Variation in penicillin testing

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.


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. In this test method a bulk-inoculated 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.”


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

diameter (mm) of the zone of inhibition of the growth of the organism.
assay plate. A factor with levels ‘a’ to ‘x’.
penicillin sample. A factor with levels ‘A’ to ‘F’.

  • Penicillin
dotplot(reorder(plate, diameter) ~ diameter, Penicillin, groups = sample,
        ylab = "Plate", xlab = "Diameter of growth inhibition zone (mm)",
        type = c("p", "a"), auto.key = list(columns = 3, lines = TRUE,
        title = "Penicillin sample"))
(fm1 <- lmer(diameter ~ (1|plate) + (1|sample), Penicillin))

L <- getME(fm1, "L")
Matrix::image(L, main = "L",
              sub = "Penicillin: Structure of random effects interaction")
Documentation reproduced from package lme4, version 1.1-13, License: GPL (>= 2)

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