Science Practice 5: Chi-Square Hypothesis Testing
Chi-square testing measures whether observed counts differ from expected counts by more than chance alone would explain, letting you decide if a genetic ratio hypothesis still holds up.
Real crosses never match predicted ratios exactly. Flip four coins and you rarely get exactly two heads and two tails, even though 1:1 is the expected ratio. Small differences between observed and expected counts are normal sampling noise. The chi-square test gives a precise way to decide whether a gap is just that normal noise or large enough to say the expected ratio probably does not fit.
The chi-square statistic is the sum, across every phenotype category, of (observed minus expected) squared divided by expected. Each term grows fast as observed drifts from expected, because the difference is squared, and dividing by expected scales that gap relative to how many you predicted. Small deviations contribute almost nothing; large ones dominate the sum. To judge the result, find degrees of freedom, the number of categories minus one, then compare your chi-square value to the critical value in the 0.05 row of a chi-square table for that many degrees of freedom. If your calculated value exceeds the critical value, you reject the null hypothesis: the observed data deviate significantly from the expected ratio.
This test is where Science Practice 5 meets the genetics investigations most directly, since it turns a monohybrid or dihybrid cross into a number you can actually judge statistically rather than eyeballing. It also connects forward to experimental design: a significant chi-square should push you to ask what caused the deviation, not just to report a number.
Key terms
- Null hypothesis
- The assumption that any difference between observed and expected counts is due to chance alone.
- Degrees of freedom
- The number of phenotype categories minus one, used to pick the correct row in the chi-square table.
- Critical value
- The chi-square value from the table that observed data must exceed to be considered significantly different from expected.
- Observed vs expected counts
- Observed counts are what the experiment actually produced; expected counts are what the hypothesized ratio predicts for the same sample size.
Watch it explained
- How it worksHow does the chi-square statistic grow as observed values drift from expected ones?
- How it worksWalk me through picking degrees of freedom and reading the 0.05 row of the table.
- Worked exampleFind whether 120 red and 80 white flowers fit a 3 to 1 ratio at p equals 0.05.
- Common mistakeWhy doesn't a large chi-square value prove your hypothesis is wrong about the mechanism?
Check yourself
End of topic.