+-----------------+-------------------+
| UCBAdmissions   | R Documentation   |
+-----------------+-------------------+

Student Admissions at UC Berkeley
---------------------------------

Description
~~~~~~~~~~~

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

Usage
~~~~~

::

    UCBAdmissions

Format
~~~~~~

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     |
+------+----------+----------------------+

Details
~~~~~~~

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
(`http://www.math.yorku.ca/SCS/friendly.html <http://www.math.yorku.ca/SCS/friendly.html>`_)
for further information.

References
~~~~~~~~~~

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

Examples
~~~~~~~~

::

    require(graphics)
    ## 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)

