One-Way ANOVA Example
Consider the example given below to understand step by step how to perform this test. The marks of 3 subjects (out of 5) for a group of students is recorded. (as given in the table below)
[Take α = 0.05]
Std/Sub | English (e) | Math (m) | Science (s) |
---|---|---|---|
Student 1 | 2 | 2 | 1 |
Student 2 | 4 | 3 | 2 |
Student 3 | 2 | 4 | 5 |
Step 1: Define the hypothesis
- Null hypothesis, (where μ = mean)
- Alternate hypothesis, .
Step 2: Degres of Freedom
As per the table, k = 3, n = 9
Step 3 Find the F-value corresponding to Degree of Freedom and alpha
On referring to the F-Distribution table, using df1 = 2 and df2 = 6 at α = 0.05: we get, Ftable = 5.14
Step 4 Compute the mean
Step 5 Compute the Sum of Squares
Step 6 Find the variance
Step 7 Compute F-statistics
Since, Fcalc < Ftable (0.05 < 5.14)
We cannot reject the null hypothesis.
Thus, we can say that the means of all three subjects is the same.
One-Way ANOVA
ANOVA, or Analysis of Variance, is a statistical method for comparing means among three or more groups, crucial in understanding group differences and relationships in diverse fields. In this article, we’ll focus on One-way ANOVA.
Table of Content
- What is ANOVA?
- Assumptions for ANOVA
- Types of ANOVA
- How to perform One-Way ANOVA?
- One-Way ANOVA Example
- Frequently Asked Questions (FAQs)