PENICILLIN

(Variation in penicillin testing)

Data:

    diameter plate sample
1         27     a      A
2         23     a      B
3         26     a      C
4         23     a      D
5         23     a      E
6         21     a      F
7         27     b      A
8         23     b      B
9         26     b      C
10        23     b      D
11        23     b      E
12        21     b      F
13        25     c      A
14        21     c      B
15        25     c      C
16        24     c      D
17        24     c      E
18        20     c      F
19        26     d      A
20        23     d      B
21        25     d      C
22        23     d      D
23        23     d      E
24        20     d      F
25        25     e      A
26        22     e      B
27        26     e      C
28        22     e      D
29        23     e      E
30        20     e      F
31        24     f      A
32        22     f      B
33        25     f      C
34        23     f      D
35        22     f      E
36        19     f      F
37        24     g      A
38        20     g      B
39        23     g      C
40        21     g      D
41        22     g      E
42        19     g      F
43        26     h      A
44        22     h      B
45        26     h      C
46        24     h      D
47        24     h      E
48        21     h      F
49        24     i      A
50        21     i      B
51        24     i      C
52        22     i      D
53        22     i      E
54        20     i      F
55        24     j      A
56        21     j      B
57        24     j      C
58        23     j      D
59        22     j      E
60        19     j      F
61        26     k      A
62        23     k      B
63        26     k      C
64        24     k      D
65        24     k      E
66        21     k      F
67        25     l      A
68        22     l      B
69        26     l      C
70        24     l      D
71        24     l      E
72        20     l      F
73        26     m      A
74        24     m      B
75        26     m      C
76        24     m      D
77        25     m      E
78        22     m      F
79        26     n      A
80        23     n      B
81        26     n      C
82        23     n      D
83        23     n      E
84        20     n      F
85        26     o      A
86        23     o      B
87        25     o      C
88        24     o      D
89        24     o      E
90        22     o      F
91        25     p      A
92        22     p      B
93        25     p      C
94        23     p      D
95        23     p      E
96        20     p      F
97        25     q      A
98        21     q      B
99        24     q      C
100       23     q      D
101       23     q      E
102       20     q      F
103       25     r      A
104       22     r      B
105       24     r      C
106       23     r      D
107       23     r      E
108       19     r      F
109       24     s      A
110       21     s      B
111       23     s      C
112       21     s      D
113       21     s      E
114       19     s      F
115       26     t      A
116       23     t      B
117       26     t      C
118       24     t      D
119       24     t      E
120       21     t      F
121       25     u      A
122       21     u      B
123       24     u      C
124       22     u      D
125       22     u      E
126       18     u      F
127       25     v      A
128       22     v      B
129       25     v      C
130       22     v      D
131       22     v      E
132       20     v      F
133       24     w      A
134       21     w      B
135       24     w      C
136       22     w      D
137       24     w      E
138       19     w      F
139       24     x      A
140       21     x      B
141       24     x      C
142       22     x      D
143       21     x      E
144       18     x      F

Description:

Six samples of penicillin were tested using the B. subtilis plate method on each of 24 plates. The response is the diameter (mm) of the zone of inhibition of growth of the organism.

Format:

A data frame with 144 observations on the following 3 variables.

diameter
- diameter (mm) of the zone of inhibition of the growth of the organism.

plate
- assay plate. A factor with levels ‘a’ to ‘x’.

sample
- penicillin sample. A factor with levels ‘A’ to ‘F’.

Details:

The data are described in Davies and Goldsmith (1972) as coming from an investigation to “assess the variability between samples of penicillin by the B. subtilis method. I this test method a bulk-innoculated nutrient agar medium is poured into a Petri dish of approximately 90 mm. diameter, known as a plate. When the medium has set, six small hollow cylinders or pots (about 4 mm. in diameter) are cemented onto the surface at equally spaced intervals. A few drops of the penicillin solutions to be compared are placed in the respective cylinders, and the whole plate is placed in an incubator for a given time. Penicillin diffuses from the pots into the agar, and this produces a clear circular zone of inhibition of growth of the organisms, which can be readily measured. The diameter of the zone is related in a known way to the concentration of penicillin in the solution.”

Source:

O.L. Davies and P.L. Goldsmith (eds), Statistical Methods in Research and Production, 4th ed., Oliver and Boyd, (1972), section 6.6

Task:

Model the diameter of the zone of inhibition of growth of the organism.