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.
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
penicillin sample. A factor with levels
‘A’ to ‘F’.
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
O.L. Davies and P.L. Goldsmith (eds), Statistical
Methods in Research and Production, 4th ed., Oliver and
Boyd, (1972), section 6.6
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")
Dataset imported from https://www.r-project.org.