On this Picostat.com statistics page, you will find information about the Penicillin data set which pertains to Variation in penicillin testing. The Penicillin data set is found in the lme4 R package. You can load the Penicillin data set in R by issuing the following command at the console data("Penicillin"). This will load the data into a variable called Penicillin. If R says the Penicillin data set is not found, you can try installing the package by issuing this command install.packages("lme4") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Penicillin R data set. The size of this file is about 1,612 bytes.
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.