Suppose in the manufacturing process, we want to compare and check which are the most reliable procedures, materials, etc. We can use the ANOVA test to compare different suppliers and select the best available.
ANOVA (Analysis of Variance) is used when we have more than two sample groups and determine whether there are any statistically significant differences between the means of two or more independent sample groups. In other words, we can say that it checks the impact of one or more factors by comparing the means of different samples. When we have less than or equal to two sample groups – we go for one sample and two sample tests.
(To know more about one sample and two sample tests, please visit our page "Hypothesis Testing".)
What are the types of ANOVA?
There are two main types of ANOVA i.e. one–way ANOVA and two–way ANOVA.
We have discussed the basic concepts of ANOVA when we have one factor, we use oneway ANOVA and when we have two factors, we use twoway ANOVA. I guess this concept is clear and understandable.
Now, let’s discuss some of the assumptions which we should keep in mind while performing ANOVA.
Example
One factor ANOVA – In an automobile industry, three quality inspectors (A, B, C) measure the breaking strength of car seat fabric and the management wants to test for a difference between their measurements by comparing means.
A  B  C 
11.3  9.98  10.58 
10.62  8.68  9.46 
10.36  11.39  10.15 
10.23  9.16  10.39 
10.42  9.64  9.71 
12.64  8.49  9.48 
8.75  9.69  10.74 
10.49  11.14  10.16 
10.33  9.02  11 
10.04  9.47  12.54 
10.12  10.78  9.88 
9.89  9.78  10.1 
10.31  10.1  8.85 
10.46  10.27  12.52 
9.69  10.01  10.74 
9.29  9.01  9.19 
10.79  9.78  10.08 
10.15  9.99  10.51 
8.83  9.27  11.42 
8.47  10.41  12.12 
9.55  9.42  10.16 
11.03  9.27  12.06 
9.74  8.15  9.49 
11.21  9.69  11.05 
11.04  10.63 
8.53 
Source  DF  Adj SS  Adj MS  F  P 
Inspector  2  6.7  3.4  3.9  0.026 
Error  72  61.9  0.9  
Total  74  68.6 
Since our null hypothesis is rejected, we need to find out which sample group is different and so we can work for improvement.
Let’s make it clear that
PostANOVA Analysis
We will use the Tukey test (also known as Honestly significant difference – HSD test). With reference to the above example for one way ANOVA, our null hypothesis was rejected and we will conduct Tukey test by using MINITAB.
Grouping Information Using the Tukey Method and 95% Confidence
Inspector 
N  Mean  Grouping  
C 
25  10.436  A  
B 
25 
10.230 
A 
B 

A 
25 
9.729 
B 
Means that do not share a letter are significantly different.