UCBAdmissions              package:base              R Documentation

_S_t_u_d_e_n_t _A_d_m_i_s_s_i_o_n_s _a_t _U_C _B_e_r_k_e_l_e_y

_D_e_s_c_r_i_p_t_i_o_n:

     Aggregate data on applicants to graduate school at Berkeley for
     the six largest departments in 1973 classified by admission and
     sex.

_U_s_a_g_e:

     data(UCBAdmissions)

_F_o_r_m_a_t:

     A 3-dimensional array resulting from cross-tabulating 4526
     observations on 3 variables.  The variables and their levels are
     as follows:

       No  Name    Levels
        1  Admit   Admitted, Rejected
        2  Gender  Male, Female
        3  Dept    A, B, C, D, E, F

_D_e_t_a_i_l_s:

     This data set is frequently used for illustrating Simpson's
     paradox, see Bickel et al. (1975).  At issue is whether the data
     show evidence of sex bias in admission practices.  There were 2691
     male applicants, of whom 1198 (44.5%) were admitted, compared with
     1835 female applicants of whom 557 (30.4%) were admitted.  This
     gives a sample odds ratio of 1.83, indicating that males were
     almost twice as likely to be admitted.  In fact, graphical methods
     (as in the example below) or log-linear modelling show that the
     apparent association between admission and sex stems from
     differences in the tendency of males and females to apply to the
     individual departments (females used to apply "more" to
     departments with higher rejection rates).

     This data set can also be used for illustrating methods for
     graphical display of categorical data, such as the general-purpose
     mosaic plot or the "fourfold display" for 2-by-2-by-k tables.  See
     the home page of Michael Friendly (<URL:
     http://www.math.yorku.ca/SCS/friendly.html>) for further
     information.

_R_e_f_e_r_e_n_c_e_s:

     Bickel, P. J., Hammel, E. A., and O'Connell, J. W. (1975) Sex bias
     in graduate admissions: Data from Berkeley. _Science_, *187*,
     398-403.

_E_x_a_m_p_l_e_s:

     require(graphics)
     data(UCBAdmissions)
     ## Data aggregated over departments
     apply(UCBAdmissions, c(1, 2), sum)
     mosaicplot(apply(UCBAdmissions, c(1, 2), sum),
                main = "Student admissions at UC Berkeley")
     ## Data for individual departments
     opar <- par(mfrow = c(2, 3), oma = c(0, 0, 2, 0))
     for(i in 1:6)
       mosaicplot(UCBAdmissions[,,i],
         xlab = "Admit", ylab = "Sex",
         main = paste("Department", LETTERS[i]))
     mtext(expression(bold("Student admissions at UC Berkeley")),
           outer = TRUE, cex = 1.5)
     par(opar)

