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Ch. 3 - Mendelian Genetics
Klug - Concepts of Genetics 12th Edition
Klug12th EditionConcepts of GeneticsISBN: 9780135564776Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 19

In assessing data that fell into two phenotypic classes, a geneticist observed values of 250:150. She decided to perform a χ\(\chi\)² analysis by using the following two different null hypotheses:
(a) the data fit a 3:1 ratio, and
(b) the data fit a 1:1 ratio.
Calculate the χ\(\chi\) ² values for each hypothesis. What can be concluded about each hypothesis?

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Step 1: Identify the observed values and total number of observations. Here, the observed counts are 250 and 150, so the total is 250 + 150 = 400.
Step 2: For hypothesis (a), where the expected ratio is 3:1, calculate the expected counts by dividing the total according to this ratio. The expected count for the first class is \(\frac{3}{4} \times 400\), and for the second class is \(\frac{1}{4} \times 400\).
Step 3: For hypothesis (b), where the expected ratio is 1:1, calculate the expected counts by dividing the total equally. Each class is expected to have \(\frac{1}{2} \times 400\) individuals.
Step 4: Use the chi-square formula to calculate the chi-square value for each hypothesis: \(\chi^{2} = \sum \frac{(O - E)^2}{E}\) where \(O\) is the observed count and \(E\) is the expected count for each phenotypic class. Calculate this sum separately for each hypothesis using their respective expected counts.
Step 5: Compare the calculated chi-square values to the critical chi-square value from the chi-square distribution table at the appropriate degrees of freedom (df = number of classes - 1) and significance level (commonly 0.05). If the calculated value is less than the critical value, the hypothesis fits the data well; if greater, the hypothesis is rejected.

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Chi-Square (χ²) Test

The chi-square test is a statistical method used to compare observed data with expected data based on a specific hypothesis. It calculates a χ² value that measures the difference between observed and expected frequencies. A higher χ² value indicates a greater deviation from the expected ratio, helping to determine if the null hypothesis can be rejected.
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Chi Square Analysis

Null Hypothesis in Genetic Ratios

In genetics, the null hypothesis often states that observed phenotypic ratios fit a predicted Mendelian ratio, such as 3:1 or 1:1. This hypothesis assumes no significant difference between observed and expected data. Testing different null hypotheses helps identify which genetic model best explains the observed data.
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Translation:Wobble Hypothesis

Interpreting Chi-Square Results

After calculating the χ² value, it is compared to a critical value from the chi-square distribution table based on degrees of freedom and significance level. If χ² is less than the critical value, the null hypothesis is accepted; if greater, it is rejected. This interpretation determines whether observed deviations are due to chance or indicate a different genetic pattern.
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