Testing deviations from Mendel

What is linkage?

When alleles of 2 genes are on the same chromosome.

• They cannot segregate independently, i.e. they cannot move to opposite poles of the cell at meiosis.

• There is a higher probability of these alleles being inherited together.

Why may you expect large differences in observed ratios compared to the ratios you would expect?

Because fertilisation is random i.e. independent assortment, crossing over etc.

What is the Chi squared (X²) test?

The Chi squared (X²) test is a statistical test that can be used to compare your observed results with expected results and determine if the difference between observed and expected results is due to chance or not.

When is the Chi squared test used?

• the data is nominal / discrete – i.e. can be given categories such as different phenotypes

• you have actual observations rather than percentages or fractions.

• you can calculate expected values, e.g., based on a Mendelian ratio.

State the null hypothesis used in a chi squared test.

There is no significant difference between the observed and the expected results.

In genetics, a null hypothesis states that the observed results are due to Mendelian inheritance and that any deviation from the expected ratio is due to chance.

Describe how you would carry out a chi squared test.

• Calculate the expected values (E) based on the expected ratio of 9:3:3:1.

• For each phenotype, calculate (O-E), i.e. the differences between the observed and the expected values.

• For each phenotype, square the differences to calculate (O-E)².

• For each phenotype, divide (O-E)² by E, the expected value.

• Add up all the values of (O-E)² / E to find the chi squared value.

How do you calculate the degrees of freedom in a chi squared test?

1. Decide how many sets of data (number of different phenotypes) you have.

   = n

The degrees of freedom is:
df= n-1

What probability is used in a chi squared test?

5% (0.05)

How do you find the critical value in a chi squared test?

You find the critical value for Chi² by using a probability table;

Find the number of degrees of freedom and the 0.05 probability and this gives you the critical value for Chi².

If the chi squared value lies to the LEFT of the critical value, the null hypothesis is…?

Accepted.

If the chi squared value lies to the RIGHT of the critical value, the null hypothesis is…?

Rejected.

What does it mean if the null hypothesis is rejected?

There IS a significant difference between the observed and expected values; any differences is NOT due to chance alone.