

   UCBAdmissions {base}                         R Documentation

   SSttuuddeenntt AAddmmiissssiioonnss aatt UUCC BBeerrkkeelleeyy

   DDeessccrriippttiioonn::

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

   UUssaaggee::

        data(UCBAdmissions)

   FFoorrmmaat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Deettaaiills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Reeffeerreennccees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Exxaammppllees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)

