Chi Square Test

Background Information: Chi-Square (chi2) Goodness of Fit Test

In biology, things rarely go exactly as predicted. If you cross two heterozygous pea plants, you expect a 3:1 ratio of dominant to recessive traits. But if you actually grow 100 plants, you might get 72 dominant and 28 recessive.

Is that slight difference just random variation (chance), or is there a biological reason your plants aren't following the rules (like a lethal mutation or linked genes)?

The Chi-Square (chi2) test is a statistical tool used to determine if the difference between your Observed data and your Expected data is statistically significant.

The Null Hypothesis (H0):

Before running this test, you must state a Null Hypothesis. This is the assumption that there is no significant difference between your observed and expected results, and any minor deviations are purely due to chance.

How to Interpret Your Results:

To interpret your chi2 value, you will need to look at a standard critical values table using your Degrees of Freedom (df) and a probability level of p = 0.05 (the standard in biology).

• If your calculated chi2 is LESS than the critical value: You accept the Null Hypothesis. Your data fits the expected model, and variations are due to random chance.

• If your calculated chi2 is GREATER than the critical value: You reject the Null Hypothesis. There is a statistically significant difference, meaning some biological factor is causing your results to deviate from expectations.

Note for IA Students: This test is most commonly used in Genetics (comparing actual offspring to Punnett square predictions) and Ecology (determining if a species' distribution in quadrats is random or influenced by the environment).

How to Use the Calculator

1. Gather Your Data: You must have the raw counts for your Observed (O) data. You also need to calculate your Expected (E) values based on your biological model (e.g., a genetic ratio). Note: You must use raw counts, not percentages or frequencies!

2. Enter Your Categories: * In the first row, enter the Observed and Expected numbers for your first phenotype or category.

   • In the second row, enter the Observed and Expected numbers for your second category.

3. Add More Categories: If you have a more complex cross (like a dihybrid 9:3:3:1 ratio) or multiple quadrats, click "+ Add Another Category" until you have enough rows.

4. Calculate: Click the "Calculate chi2" button.

5. Record Your Results: The calculator will give you your final $\chi^2$ value and your Degrees of Freedom (df). Use these two numbers to check your IB statistics table! The calculator also provides a breakdown showing which specific category caused the largest deviation from your expected model.