6.2.8 Predicting Inheritance: Chi-squared Test

Question 1

What does chi-squared test do?

Answer 1

A statistical test called the chi-squared test determines whether or not there is a significant difference between the observed and expected results in an experiment
If the difference between results is statistically significant this suggests the presence of a factor that isn’t being accounted for
E.g. linkage between genes
When a difference is not significant, any differences that are observed can be said to be due to chance alone

The chi-squared test is carried out when the data is categorical, i.e. falls into distinct groups

Question 2

How do you calculate it?

Answer 2

Obtain the expected (E) and observed (O) results for the experiment

Calculate the difference between each set of results

Square each difference
It is irrelevant whether the difference is positive or negative

Divide each squared difference by the expected value

Add the resulting values together to get a sum of these answers to obtain the chi-squared value

Question 3

How do you analyse chi-squared values?

Answer 3

To work out what the chi-squared value means we need to compare the chi-squared value to a critical value
The critical value is read from a table of critical values and depends on the probability level used and the degrees of freedom
Biologists generally use a probability level of 0.05 or 5 %
This means that there is only a 5 % probability that any difference between O and E has occurred by chance
The degrees of freedom takes into account the number of comparisons made, and is calculated as follows:
degrees of freedom = number of classes - 1

E.g. if there are 2 phenotypes then 2 - 1 = 1 and there is 1 degree of freedom
When the chi-squared value is compared to the critical value conclusions are drawn as follows:
If the chi-squared value is greater than, or equal to, the critical value then there is a significant difference between observed and expected results
A factor other than chance is causing the difference
The null hypothesis can be rejected
If the chi-squared value is smaller than the critical value then there is no significant difference between observed and expected values
Any differences are due to chance
The null hypothesis is accepted
It is possible to use the critical values table to make an assessment of the probability level at which any difference between observed and expected valued becomes significant, e.g.
A chi-squared value might be smaller than the critical value at a probability level of 0.05, but larger than the critical value at a probability level of 0.1
This would indicate that the probability that any difference is due to chance is between 5 -10 %
A chi-squared value might be larger than the critical value at a probability level of 0.001
This indicates that there is a less than 0.1 % probability that any difference between O and E is due to chance