Chi-square tests are fair game for this year’s revised AP Biology exam and I’ve had multiple students asking about how to perform and use them. Because Chi-square tests are typically used one experimental data, this is likely to show up as part of Question #1 on the exam.

First, let’s clarify the purpose of a Chi-square test. It is a statistical test that determines whether there is a significant difference between different groups in an experiment (for instance, three groups of plants grown in different conditions). The null hypothesis, or default case, is that there is no difference between groups. The alternative hypothesis is that there is a difference between groups.

Of course, typically in an experiment, the goal is to show that there is indeed a difference between different treatment groups. For example, let’s say you put a tomato plant A near sunlight and another tomato plant B in the dark, all other factors held the same. The goal is to show whether there is a difference in growth between the plants after one month. As the experimenter, do you hope there is a difference in growth? Yes, of course you do. Then you can say that you have found this factor (sunlight) to be associated with plant growth.

### Conduct a Chi-square Test

The Chi-square test computes the difference between experimental (observed) and expected values for the different groups involved. These calculations yield the Chi-square. That value is then compared to a critical value. We can find this value on the probability table provided on the exam using both the degrees of freedom (d.f., will be explained later) and the level of error (usually 0.05).

Below is an example of a probability table. If the experiment of interest has 3 groups and we aim for an error level of 0.05, what is the critical value?

Answer: It is 5.99, because the degrees of freedom is (3 - 1) = 2, and the error level is 0.05.

### Drawing conclusions from the Chi-square test:

If the Chi-square value is greater than the critical value, we reject the null hypothesis and say the groups are significantly different.

If the Chi-square value is less than the critical value, we fail to reject the null hypothesis and say there is not a significant difference.

The diagram below summarizes the steps in a Chi-square test:

### Practice Problems:

Now that we have walked through how to conduct Chi-square tests, it’s time to use them. It’s important to understand both how to do the tests and how to interpret the results of the test. Here are some good practice problems:

Note: this worksheet does not provide the probability table. You can easily find one on Google

Please comment below if you have any questions as you go through the problems. Happy studying!

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