​What is ‘ANOVA’?​

Correct option is B

Introduction:    

ANOVA stands for Analysis of Variance. It is a statistical technique used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups. ANOVA was developed by Ronald A. Fisher and is widely used in experimental and observational studies.

Information Booster:

Purpose:
ANOVA checks if the observed differences in sample means are due to actual effects or just due to random chance.

• Null Hypothesis (H₀):
  All group means are equal.

• Alternative Hypothesis (H₁):
  At least one group mean is different.

• Basic Assumptions of ANOVA:

• Independence of observations

• Normally distributed populations

• Homogeneity of variance (equal variances across groups)

• Types of ANOVA:
  
  

• One-way ANOVA: Tests differences between groups based on one independent variable.

• Two-way ANOVA: Tests the effect of two independent variables and their interaction.

• Repeated Measures ANOVA: Used when the same subjects are tested multiple times.

• Key Output:
  ANOVA produces an F-ratio (F-statistic). A high F-value with a corresponding p-value < 0.05 usually leads to rejection of the null hypothesis.

Additional Knowledge:

• Post-hoc Tests:
  If ANOVA shows a significant difference, post-hoc tests like Tukey’s HSD, Bonferroni, etc., are used to identify specifically which means differ.

• Comparison with t-test:

• t-tests compare two means; ANOVA compares three or more.

• Using multiple t-tests instead of ANOVA increases the risk of Type I error (false positives).

• Applications:
  
  

• Education (e.g., comparing test scores across teaching methods)

• Healthcare (e.g., comparing drug effectiveness)

• Marketing (e.g., comparing customer responses across regions)