The t-test: Comparing Two Means

Revise The t-test: Comparing Two Means for Biology 6 (IAL) WBI16 (A2 Level) — revision notes, 6 practice questions and instant AI marking.

📖 Revision notes · preview

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 %."

🔓 Read the full The t-test: Comparing Two Means note → You're seeing the preview · sign in to read it all

Also in the full note

Practice Questions
What to Memorise
Concepts Checklist
Exam Tips
5. What Significance Does Not Mean

What's inside

📖 Revision notes ◉ 6 practice questions 🎯 Learn mode ✦ AI flashcards ✓ Instant AI marking 🧊 3D explorers 🧪 Experiments & simulations 📈 Progress tracking