# Punnet Squares and Chi-Square Tests in Genetics

Many may think that genetics is just a method used for looking at the chromosomes of an organism and attempting to determine what genes are specific to proteins and general characteristics, such as eye color or even hair color, within that organism. However, there is much more related to genetics than many suppose is involved. In genetics there are a variety of statistical test that can be run in order to test the likelihood a specific gene will happen dominantly or recessively in an organism or even to test the statistical probability that something happens in nature naturally, by chance.

There are certain types of statistical tests that are practiced today by geneticists, aiding them in determining gene dominance such as the Punnet square. Additionally, chi-square tests, are used to test the likelihood of a specific trait being observed in nature is dominant and likely to occur frequently. These are only a few tests practiced today that allow anyone willing to do the simple math, to determine the genotypic probabilities of offspring who have parents of a specific known genotype.

Punnet squares began with Mendel’s laws. It allows anyone to determine the probability of an offspring having a specific genotype when the genotypes of both parents are known. For example if both parents have a genotype of “Aa”, then the cross can be considered “Aa x Aa” This cross of one gene is called a monohybrid cross. The cross is done in a diagram of four squares put together. This test could be used to test the potential phenotypes an offspring could have. In genetics, this test is also used to test for potential carriers of different diseases such as colorblindness and sickle-cell disease.

Moreover, the punnet square goes on to apply to Mendel’s law of independent assortment with dihybrid crosses. This test uses four columns and four rows unlike the monohybrid cross. The dihybrid cross likes to look at two genes at the same time, and test how likely both genes will be seen together. Mendel tested this with his notorious study of the different kinds of peas. Typically, the phenotypic ratio for a monohybrid cross is 3:1 and the dihybrid cross is 9:3:3:1.

Finally, Chi-square or the goodness of fit test is also used in genetics to test how likely a group of phenotypes corresponds to statistical information. In other words, this test is used to see how close a group of observed phenotypes matches with statistical data. This test has a simple formula: χ^{2}= ∑ (O-E)^{2} /E. Chi-square testing is simply a way of testing probability that the phenotype will occur in nature. Next, you need to find the degrees of freedom of the calculations which is (n-1), where n is the number of independent variables.

Once the χ^{2 }values are calculated and you have your degrees of freedom, the critical values must be compared to a χ^{2} distribution table. This table allows you to see how statistically significant. When P< 0.05 it is likely that the experiment deviated from what should have been expected. This test will prove or disprove your original hypothesis about the experiment, depending on your χ^{2} value and if P< 0.05.

Punnet squares and Chi-square tests are not the only type of genetic analysis available to everyone, but rather only a small fraction of the many available. There are many benefits to these tests when you are attempting to find the phenotypic probability that an offspring will have a specific trait and how likely it is to see a group of the phenotype in nature. Chi square is an excellent way to test how fit a phenotype is, according to the expected ratios.

I am very familiar with the punnet squares and have even used them here in my articles on genetics in regards to pet colors - but am not as familiar with chi squares.