AP Biology · Exam guide
AP Biology Statistics and Data Analysis: Chi-Square, Error Bars, and Conclusions
The AP Biology exam asks you to analyze data, not only collect it. The statistics are limited, so you can learn them well: chi-square for genetics and choice experiments, standard error and error bars for comparing means, and a short conclusion that connects the numbers to the biology.
Chi-square: the routine
- State the null hypothesis: any difference between observed and expected counts is due to chance.
- Compute expected counts from the null hypothesis, not from the observed data.
- Compute the chi-square value, the sum of (observed minus expected) squared, divided by expected.
- Find the degrees of freedom: the number of categories minus 1.
- Compare the value with the critical value at p = 0.05 from the table. If the value is smaller, you fail to reject the null hypothesis.
A worked example
A cross between two heterozygous pea plants gives 80 offspring: 62 with the dominant phenotype and 18 with the recessive phenotype. The null hypothesis predicts a 3:1 ratio, so the expected counts are 60 and 20.
Chi-square = (62 - 60)^2 / 60 + (18 - 20)^2 / 20 = 0.067 + 0.200 = 0.267. With 2 categories, the degrees of freedom are 1, and the critical value at p = 0.05 is 3.84. Because 0.267 is less than 3.84, we fail to reject the null hypothesis. The data are consistent with a 3:1 ratio, and the difference from expected can be explained by chance.
Statistics cannot prove a hypothesis. They can only fail to reject it.
It compares to the critical value, uses the degrees of freedom, and states the conclusion in the right words.
Error bars
- Error bars usually show standard error of the mean, or two standard errors for about a 95 percent interval.
- If the error bars of two groups overlap a lot, the difference is probably not significant.
- If they do not overlap at all, the difference is probably significant.
- Always say what the error bars represent, and refer to the sample size if it is given.
Writing the conclusion
A strong conclusion has three parts: the statistical result (reject or fail to reject, with the numbers), what it means for the hypothesis, and a biological explanation for why.
Common mistakes
- Using observed counts as the expected counts.
- Using the number of individuals, instead of the number of categories, for the degrees of freedom.
- Saying "accept the null hypothesis" or "prove" anything.
- Forgetting to state the null hypothesis when the question asks for it.
Frequently asked questions
What is the critical value for 3 degrees of freedom?
At p = 0.05 it is 7.81. A table is provided on the exam.
What does p = 0.05 mean?
It means that a result this extreme would occur by chance about 5 percent of the time if the null hypothesis were true.
When do I use chi-square?
When comparing observed counts in categories with the counts expected from a hypothesis, such as a genetic ratio or an animal's choice.
Do I have to calculate standard error?
Sometimes. The formula is on the exam equation sheet.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every unit in the AP Biology course ends with a quiz of multiple-choice and short free-response questions, with a writing space that scores against the four-point rubric and a model response to compare against. These free lessons also build the skills the free-response section tests:
See the AP Biology course Free lessons and lesson list
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Multiple choice
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