Side-by-Side Boxplots Example – Comparison of Optical Lens Coatings
In the development of coatings (such as for UV protection or anti-reflexiveness) for optical lenses, it is
important to study the durability of the coating. One such durability test is an abrasion test, simulating
day-to-day treatment of lenses (consider how one cleans lenses, on the corner of a T-shirt, etc.). In this
study1 the controlled variable is the surface treatment of the lens, and the response variable y is the
increase in haziness of the lens after 150 cycles of abrasion. Minimal increase in haziness is desired.
The data are given in the table below, for 4 possible surface coatings, with each coating applied to 7
lenses. Each lens (in random order) was subjected to the abrasion test, and the increase in the haziness of
the lens was then measured. At the end of each column of data, the sample statistics are given.
Table 1 – Optical Lens Data
Surface Coating
1
2
3
4
8.52
12.50
8.45
10.73
9.21
11.84
10.89
8.00
10.45
12.69
11.49
9.75
10.23
12.43
12.87
8.71
8.75
12.78
14.52
10.45
9.32
13.15
13.94
11.38
9.65
12.89
13.16
11.35
𝑥̅ = 9.45
𝑥̅ = 12.61
𝑥̅ = 12.19
𝑥̅ = 10.05
𝑠 = 0.716
𝑠 = 0.417
𝑠 = 2.084
𝑠 = 1.302
Below are side-by-side boxplots of the data (This chart was constructed using SAS).
1
Nelson, P. R.; Coffin, M.; and Copeland, K. A. F. Introductory Statistics for Engineering Experimentation, Elsevier
Academic Press (2003)