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Edexcel IAL Biology • Unit 6: Practical Skills in Biology II
The t-test: Comparing Two Means
⚖️ Big idea: The t-test answers one question: is the difference between two means bigger than the variation within the groups would lead you to expect by chance? A large difference between noisy groups may mean nothing; a small difference between consistent groups can be highly significant.
Summary — What This Topic Covers
When a t-test is the right test — and when it is not
The null hypothesis and what it means to reject it
Calculating degrees of freedom and reading the critical value
Comparing calculated t with the critical value at p = 0.05
Writing the conclusion in the form examiners expect
1. When to Use It
Use a t-test when
you are comparing the means of two groups of continuous measurements, the data is roughly normally distributed, and the samples are reasonably sized (about n ≥ 10 each is a sensible target).
✓ mean shell height of snails from two shores
✓ mean leaf area in sun and shade
✓ mean reaction time before and after caffeine
✗ numbers of each phenotype in a cross → chi-squared
✗ whether height and mass are related → Spearman's rank
✗ three or more groups compared at once → beyond this course
The commonest wrong choice
Using a t-test on counts in categories. Counts of phenotypes, or numbers of organisms in habitat types, are frequency data — that is chi-squared.
2. The Null Hypothesis
Key Term
The null hypothesis (H₀) states that there is no significant difference between the two means, and that any difference observed is due to chance.
The test never proves your idea correct. It only tells you whether the null hypothesis can be rejected. Everything is phrased in those terms, and marks are awarded for phrasing it correctly.
H₀ there is no significant difference between the mean shell heights
of snails from the two shores
reject H₀ → there IS a significant difference
accept H₀ → no significant difference was demonstrated
(NOT "the means are the same")
The wording that costs marks
Failing to reject H₀ does not prove the means are equal — it means you did not find enough evidence that they differ. Write "no significant difference was found", never "there is no difference".
3. Degrees of Freedom and the Critical Value
Degrees of freedom
For an unpaired t-test comparing two groups: df = n₁ + n₂ − 2
group 1: n = 12 group 2: n = 10
df = 12 + 10 − 2 = 20
read the critical value from the table at df = 20, p = 0.05
critical value = 2.086
Why p = 0.05
It is the agreed threshold in biology: a 5 % probability that a difference this large could have arisen by chance. Below that, the result is called significant.
4. Comparing and Concluding
The decision
If calculated t ≥ critical value: reject H₀ — the difference is significant at p = 0.05.
If calculated t < critical value: accept H₀ — no significant difference was found.
WORKED CONCLUSION
calculated t = 2.94
df = 20
critical value = 2.086 at p = 0.05
2.94 > 2.086, so the null hypothesis is REJECTED.
"There is a significant difference between the mean shell heights of
snails from the two shores (t = 2.94, df = 20, p < 0.05). The
probability that a difference this large arose by chance is less
than 5 %."
What mark schemes look for
Four things in the conclusion: the calculated value, the degrees of freedom, the critical value or p, and the decision about H₀ in words. Dropping any one usually costs a mark.
5. What Significance Does Not Mean
Significant does not mean large or important — with a big enough sample, a tiny difference can be significant
Significant does not establish a cause; it says the difference is unlikely to be chance
Not significant does not mean "no difference" — it may mean your sample was too small to detect one
A test cannot rescue a badly designed experiment; if a confounding variable differed between groups, a significant result just means that variable had an effect
Worth remembering
The commonest way to fail to reach significance is too small a sample. If t falls just short, "increase n" is a legitimate and expected suggestion.
Practice Questions
Practice Question 1
State the null hypothesis for an investigation comparing the mean leaf area of a plant grown in sun and in shade.
Practice Question 2
A t-test gives a calculated value of 1.86. The samples were n = 8 and n = 8, and the critical value at p = 0.05 is 2.145. State and explain the conclusion.
Practice Question 3
A student uses a t-test to compare the numbers of woodlice found in damp and dry conditions in a choice chamber. Explain why this is the wrong test.
Practice Question 4
Explain why a statistically significant difference does not necessarily mean the difference is biologically important.
What to Memorise
t-test = two means, continuous dataH₀ = no significant differencedf = n₁ + n₂ − 2p = 0.05 is the thresholdt ≥ critical → reject H₀t < critical → accept H₀Quote t, df, p and the decisionCounts in categories → chi-squaredSignificant ≠ large or important
Concepts Checklist
Exam Tips
What mark schemes look for
The conclusion must contain the calculated value, the degrees of freedom, the critical value or p, and a decision about H₀ in words. All four.
The trap
"There is no difference between the means." Write "no significant difference was found" — failing to reject H₀ is not proof of equality.
Easy marks
Degrees of freedom is n₁ + n₂ − 2, and the table is provided. Two marks for arithmetic and careful reading.
Worth remembering
If t falls just below the critical value, suggesting a larger sample is the expected improvement — small samples are the usual reason for missing significance.