015. Contingency Tables (Cross-Tabulations or Cross-Tabs)

The data sets in Example 2.2 involved only one variable: the number of passengers, or the number of miles flown. To examine two variables simultaneously Contingency tables can be used. These tables indicate the number of observations for both variables that fall jointly in age level category of passengers, for example. If statistician obtained data relating to age and frequency of flying, he could present this information in the form of a contingency table such as Table 2.10.

Table 2.10 – P&P’s Contingency Table for Age and Flights

Number of Flights per Year
Age	1-2	3-5	Over 5	Total
0 to less than 25	1 (0.02)	1 (0.02)	2 (0.04)	4 (0.08)
25 to less than 40	2 (0.04)	8 (0.16)	10 (0.20)	20 (0.40)
40 to less than 65	1 (0.02)	6 (0.12)	15 (0.30)	22 (0.44)
65 and over	1 (0.02)	2 (0.04)	1 (0.02)	4 (0.08)
Total	5 (0.10)	17 (0.34)	28 (0.56)	50 (1.00)

In this table there is four age categories and three flight categories. Each of the 50 people in this sample will fall into one of these 12 joint categories. The percentage within each cell is shown in parentheses. For example, 8 of the 50 passengers, or 16 percent, between ages 25 and 40 fly between three and five times a year; the most of the passengers come from the second and third age categories; people in the 40 to less than 65 age group flew over five times a year more often than any other frequency.

The information contained in each cell could be displayed on the basis of sex. Thus, of the eight people in the second age category who fly between three and five times a year, six might be males and the other two females. The entry in that cell could then appear as 6, 2 (0.16).

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