Once you have your expected values you can compare them to the observed ones, but doing so based on your intuition isn't reliable. Instead, you need to perform a statistical test that allows us to determine if our values are too far apart to be correct. The test we use is called the chi-square goodness of fit test (abbreviated as χ2). This test is calculated by taking the difference between the actual number of individuals in each genotype in the population and the numbers of each genotype that you expected if the Hardy-Weinberg equation is true. You compare those numbers using this formula:
For a H-W test, you will calculate three values (one for each genotype) and sum them together to determine the χ2 value. You then compare this value to a critical value to see if there is a significant difference, or if the differences between the observed and expected are just due to random noise. Normally, you need to have a statistical table to see if your value is significant or not, but that isn't necessary for us. For reasons we don't need to address here, the comparison value for H-W tests is always 3.841. Note: a common misunderstanding is to use a value of 5.991. This is based on an incorrect interpretation of how the χ2 test is done (see this website for more explanation). If the χ2 value is greater than 3.841, then we would say that the differences between the observed and expected are large enough to say that the H-W equation probably doesn't apply to that population. In other words, this would mean the population is evolving for this gene because at least one of the H-W assumptions is not correct. Further work would be needed to determine which assumption(s) are being violated.
For the example data we have been using recall that there were 252 AA, 640, Aa, and 382 aa individuals. These are the observed values. If the H-W equation is true, we expect 257.4, 630.6, and 387.3 for each genotype. This gives the following calculations
Solving for each equation gives us
So the total is χ2 = 0.326.
Because this value is less than 3.841, there is no significant difference between the expected and observed values, leading us to conclude that this population is not evolving for this gene because it meets all the assumptions required by the H-W equation.
For a H-W test, you will calculate three values (one for each genotype) and sum them together to determine the χ2 value. You then compare this value to a critical value to see if there is a significant difference, or if the differences between the observed and expected are just due to random noise. Normally, you need to have a statistical table to see if your value is significant or not, but that isn't necessary for us. For reasons we don't need to address here, the comparison value for H-W tests is always 3.841. Note: a common misunderstanding is to use a value of 5.991. This is based on an incorrect interpretation of how the χ2 test is done (see this website for more explanation). If the χ2 value is greater than 3.841, then we would say that the differences between the observed and expected are large enough to say that the H-W equation probably doesn't apply to that population. In other words, this would mean the population is evolving for this gene because at least one of the H-W assumptions is not correct. Further work would be needed to determine which assumption(s) are being violated.
For the example data we have been using recall that there were 252 AA, 640, Aa, and 382 aa individuals. These are the observed values. If the H-W equation is true, we expect 257.4, 630.6, and 387.3 for each genotype. This gives the following calculations
Because this value is less than 3.841, there is no significant difference between the expected and observed values, leading us to conclude that this population is not evolving for this gene because it meets all the assumptions required by the H-W equation.
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