Question

Variance ratio test is otherwise called

• A. F-test
• B. t-test
• C. Z-test
• D. Chi square test

Hint:

Statistical Test Equivalents:
Variance Ratio Test = F-TEST (Compares variances ANOVA).
Student's Test = t-test (Compares two sample means).
Non-parametric variance test = Kruskal-Wallis test.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Statistical hypothesis testing: the F-test (Fisher-Snedecor test) evaluates whether the ratio of two sample sample variances ($F = s_1^2 / s_2^2$) differs significantly from unity.
Key Formula or Approach:
\[ F = \frac{s_1^2}{s_2^2} = \frac{\text{Mean Square Between Groups (MSB)}}{\text{Mean Square Within Groups (MSW)}} \quad [\text{Variance Ratio Test}] \]

Step 2: Detailed Explanation:
In theoretical and applied biostatistics:
- The Variance Ratio Test is formally and universally designated as the F-Test (A) (named in honor of Sir Ronald A. Fisher by George W. Snedecor).
- It tests the null hypothesis of equality between two independent population variances by calculating the ratio of two mean square sample variances ($F = s_1^2 / s_2^2$).
- It forms the mathematical foundation for the Analysis of Variance (ANOVA) to compare multiple treatment means simultaneously.
- (t-test and Z-test compare means; Chi-square tests goodness of fit/independence).

Step 3: Final Answer:
Therefore, Variance ratio test is otherwise called F-test, matching option (A).