Question

Under the assumption of analysis of variance, the parent population should be-

• A. Normally Distributed
• B. Binomial Distribution
• C. Poisson Distribution
• D. Beta Distribution

Hint:

ANOVA requires: Normality, independence, and equal variance (homoscedasticity).

Answer 1

The Correct Option is A

Step 1: ANOVA Overview.
Analysis of Variance (ANOVA) is a statistical method for comparing the means of more than two groups.
It operates by dividing the total variability into variability between groups and variability within groups.
Step 2: Distributional Requirement.
The validity of the F-test in ANOVA necessitates that the source population (from which samples originate) follows a normal distribution.
This condition ensures that the sampling distribution of the test statistic conforms to the F-distribution.
Step 3: Evaluation of Distributions.
- (1) Normal Distribution: Accurate. This is the essential assumption for ANOVA.
- (2) Binomial Distribution: Pertains to dichotomous outcomes (success/failure) and is not applicable to ANOVA assumptions.
- (3) Poisson Distribution: Used for modeling rare events; irrelevant to ANOVA's distributional assumption.
- (4) Beta Distribution: A continuous distribution for variables within a specific range; not an ANOVA assumption.
Step 4: Final Determination.
Consequently, for ANOVA to be applicable, the parent population must be normally distributed.