Summary
Compares observed and expected counts, for example testing Mendelian ratios.
In depth
χ² = Σ (O-E)²/E; compare to a critical value with degrees of freedom = categories - 1. Used for ratios such as 9:3:3:1. If χ² is above the critical value at p = 0.05, reject the null hypothesis.
Use counts, not percentages. Expected frequencies should be at least 5. Degrees of freedom equal categories minus one.
Key idea: it tests whether observed deviations from expectation are bigger than chance.
The chi-squared test compares observed counts with those expected under a hypothesis, for categorical data. The test statistic is the sum over categories of (observed - expected)^2 / expected.
It is compared with a critical value from a table, depending on the degrees of freedom (number of categories minus 1) and the significance level (usually 0.05). If the statistic exceeds the critical value, the null hypothesis is rejected, meaning the difference is unlikely to be due to chance. Expected counts should generally be 5 or more, and raw counts, not percentages, must be used.
Example: testing whether offspring from a dihybrid cross fit a 9:3:3:1 ratio.
Key idea: a non-significant result means the data are consistent with the expected ratio, not that it is proved.
Frequently asked questions
What is Chi-Squared Test?
Compares observed and expected counts, for example testing Mendelian ratios.
Which area of biology covers Chi-Squared Test, and how advanced is it?
Chi-Squared Test is one of the 51 topics in Lab Methods & Biostatistics. It is rated Intermediate, so it suits learners who already know the core vocabulary. Related topics in this area include ANOVA, t-Test, Null Hypothesis.
Can you give an example of Chi-Squared Test?
Testing whether fly offspring match a 3:1 ratio.
What should I learn before Chi-Squared Test?
Work through the Beginner topics in Lab Methods & Biostatistics first, such as Scientific Method, Hypothesis, Variables, then return to Chi-Squared Test. Intermediate topics assume the Beginner vocabulary.
What topics are related to Chi-Squared Test?
The closest topics to Chi-Squared Test are ANOVA, t-Test, Null Hypothesis, P-Values and Multiple Testing. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Chi-Squared Test?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Chi-Squared Test. To practise the whole of Lab Methods & Biostatistics, use the Lab Methods & Biostatistics quiz.
How is Chi-Squared Test different from ANOVA?
Chi-Squared Test: Compares observed and expected counts, for example testing Mendelian ratios. ANOVA: Compares means across three or more groups by partitioning variance. Read both side by side and note what each one explains.
How should I study Chi-Squared Test step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with ANOVA and explain the difference aloud. Finally, take the Lab Methods & Biostatistics quiz and come back to this page for any question you miss.