Chi-Square & Experimental Evidence
Choose an expected ratio, test it, and explain what the evidence supports.
What to do when the question looks unfamiliar
- Step 1State the null and turn its expected proportions into counts.
- Step 2Compute χ² = Σ (observed − expected)² / expected.
- Step 3Compare with the appropriate critical value and limit your claim.
Pick the expected model before doing the math
The null specifies a ratio, such as 3:1 or 1:1:1:1, based on the genetic hypothesis. Expected counts are sample size times the proposed proportions. They are not the observed counts and do not have to be whole numbers.
For a goodness-of-fit test with fixed expected probabilities, degrees of freedom = number of categories − 1. Estimating parameters from the same sample can change degrees of freedom. Sparse expected counts can make the approximation unreliable.
Write a conclusion the data can support
A statistic exceeding the critical value supports rejecting the stated null at the given threshold. A smaller statistic means fail to reject. Neither result tells you the probability that the null is true.
Rejecting a ratio does not prove which biological mechanism caused the difference. Look for controlled comparisons and replication. When interpreting error bars, read the legend and use the inference the problem specifies; not every type of error bar supports the same conclusions.