The chi-squared test and the gibberellin gene

Last time

Before we start: last time, in Monohybrid crosses, codominance and sex linkage, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Is it chance?

A genetic cross gives results that are close to the expected ratio, but never exactly on it. So how close is close enough? Chance alone will always cause some scatter. The chi-squared test answers that question with a number, and then the sweet pea gene Le shows how a single amino acid can make a plant tall or dwarf.

When to use chi-squared

The chi squared test compares observed results with expected results, for categories such as phenotypes. The data must be counts, not percentages or measurements. The null hypothesis says there is no significant difference between the observed and the expected results. Any difference is due to chance. You need a sample large enough that every expected number is at least five.

The method

First state the null hypothesis. Then calculate the expected numbers from the ratio, such as nine to three to three to one. For each category, subtract the expected from the observed, square it, and divide by the expected. Add them all. That total is chi squared. Find the degrees of freedom: the number of categories minus one. Compare chi squared with the critical value at the 0.05 probability level.

A worked example

A cross gives 315, 101, 108 and 32 offspring. The total is 556. The expected counts, in the ratio nine to three to three to one, are 312.75, 104.25, 104.25 and 34.75. The four terms are 0.02, 0.10, 0.13 and 0.22. They add to 0.47. There are four categories, so three degrees of freedom. The critical value at p equals 0.05 is 7.82. Our 0.47 is smaller. So we accept the null hypothesis: there is no significant difference, and the results fit the 9 to 3 to 3 to 1 ratio.