(c) using the chi-squared (χ²) test to determine the significance of the…

The idea

The chi-squared (χ²) test compares observed counts with expected counts to judge whether a difference is due to chance. First state a null hypothesis that there is no significant difference between observed and expected results. Calculate expected values from the genetic ratio and total, then compute χ² = Σ (O − E)² / E for each class and sum them. Determine degrees of freedom as the number of categories minus one. Compare the calculated χ² with the critical value at the chosen probability level (commonly p = 0.05) for those degrees of freedom. If the calculated value is greater than the critical value, reject the null hypothesis: the difference is significant and not due to chance. If it is less, accept the null hypothesis. The test uses raw counts, not percentages or ratios, and each expected value should be at least five.

What earns the marks

• State a null hypothesis that there is no significant difference between observed and expected results.
• Calculate expected values from the expected ratio and the total number of offspring, using counts rather than percentages.
• Compute χ² = Σ (O − E)² / E, squaring each difference, dividing by the expected value and summing across categories.
• Determine degrees of freedom as the number of phenotypic categories minus one.
• Compare the calculated χ² with the critical value at the chosen probability level; if calculated exceeds critical, reject the null hypothesis and conclude the difference is significant.

Common mistakes and how to put them right

• Using percentages or ratios instead of raw counts in the calculation.

  Put it right: Is to convert all data to actual numbers of individuals before computing χ².

• Setting degrees of freedom equal to the number of categories.

  Put it right: Is that degrees of freedom equals categories minus one.

• Rejecting the null hypothesis when the calculated value is below the critical value.

  Put it right: Is that a calculated value smaller than critical means the difference is not significant, so the null hypothesis is accepted.

• Omitting the null hypothesis.

  Put it right: Is to state it explicitly before calculating so the conclusion has a clear basis.

Exam tips

• Always write the null hypothesis before any calculation so the final conclusion refers back to it.
• Show the working for each (O − E)² / E term, then the summed total, to secure method marks.
• State the probability level and degrees of freedom used when quoting the critical value, and phrase the conclusion in terms of rejecting or accepting the null hypothesis.