What is the chi-squared test used for in genetics?

To find whether the difference between the observed numbers of offspring in each class and the numbers expected from a ratio is significant or due to chance.

State the formula for chi-squared and how its degrees of freedom are found.

χ² = Σ(O − E)²/E, where O is observed and E is expected; the degrees of freedom are the number of classes minus one.

State a null hypothesis for a chi-squared test on a monohybrid cross.

There is no significant difference between the observed numbers and those expected from a 3:1 ratio, so any difference is due to chance.

A monohybrid cross gives 140 tall and 60 dwarf plants. Test the fit to a 3:1 ratio (critical value 3.84 at p = 0.05).

Expected values are 150 and 50. χ² = 100/150 + 100/50 = 0.67 + 2.00 = 2.67, which is below 3.84 at one degree of freedom, so the difference is not significant and the null hypothesis is accepted.

A dihybrid cross of 160 offspring gives 95, 28, 27 and 10. Test the fit to 9:3:3:1 (critical value 7.82).

Expected values are 90, 30, 30 and 10. χ² = 25/90 + 4/30 + 9/30 + 0 = 0.71, below 7.82 at three degrees of freedom, so the results fit a 9:3:3:1 ratio.

What does it mean if the calculated chi-squared value exceeds the critical value at p = 0.05?

The probability that the difference arose by chance is less than 5%, so the difference is significant and the null hypothesis is rejected, for example because genes are linked.

CCEA A-Level Biology 1010

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Genes and Patterns of Inheritance

The chi-squared test

3 things to know
Unit A2 2

Overview

The chi-squared formula, expected numbers and degrees of freedom, null hypotheses, and worked tests of monohybrid and dihybrid ratios read against the critical value at p = 0.05.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Process

Why must raw counts rather than percentages be used in a chi-squared test?

Process

Why is the chi-squared test unreliable when expected numbers are very small?

Process

A cross gives 290 tall and 110 dwarf where 3:1 is expected. Is the difference significant?

Questions from this subtopic

Each one with the model answer underneath.

1
What is the chi-squared test used for in genetics?
Model answer
To find whether the difference between the observed numbers of offspring in each class and the numbers expected from a ratio is significant or due to chance.
2
State the formula for chi-squared and how its degrees of freedom are found.
Model answer
χ² = Σ(O − E)²/E, where O is observed and E is expected; the degrees of freedom are the number of classes minus one.
3
State a null hypothesis for a chi-squared test on a monohybrid cross.
Model answer
There is no significant difference between the observed numbers and those expected from a 3:1 ratio, so any difference is due to chance.
4
A monohybrid cross gives 140 tall and 60 dwarf plants. Test the fit to a 3:1 ratio (critical value 3.84 at p = 0.05).
Model answer
Expected values are 150 and 50. χ² = 100/150 + 100/50 = 0.67 + 2.00 = 2.67, which is below 3.84 at one degree of freedom, so the difference is not significant and the null hypothesis is accepted.
5
A dihybrid cross of 160 offspring gives 95, 28, 27 and 10. Test the fit to 9:3:3:1 (critical value 7.82).
Model answer
Expected values are 90, 30, 30 and 10. χ² = 25/90 + 4/30 + 9/30 + 0 = 0.71, below 7.82 at three degrees of freedom, so the results fit a 9:3:3:1 ratio.
6
What does it mean if the calculated chi-squared value exceeds the critical value at p = 0.05?
Model answer
The probability that the difference arose by chance is less than 5%, so the difference is significant and the null hypothesis is rejected, for example because genes are linked.

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