Tabulation and association

• Categorical data lends itself to tabulation:
  • Tabulation retains all the information in the data, and
  • makes the structure of the data clearer.

                    FSEX         Page 1 of 1
            Count  |
                   |Male     Female
                   |                    Row
                   |       1|       2| Total
FJBSTAT    --------+--------+--------+
                1  |   546  |   175  |   721
  Self-employed    |        |        |   7.7
                   +--------+--------+
                2  |  2359  |  2382  |  4741
  Employed         |        |        |  50.3
                   +--------+--------+
                3  |   261  |   132  |   393
  Unemployed       |        |        |   4.2
                   +--------+--------+
                4  |   708  |   950  |  1658
  Retired          |        |        |  17.6
                   +--------+--------+
                5  |        |    34  |    34
  Maternity leave  |        |        |    .4
                   +--------+--------+
                6  |    24  |   795  |   819
  Family care      |        |        |   8.7
                   +--------+--------+
                7  |   313  |   360  |   673
  FT studt, school |        |        |   7.1
                   +--------+--------+
                8  |   193  |   153  |   346
  LT sick, disabld |        |        |   3.7
                   +--------+--------+
                9  |    22  |    15  |    37
  Other            |        |        |    .4
                   +--------+--------+
            Column    4426     4996     9422
             Total    47.0     53.0    100.0

(Source: BHPS wave 6)

• Tabulation allows us to see four things not apparent from the raw data:
  1. The overall male-female distribution;
  2. The overall employment-status distribution;
  3. The different employment-status distributions within the sexes; and
  4. The different sex proportions in each employment status.

• The latter two constitute the association between the two variables.
• We can see this more clearly with percentages
  • To focus on how employment status varies across sex we use column percentages ...
  • ... to get proportions within each sex.

                      FSEX         Page 1 of 1
              Count  |
             Col Pct |Male     Female
                     |                    Row
                     |       1|       2| Total
  FJBSTAT    --------+--------+--------+
                  1  |   546  |   175  |   721
    Self-employed    |  12.3  |   3.5  |   7.7
                     +--------+--------+
                  2  |  2359  |  2382  |  4741
    Employed         |  53.3  |  47.7  |  50.3
                     +--------+--------+
                  3  |   261  |   132  |   393
    Unemployed       |   5.9  |   2.6  |   4.2
                     +--------+--------+
                  4  |   708  |   950  |  1658
    Retired          |  16.0  |  19.0  |  17.6
                     +--------+--------+
                  5  |        |    34  |    34
    Maternity leave  |        |    .7  |    .4
                     +--------+--------+
                  6  |    24  |   795  |   819
    Family care      |    .5  |  15.9  |   8.7
                     +--------+--------+
                  7  |   313  |   360  |   673
    FT studt, school |   7.1  |   7.2  |   7.1
                     +--------+--------+
                  8  |   193  |   153  |   346
    LT sick, disabld |   4.4  |   3.1  |   3.7
                     +--------+--------+
                  9  |    22  |    15  |    37
    Other            |    .5  |    .3  |    .4
                     +--------+--------+
              Column    4426     4996     9422
               Total    47.0     53.0    100.0
  

• Percentages facilitate comparison by `controlling' for marginal (i.e., row and column distribution) differences.