crimtab           package:datasets           R Documentation(latin1)

_S_t_u_d_e_n_t'_s _3_0_0_0 _C_r_i_m_i_n_a_l_s _D_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

     Data of 3000 male criminals over 20 years old undergoing their
     sentences in the chief prisons of England and Wales.

_U_s_a_g_e:

     data(crimtab)

_F_o_r_m_a_t:

     A 'table' object of  'integer' counts, of dimension 42 * 22 with a
     total count, 'sum(crimtab)' of 3000.

     The 42 'rownames' ('"9.4"', '"9.5"', ...) correspond to midpoints
     of intervals of finger lengths whereas the 22 column names
     ('colnames') ('"142.24"', '"144.78"', ...) correspond to (body)
     heights of 3000 criminals, see also below.

_D_e_t_a_i_l_s:

     Student is the pseudonym of William Sealy Gosset. In his 1908
     paper he wrote (on page 13) at the beginning of section VI
     entitled _Practical Test of the forgoing Equations_:

     "Before I had succeeded in solving my problem analytically, I had
     endeavoured to do so empirically.  The material used was a
     correlation table containing the height and left middle finger
     measurements of 3000 criminals, from a paper by W. R. MacDonell
     (_Biometrika_, Vol. I., p. 219).  The measurements were written
     out on 3000 pieces of cardboard, which were then very thoroughly
     shuffled and drawn at random.  As each card was drawn its numbers
     were written down in a book, which thus contains the measurements
     of 3000 criminals in a random order.  Finally, each consecutive
     set of 4 was taken as a sample-750 in all-and the mean, standard
     deviation, and correlation of each sample determined.  The
     difference between the mean of each sample and the mean of the
     population was then divided by the standard deviation of the
     sample, giving us the _z_ of Section III."

     The table is in fact page 216 and not page 219 in MacDonell(1902).
     In the MacDonell table, the middle finger lengths were given in mm
     and the heights in feet/inches intervals, they are both converted
     into cm here.  The midpoints of intervals were used, e.g., where
     MacDonell has 4' 7''9/16 - 8''9/16, we have 142.24 which is
     2.54*56 = 2.54*(4' 8'').

     MacDonell credited the source of data (page 178) as follows: _The
     data on which the memoir is based were obtained, through the
     kindness of Dr Garson, from the Central Metric Office, New
     Scotland Yard..._ He pointed out on page 179 that : _The forms
     were drawn at random from the mass on the office shelves; we are
     therefore dealing with a random sampling._

_S_o_u_r_c_e:

     <URL: http://pbil.univ-lyon1.fr/R/donnees/criminals1902.txt>
     thanks to Jean R. Lobry and Anne-Beatrice Dufour.

_R_e_f_e_r_e_n_c_e_s:

     Garson, J.G. (1900) The metric system of identification of
     criminals, as used in in Great Britain and Ireland. _The Journal
     of the Anthropological Institute of Great Britain and Ireland_
     *30*, 161-198.

     MacDonell, W.R. (1902) On criminal anthropometry and the
     identification of criminals. _Biometrika_ *1*, 2, 177-227.

     Student (1908) The probable error of a mean. _Biometrika_ *6*,
     1-25.

_E_x_a_m_p_l_e_s:

     require(stats)
     dim(crimtab)
     utils::str(crimtab)
     ## for nicer printing:
     local({cT <- crimtab
            colnames(cT) <- substring(colnames(cT), 2,3)
            print(cT, zero.print = " ")
     })

     ## Repeat Student's experiment:

     # 1) Reconstitute 3000 raw data for heights in inches and rounded to
     #    nearest integer as in Student's paper:

     (heIn <- round(as.numeric(colnames(crimtab)) / 2.54))
     d.hei <- data.frame(height = rep(heIn, colSums(crimtab)))

     # 2) shuffle the data:

     set.seed(1)
     d.hei <- d.hei[sample(1:3000), , drop = FALSE]

     # 3) Make 750 samples each of size 4:

     d.hei$sample <- as.factor(rep(1:750, each = 4))

     # 4) Compute the means and standard deviations (n) for the 750 samples:

     h.mean <- with(d.hei, tapply(height, sample, FUN = mean))
     h.sd   <- with(d.hei, tapply(height, sample, FUN = sd)) * sqrt(3/4)

     # 5) Compute the difference between the mean of each sample and
     #    the mean of the population and then divide by the
     #    standard deviation of the sample:

     zobs <- (h.mean - mean(d.hei[,"height"]))/h.sd

     # 6) Replace infinite values by +/- 6 as in Student's paper:

     zobs[infZ <- is.infinite(zobs)] # 3 of them
     zobs[infZ] <- 6 * sign(zobs[infZ])

     # 7) Plot the distribution:

     require(grDevices); require(graphics)
     hist(x = zobs, probability = TRUE, xlab = "Student's z",
          col = grey(0.8), border = grey(0.5),
          main = "Distribution of Student's z score  for 'crimtab' data")

