The theory behind the Chi2 test

Most textbooks do a pretty bad job in describing how the Chi² test works and how to apply it.

Here's my first video on the subject.  It goes into the theory behind the Chi² formula and when you would apply the statistic to your data.  The components of the Chi² formula are discussed so you should be able to get an idea what it measures.  

The Chi² test is commonly taught in Genetics courses to give students a tool to assess whether data could belong to particular ratios (e.g. 3:1, 1:2:1, 9:3:3:1). After viewing this video, you should:

•  recognize that the Chi² formula measures deviation of and observed value from a theoretical value for purposes of comparison
• be able to calculate the Chi² score from a set of data
• determine the degrees of freedom for a particular sample 
• be able to reject or fail to reject a set of data from a theoretical population by using the Chi² table

Actually doing the Chi²  test is quite simple.  I'll provide a few examples of calculating the Chi² value and interpreting it using the Chi²  table.

Determining Gene Order

I had a lot of office visits today regarding how to set up the F₁ chromosomes in order to figure out the gene order.  The textbook uses examples where all the wild-type alleles are on one chromosome and all the mutants are on the other.  This is called a coupling arrangement:

e.g.

 a+ b+ c+

==========

 a  b  c

However, it's certainly permissible to have an F₁ organism that has some alleles in repulsion:

e.g. 

 a+ b   c

==========

 a  b+  c+

You should note that in both cases, the genotypes of the F₁ are the same:  they both represent heterozygous creatures.  This will dramatically change the ratios from your testcross and which numbers represent the "parentals" (which actually just give the chromosomes for your F₁).

For the first case (all in coupling), if the het is derived from two true-breeding parentals, they might have the genotypes of:

 a+ b+ c+          a  b  c

==========   x    =========

 a+ b+ c+          a  b  c

The double crossover class from the testcross would be:

 a+ b  c+         a  b+ c

==========  or   ==========

 a  b  c          a  b  c      <=== This came from the testcross parent

For the second (some repulsion), the double crossover classes from the testcross would be:

 a+ b+ c         a  b  c+

=========  or   ==========

 a  b  c         a  b  c      <=== This came from the testcross parent

Here's an exercise to help you with this concept.

A solution is shown below (click on the YouTube icon to go to the YouTube site so you can view it in full screen and high definition).

Solving Pedigrees - Now testing for X-linkage!

Here are those same two pesky pedigrees from before.  In the previous post you had a chance to determine whether the mutant allele was dominant or recessive to wild-type.

 The one above MUST be recessive because two unaffected parents produced affected children.  Now try it with X-linkage.  You can use the symbols X^r and X^R to denote a recessive mutant allele and the dominant wild-type allele, respectively.  Here's a solution:

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And as for this one, we can't rule out dominant so easily!  Check this for both an X-linked recessive and an X-linked dominant pattern of inheritance.  The solution is below.

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Solving pedigrees

Here's a good warm-up exercise.  You should be able to determine all possible inheritance patterns for these pedigrees.  For now, ignore whether they are autosomal or sex-linked.  Determine whether the inheritance is consistent with a dominant or a recessive allele.  You may assume that there is a simple Mendelian interaction here:  the allele that causes the special phenotype (shaded symbols) is either completely recessive or completely dominant to the wild-type (unfilled symbols).

Pedigree 1:

Solution for the pedigree above.  (Click on the YouTube logo at the bottom right if you want to be able to open a full-screen version).

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Pedigree 2:

The solution for Pedigree 2 is below (same notation regarding full-screen view).

Determining Parental Genotypes from Offspring Ratios

Here is an exercise that calls for figuring out the genotypes of parents based on the ratios of their offspring.  Here are the data:

The solution can be found below.  If you want to make it full size, you should click on the YouTube logo on the bottom right corner of the embedded file, then you can zoom it.  (Blogspot doesn't zoom).

Click here for an interactive exercise you can try!  Select "Exercise: Determining Dihybrid Genotypes" to expand it.

Questions from the review session

Chromosomal Rearrangements

Here's a worksheet for you to practice with.

A solution video is below.  I had trouble uploading it, so it's in lower-quality and I'm not sure it started at the exact right point.  It should work for you, though.  You can make it larger by clicking on the YouTube logo in the bottom-right corner of the embedded file and running it straight from YouTube.