Final answer:
To perform a chi-square test on F₂ results, one must compare observed frequencies with expected frequencies, calculate the chi-square statistic, determine degrees of freedom, and find the p-value to evaluate the null hypothesis. Expected frequencies must be rounded to two decimal places and each expectational frequency should be at least five for the test's validity.
Step-by-step explanation:
To perform a chi-square test on F₂ results to check if deviations are by chance, one needs to compare observed frequencies to expected frequencies under the assumption that they follow a specific genetic distribution (commonly Mendelian inheritance ratios in biology).
Goodness-of-Fit hypothesis test is used when you have a single data set and you want to see how well it fits a theoretical distribution. For example, observing the distribution of a single trait in an F₂ generation from a breeding experiment and comparing it to Mendelian expectations.
The test involves the following steps:
State your null hypothesis, which usually is that there is no difference between observed and expected frequencies.
Calculate expected frequencies based on the expected ratios, rounding to two decimal places.
Compute the chi-square statistic, which is the sum of the squared differences between observed and expected frequencies, divided by the expected frequencies (χ² = ∑((observed - expected)² / expected)).
Determine the degrees of freedom (df = number of categories - 1) and use it, along with the chi-square value, to find the p-value.
Compare the p-value to your significance level to decide whether to reject or not reject the null hypothesis.
Ensure each expected value is at least five to meet the test criteria for validity. Remember, the test is right-tailed: larger chi-square values signal a larger discrepancy between observed and expected frequencies, pointing towards the possibility of rejecting the null hypothesis if p-value is less than the significance level.