Penicillin               package:lme4               R Documentation

_V_a_r_i_a_t_i_o_n _i_n _p_e_n_i_c_i_l_l_i_n _t_e_s_t_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     data(Penicillin)

_F_o_r_m_a_t:

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

     '_d_i_a_m_e_t_e_r' diameter (mm) of the zone of inhibition of the growth
          of the organism.

     '_p_l_a_t_e' assay plate.  A factor with levels 'a' to 'x'.

     '_s_a_m_p_l_e' penicillin sample.  A factor with levels 'A' to 'F'.

_D_e_t_a_i_l_s:

     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."

_S_o_u_r_c_e:

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

_E_x_a_m_p_l_e_s:

     str(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))
     image(fm1@L,
           sub = "Structure of random effects interaction in penicillin model")

