Question

The formula: [Sum of (Observed-Expected)$^2$/Expected] is also known as

• A. F-test statistic
• B. Chi-square statistic
• C. T-test statistic
• D. Variance statistic

Hint:

When performing genetic Chi-square calculations, the degrees of freedom (\(df\)) are calculated as \(n - 1\).
Here, \(n\) represents the total number of phenotypic classes expected from the cross.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In genetics and statistics, researchers must determine if experimental data matches theoretical expectations.
The Chi-square (\(\chi^2\)) test of goodness of fit is used to evaluate deviations between observed and expected frequencies.

Step 2: Key Formula or Approach:
The mathematical formula for calculating the Chi-square statistic is:
\[ \chi^2 = \sum \frac{(O - E)^2}{E} \] Where:
\(O = \text{Observed frequency in each category}\)
\(E = \text{Expected frequency in each category}\)
\(\sum = \text{Summation over all phenotypic or genotypic categories}\)

Step 3: Detailed Explanation:
Let us compare this formula to the other statistical parameters listed:
F-test statistic: This is used to compare the variances of two independent populations:
\[ F = \frac{s_1^2}{s_2^2} \] T-test statistic: This is used to determine if the means of two groups are significantly different from each other.
It divides the difference between sample means by the pooled standard error of the samples.
Variance: This is a metric that describes the spread of data points around their arithmetic mean value.
Consequently, the formula given in the question uniquely describes the Chi-square statistic.
In genetics, this test is used to evaluate if the results of a cross follow Mendelian inheritance ratios.

Step 4: Final Answer:
The given mathematical relationship represents the Chi-square statistic, matching Option (B).