Example:

A D value of 0.8 indicates very high diversity, while 0.2 indicates very low diversity dominated by one species

📐 Worked Example

A sample has 3 species: 10 daisies, 5 dandelions, 2 clover. Calculate Simpson's D.

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Step 1: Calculate total N = 10 +5 +2 =17
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Step 2: Calculate sum of n(n-1): 109 +54 +2*1 = 90 +20 +2 =112
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Step 3: Calculate denominator N(N-1) =17*16=272
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Step 4: D = 1 - (112/272) ≈ 0.59, indicating moderate diversity

5. Mark-Release-Recapture Population Estimation★★★★☆⏱ 12 min

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This method for estimating mobile animal populations relies on 3 core assumptions: no births, deaths or migration during the sampling period, marks do not fall off, and marked individuals mix fully back into the population before recapture.

📐 Worked Example

You mark 50 snails, release them, then recapture 40 snails 3 days later, 8 of which are marked. Estimate total population size.

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Step 1: Use formula N = \frac{M * R}{m}, where M = number marked initially, R = total recaptured, m = number of marked recaptured
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$N = \frac{50 * 40}{8} = 250$
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Step 3: Interpret result: estimated total snail population is 250 individuals

6. Common Pitfalls

Wrong move:

Using Pearson correlation for non-linear transect data

Why:

Pearson only measures linear correlation, so it will return artificially low r values for clear non-linear relationships

Correct move:

Use Spearman's rank for all ecological transect data unless you confirm normality and linearity

Wrong move:

Forgetting to compare calculated test statistic to critical value

Why:

You cannot confirm statistical significance without referencing the 95% confidence threshold for your degrees of freedom

Correct move:

Always cross-reference your calculated statistic against the provided critical value table before drawing conclusions

Wrong move:

Calculating Simpson's index for samples with fewer than 10 total individuals

Why:

Small sample sizes skew D to artificially low values that do not reflect real habitat diversity

Correct move:

Collect a sufficiently large representative sample before calculating diversity metrics

Wrong move:

Extending mark-release-recapture sampling over more than 7 days

Why:

Population turnover (births, deaths, migration) breaks the core assumptions of the method

Correct move:

Complete recapture within 48 hours to minimise changes to the population

Wrong move:

Using a paired t-test for two separate independent habitat datasets

Why:

Paired t-test is designed for matched samples from the same site, not two unrelated sites

Correct move:

Use unpaired t-test when comparing biodiversity of two geographically separate locations

7. Quick Reference Cheatsheet

Method	Core Use Case	Key Formula	Significance Rule
Unpaired t-test	Compare two independent sample means	$t = \frac{∣ x _{1} ˉ - x _{2} ˉ ∣}{\frac{s _{1}^{2}}{n _{1}} + \frac{s _{2}^{2}}{n _{2}}}$	Significant if calculated t > critical t at p=0.05
Spearman's Rank	Test correlation for non-linear data	$r_{s} = 1 - \frac{6 \sum d ^{2}}{n ( n ^{2} - 1 )}$	Significant if $r_{s}$ > critical value at p=0.05
Pearson Correlation	Test linear correlation for normal data	$r = \frac{\sum ( x - x ˉ ) ( y - y ˉ )}{s _{x} s _{y}}$	Significant if r > critical value at p=0.05
Simpson's Index	Measure species diversity	$D = 1 - \frac{\sum n ( n - 1 )}{N ( N - 1 )}$	No significance test, D ranges 0 to 1
Mark-Release-Recapture	Estimate mobile population size	$N = \frac{M * R}{m}$	No significance test, estimate only

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2024 · Paper 4
Simpson's index calculation for two habitats
2023 · Paper 5
t-test for comparing pollinator abundance
2022 · Paper 3
Mark-release-recapture practical planning

What's Next

Mastering these statistical methods is critical for scoring full marks on Paper 5 practical analysis questions, which make up 20% of your total A Level Biology grade. You will now be able to confidently answer questions that ask you to justify test selection, perform calculations, and draw valid conclusions from field ecology data. Next, you can build on this knowledge by exploring how to design a full controlled ecological investigation, and learn to identify sources of error in field sampling that skew your statistical results. You will also connect these methods to broader biodiversity conservation assessments, where Simpson's index is routinely used to measure the impact of habitat restoration projects.