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)