Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

2.4.6Topic 2 · Genes and Health

Chi-squared Test — Edexcel A Level Biology A (SNAB) 9BI0 Revision Notes & Topical Questions

5 min read 9 parts Lesson 31 of 35 1 quiz

📚 Edexcel A Level Biology A (SNAB) 9BI0 Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

2.4.6 Chi-squared Test — Edexcel A Level Biology A (SNAB) 9BI0 notes: Use the chi-squared test to decide whether the difference between observed and expected results in a genetic cross is significant.A genetic cross predicts a ratio, such as 3:1 or 9:3:3:1, but actual results dif…

  • chi-squared (χ2) test
  • actual counts
  • null hypothesis
  • χ2 = Σ (O − E)2 / E
  • degrees of freedom
  • greater than or equal to

Part 1 of 7Why we need a statistical test

A genetic cross predicts a ratio, such as 3:1 or 9:3:3:1, but actual results differ from the prediction because of chance.

The chi-squared (χ2) test is a statistical test for categorical data that tells us whether the difference between observed and expected frequencies is small enough to be due to chance or large enough to be significant (that is, that some factor,
  • such as linkage or a different mode of inheritance, is involved).
Actual counts
It can only be used on actual counts, not percentages or proportions.

Part 2 of 7The null hypothesis

Before testing, state a null hypothesis: there is no significant difference between the observed and expected results; any difference is due to chance. For example: 'there is no significant difference between the observed numbers of tall and dwarf plants and the numbers expected for a 3:1 ratio'.

Part 3 of 7Carrying out the test

The formula is χ2 = Σ (O − E)2 / E, where O is the observed number and E is the expected number in each category, and Σ means 'sum of'.

Work out the expected numbers from the ratio and the total (E = ratio fraction × total).
Calculate (O − E)2 / E for each category.
Add them to give χ2.
Degrees of freedom
Calculate the degrees of freedom = number of categories − 1.
Compare with the critical value at p = 0.05 (5%).
Degrees of freedomCritical value (p = 0.05)
13.84
25.99
37.82

Part 4 of 7Worked example

A cross of two heterozygous tall plants gives 290 tall and 110 dwarf (total 400). Expected for 3:1: 300 tall and 100 dwarf.

PhenotypeOE(O − E)2 / E
Tall290300100/300 = 0.33
Dwarf110100100/100 = 1.00

χ2 = 1.33. Degrees of freedom = 2 − 1 = 1; critical value 3.84. Since 1.33 is less than 3.84, the null hypothesis is accepted: there is no significant difference, and the difference is due to chance, so the results fit a 3:1 ratio.

Part 5 of 7Interpreting the result

If χ2 is less than the critical value, the probability of the difference being due to chance is greater than 5%, so we accept the null hypothesis: the results are consistent with the expected ratio.

Greater than or equal to
If χ2 is greater than or equal to the critical value, the probability is 5% or less,
  • so we reject the null hypothesis: there is a significant difference, and chance alone is unlikely to explain it.
Possible reasons include a different ratio due to linked genes, lethal alleles, or non-random fertilisation.
Note that p = 0.05 means that there is a 5% probability that the difference is due to chance.

A value above the critical value does not prove which alternative explanation is correct; it only says that the original hypothesis is unlikely to be right.

Part 6 of 7Conditions and links

1
Data must be in categories and be frequencies (counts).
2
Sample sizes should be large enough, with expected values at least 5 in each category.
3
Categories must be mutually exclusive, and the observations independent.
4
The degrees of freedom change with the number of categories: a dihybrid cross with four phenotype classes has 3 degrees of freedom.

The chi-squared test can also be used in ecology to test the association between species or distributions. It links to Mendelian inheritance, to Hardy-Weinberg calculations later in the course, and to the general handling of data and the null hypothesis in practical work.

Check your working by keeping a table with columns for category, observed, expected, O − E, (O − E)2 and (O − E)2/E, which reduces arithmetic mistakes.

Conditions and links
Round to two or three significant figures at the end.
Remember that the expected values must add up to the same total as the observed values, which is a quick check.
In practicals such as counting the offspring of fruit flies, the same approach is used,
  • and in a conclusion you should relate the statistical outcome back to the biology: for instance, accept a 3:1 ratio,
  • which supports a single gene with complete dominance.

Part 7 of 7Exam-style questions

  1. In a dihybrid cross, the offspring were 315 round yellow, 108 round green, 101 wrinkled yellow and 32 wrinkled green (total 556). Expected ratio 9:3:3:1 gives 312.75, 104.25, 104.25 and 34.75. Calculate χ2 and state the conclusion (critical value 7.82 for 3 d.f.). [4]4 marks

  2. Explain what is meant by the null hypothesis in a chi-squared test. [2]2 marks

  3. A calculated χ2 value is 6.2 with 1 degree of freedom. Interpret this value. [3]3 marks

Key terms

TermMeaning
Chi-squared testA statistical test comparing observed and expected frequencies.
Null hypothesisThe statement that there is no significant difference between observed and expected results.
Degrees of freedomThe number of categories minus one.
Critical valueThe value of the test statistic above which the null hypothesis is rejected.
Significant differenceA difference unlikely to be due to chance (p ≤ 0.05).
Observed (O)The actual count obtained.
Expected (E)The count predicted by a ratio.

Avoid these mistakes

1
Using percentages instead of actual numbers in the formula.
2
Using the wrong degrees of freedom (number of categories minus one).
3
Saying that the result proves the hypothesis; a test only supports or rejects the null hypothesis.
4
Concluding the results are significant when χ2 is below the critical value.

Last updated: