

UCBAdmissions {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 clas-
     sified 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 Simp-
     son'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 individ-
     ual 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://hot-
     spur.psych.yorku.ca/SCS/friendly.html>) for further
     information.

_R_e_f_e_r_e_n_c_e_s_:

     Bickel, P. J., Hammel, E. A., & 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_:

     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))
     for(i in 1:6)
       mosaicplot(UCBAdmissions[,,i],
         xlab = "Admit", ylab = "Sex",
         main = paste("Department", LETTERS[i]))
     par(opar)

