Inferential Statistics • Lesson 18
ANOVA Basics
Concept 1
When Should You Use ANOVA?
ANOVA stands for Analysis of Variance. One-way ANOVA is used to test whether there is evidence that the population means of multiple groups are not all equal.
Visual Explanation
One Question, Multiple Groups
Group A
₹2,400
Average revenue
Group B
₹2,850
Average revenue
Group C
₹3,100
Average revenue
Overall question
Are the population means all equal?
Key Idea
Group A → ₹2,400
Group B → ₹2,850
Group C → ₹3,100
↓
ANOVA
"Are the population means
all equal?"ANOVA provides one overall test when comparing the means of three or more groups.
Activity
A company wants to compare average daily sales across three independent sales teams. Which method is appropriate?
Hint
There are three groups and the outcome is quantitative. Think about the method designed to compare multiple means.
Analyst Workflow
1
Identify groups
2
State hypotheses
3
Compare variation
4
Calculate F
5
Interpret result
Quick Reference
F-STATISTIC
F = MS Between / MS Within
BETWEEN DF
k − 1
WITHIN DF
N − k
MAIN QUESTION
Are all population means equal?
Important ANOVA Assumptions
✓
Observations are independent according to the study design.
✓
The outcome variable is quantitative.
✓
The outcome is approximately normally distributed within each population group, especially for smaller samples.
✓
Population variances are reasonably similar for the standard one-way ANOVA procedure.
ANOVA vs t-Test
Feature
t-Test
One-Way ANOVA
Typical comparison
Two means
Three or more means
Main statistic
t
F
Overall question
Is the difference between two means supported by evidence?
Are all population means equal?