Analysis of Variance

Application of ANOVA: A case study in Footwear manufacturing

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Ứng Dụng ANOVA Trong Cải Tiến Chất Lượng


Abstract: ANOVA stands for ANalysis Of VAriance. The following post will show you the practical implementation of One-Way ANOVA analysis in testing the heating temperature on the surface of shoes’ outsole

Tóm tắt: ANOVA là viết tắt của từ ANalysis Of VAriance. ANOVA là một phương pháp thống kê nhằm trình bày các bằng chứng về sự khác biệt giữa các nhóm quan sát về một hoặc một số thuộc tính hay đặc điểm là có ý nghĩa thống kê hay không. Bài sau đây sẽ trình bày về một ứng dụng thực tế của phương pháp phân tích ANOVA một yếu tố trong việc kiểm định nhiệt độ xấy trên bề mặt đế giày:

Problem Background

The quality of adhesive bonding applied in shoes production is heavily affected by the heating temperature. Not too hot, not too cool but the right degree of Celsius that spreads equally the surface of bonding area will guarantee bonding is effective. However, the problem is how we can know every point in the bonding areas (including toe, mid and heel of a sole) has exposed the same temperature. I accompanied with the team to measure the temperature in the three bonding areas after the sole goes through the heating machine. The data can be accessed by clicking Temperature data. After having the data, I conducted ANOVA (Analysis of Variance) to check whether or not the temperature is different in different bonding areas (toe, mid, and heel).


The data is stored in a file named “” which is used as an input of R statistical software to execute ANOVA analysis. The structure of data is presented as below:

Graphically speaking, the boxplot diagram shows the difference in temperature across the three main bonding area of the sole. Specifically, the temperature of toe is higher than that of mid and heel part.

ANOVA Analysis

Technically speaking, ANOVA with TukeyHSD method is used to make the conclusion whether or not the different in temperature is statistically significant

  1. TukeyHSD(aov(ResponseB ~ FactorA), ordered = TRUE)
  1. Tukey multiple comparisons of means
  2.     95% family-wise confidence level
  3.     factor levels have been ordered
  5. Fit: aov(formula = Temperature ~ Position)
  7. $Position
  8.                diff        lwr       upr     p adj
  9. mid-heel 0.07272727 -0.4403096 0.5857642 0.9396555
  10. toe-heel 1.49318182  0.9801449 2.0062187 0.0000000
  11. toe-mid  1.42045455  0.9074176 1.9334915 0.0000000


As clearly can be seen that, the temperature between toe and heel, toe and mid is significantly different (p adj < 0.05-confident level -> Null hypothesis is rejected) whereas that between mid and heel is consistent. That leads to a need of investigation on inconsistent temperature causing the bonding gap at the end of assembly line.

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