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Understand the Application of ANOVA in Manufacturing Process!

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".)

We have discussed the basic concepts of ANOVA when we have one factor, we use one-way ANOVA and when we have two factors, we use two-way 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

Post-ANOVA 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.

NB - Want to learn the concepts of ANOVA and Application in Industries? Attend our Statistical Training Program starting from basic to advanced level. Some of the Statistical training certified courses are Application of Essential Quality Tools, Masterclass in Statistical Thinking, SPC Masterclass, DOE Masterclass, etc. Apart from Statistical training, we also conduct Minitab Certified Training Program, starting from basic to advanced level. Some of the Minitab software training certified courses are Minitab Essentials, Statistical Tools for Pharmaceuticals, Statistical Quality Analysis & Factorial Designs, etc. 

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