PapaMarks
Library › Biology 6 (IAL) WBI16 › Chi-squared: Observed vs Expected
A2 Level · Biology 6 (IAL) WBI16

Chi-squared: Observed vs Expected

Revise Chi-squared: Observed vs Expected for Biology 6 (IAL) WBI16 (A2 Level) — revision notes and instant AI marking.

📖 Revision notes · preview
Edexcel IAL Biology  •  Unit 6: Practical Skills in Biology II

Chi-squared: Observed vs Expected

🎲 Big idea: Chi-squared asks whether the counts you got are far enough from the counts you predicted to rule out chance. A 9:3:3:1 cross never comes out exactly 9:3:3:1 — the question is whether the deviation is the kind you would expect from sampling, or something the hypothesis cannot explain.

Summary — What This Topic Covers

  • When chi-squared is the right test — and why it needs raw counts
  • Working out expected values from a stated hypothesis
  • The formula, and setting the calculation out in a table
  • Degrees of freedom as categories − 1
  • Writing the conclusion, and what rejecting H₀ actually tells you

1. When to Use It

Use chi-squared when
you have counts (frequencies) in discrete categories, and a hypothesis that predicts what those counts should be.
✓ offspring phenotypes from a genetic cross vs a 9:3:3:1 prediction ✓ woodlice in damp vs dry halves of a choice chamber vs 50:50 ✓ numbers of a species in three habitat types vs an even distribution ✗ mean shell height on two shores → t-test ✗ is height related to mass? → Spearman's rank ✗ percentages, means or rates → chi-squared cannot be used
The absolute requirement
Chi-squared works on raw counts. 60 % could be 6 out of 10 or 600 out of 1000 — utterly different χ² values. If you recorded percentages, the data cannot be tested and cannot be recovered.
The other condition
No expected value should be less than 5. If one is, categories must be combined or a larger sample taken.

2. Working Out the Expected Values

Expected values come from the hypothesis, applied to your actual total.

A dihybrid cross predicts 9 : 3 : 3 : 1. Total offspring = 160. total ratio parts = 9 + 3 + 3 + 1 = 16 one part = 160 ÷ 16 = 10 expected: 9 × 10 = 90 3 × 10 = 30 3 × 10 = 30 1 × 10 = 10 the expected values must always ADD UP to the observed total
Easy marks
Check that your expected values sum to the same total as your observed values. If they do not, you have made an arithmetic error, and the check takes five seconds.

3. The Calculation

The formula
χ² = Σ [ (O − E)² ÷ E ]

where O is the observed count and E the expected count, summed across all categories.
category O E O − E (O − E)² (O − E)² ÷ E ────────────────────────────────────────────────────────────── round yellow 95 90 +5 25 0.278 round green 28 30 −2 4 0.133 wrinkl yellow 30 30 0 0 0.000 wrinkl green 7 10 −3 9 0.900 ────────────────────────────────────────────────────────────── totals 160 160 χ² = 1.311
What mark schemes look for
Set the working out as a table with these columns. Marks are given for the table structure and the intermediate values, not only for the final χ².

4. Degrees of Freedom and the Decision

Degrees of freedom
df = number of categories − 1

Four phenotypes gives df = 3. Two categories in a choice chamber gives df = 1.

5. Writing the Conclusion

Practice Questions

Practice Question 1
Practice Question 2

Explain why a chi-squared test cannot be carried out on data recorded as percentages.

Practice Question 3
🔓 Read the full Chi-squared: Observed vs Expected note → You're seeing the preview · sign in to read it all
Also in the full note
  • What to Memorise
  • Concepts Checklist
  • Exam Tips
What's inside
📖 Revision notes 🎯 Learn mode ✦ AI flashcards ✓ Instant AI marking 🧊 3D explorers 🧪 Experiments & simulations 📈 Progress tracking
📄 Practise Chi-squared: Observed vs Expected with Biology 6 (IAL) WBI16 past papers Every paper with its mark scheme — answer online, marked instantly. Open →

Read the full Chi-squared: Observed vs Expected notes free

That's the preview — create a free account to read the rest, plus flashcards and practice questions with instant AI marking. No credit card.

Unlock the full notes free →

More Biology 6 (IAL) topics

Techniques for the A2 Core Practicals
Respirometry & Respiratory Quotient
Designing a Whole Investigation
Aseptic Technique & Culturing Microorganisms
Planning & Analysing Whole Investigations
Uncertainty, Statistics & Evaluation
Chromatography & Photosynthetic Pigments
Quadrats, Transects & Field Sampling
Measuring Rates: Enzymes, Growth & Photosynthesis
Standard Deviation, Standard Error & Error Bars