How to perform One-Way ANOVA?

It is a type of hypothesis test where only one factor is considered. We use F-statistic to perform a one-way analysis of variance.

Steps Involved

Step 1 – Define the null and alternative hypothesis.

H0 -> μ1 = μ2 = μ3 (where μ = mean)
Ha -> At least one difference among the means.

Step 2 – Find the degree of freedom between and within the groups. [Using Eq-1 and Eq-2]

n = number of samples in all groups combined
k = number of groups.

Then, find total degree of freedom. [Using Eq-3]

For the next step, we need to understand what F-statistic is.

F-value: It is defined as the ratio of the variance between samples to variance within samples. It is obtained while performing ANOVA test.

Eq-4 shows the F-value formula for one-way ANOVA.

Step 3 – Refer the F-Distribution table and find F_table using df_between and df_within.

As per the given F-Distribution table,

[use the given value of α while referring the table.]

Step 4 – Find the mean of all samples in each group.

Then use Eq-5 to find the Grand mean.
)

where,

= sum of all sample values.
n = number of samples.

Step 5 – Find the sum of squares total using Eq-6 and sum of squares within using Eq-7.

where,

x_{i =} i_th sample.
μ_{i =} mean of i_th group.

Then find sum of squares between using Eq-8.

Step 6 – Find the variance (μ² or S²) between and within samples using Eq-9 and Eq-10.

Step 7 – Find Fcalc using Eq-11.

(Equation-11)

Interpreting the results

If Fcalc < Ftable :
- Don’t reject null hypothesis.
- i.e
If Fcalc > Ftable :
- Reject null hypothesis.

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)