Supplementary Exercise 9.44 of IPS7e
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Data (fictitious) on admission to a university categorized by gender (f/m), 
school (business/law) and admission decision (no/yes).

Minitab commands and output (exercise can also be done by calculator):

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 WOpen "R:\Chapter 9\ex09_044.mtw".
 XTABS 'Gender' 'Admit'; 
  Layout 1 1;
  Frequencies 'Count';
  Counts;
  RowPercents; 
  DMissing 'Gender' 'Admit'.

Tabulated statistics: Gender, Admit 
Using frequencies in Count

Rows: Gender   Columns: Admit

             No    Yes     All

Female      300    400     700
          42.86  57.14  100.00

Male        310    490     800
          38.75  61.25  100.00

All         610    890    1500
          40.67  59.33  100.00

Cell Contents:      Count
                    % of Row

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 XTABS 'Gender' 'Admit' 'School'; 
  Layout 1 1;
  Frequencies 'Count';
  Counts;
  RowPercents; 
  DMissing 'Gender' 'Admit' 'School'.

Tabulated statistics: Gender, Admit, School 
Using frequencies in Count
 
Results for School = Business 

Rows: Gender   Columns: Admit

             No    Yes     All

Female      100    200     300
          33.33  66.67  100.00

Male        200    400     600
          33.33  66.67  100.00

All         300    600     900
          33.33  66.67  100.00

Cell Contents:      Count
                    % of Row

 
Results for School = Law 

Rows: Gender   Columns: Admit

             No    Yes     All

Female      200    200     400
          50.00  50.00  100.00

Male        110     90     200
          55.00  45.00  100.00

All         310    290     600
          51.67  48.33  100.00

Cell Contents:      Count
                    % of Row

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Answers to questions:
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(a) + (b):
Percent admitted among males and females combined for the two schools 
(from the first table):

          admitted
female    57.1%
male      61.3%

Overall, a larger proportion of males is admitted.

(c):
Percent admitted among males and females separately for the two schools
(from the next two tables):

               admitted
          business   law
female    66.7%      50.0%
male      66.7%      45.0%

At the business school, equal proportions of females and males are
admitted. At the law school, a larger proportion of females is admitted.

(d):
The reason for the paradoxial situation (Simpson's paradox) is that the
school is a lurking variable. It is strongly associated with both admission
(the admission rate is much larger at the business school) and gender (a much
larger proportion of women apply at law school than at business school), and
therefore has the potential to distort the relation between gender and admission.

In plain words, the overall admission rate of males is higher because more
men apply at the business school where admission is easier than at law school.
Or conversely, the women appear to have a lower admission rate because a
larger proportion of women apply at the law school where the general
admission rate is low.