We are concerned with three types of variables. The dependent variable, the independent variable, and the control variable. The dependent variable is the variable we want to explain. (in the example below, whether the U.S. should send troops to invade Canada) The independent variable is the variable we are using to try to explain the dependent variable. (In this case, the respondents' ideological bias liberal or conservative). The hypothesis is that liberals will be opposed to sending troops into Canada and conservatives will be for sending troops into Canada. Classifying position on sending troops into Canada by ideological categories might produce a table of frequencies that looks like Table 1.

		Table 1
	Position on Sending Troops to Canada by Ideology.
			Number of
Position on Issue:	Liberals	Conservatives	Respondents
For Sending Troops	100	200	(300)
Against Sending Troops	400	300	(700)
Number of Respondents	(500)	(500)	(1000)

In a sample of 1,000 people, we have 500 liberals, 500 conservatives, and 300 who are for sending in troops, and 700 who are against sending in troops. (The numbers in parenthesis are the "marginal" or "univariate" distributions.) The internal numbers in the table show that 100 people are liberal and also in favor of sending troops in, 400 are liberal and against sending troops, 200 are both conservative and for sending in troops, and 300 are both conservative and against sending in troops. Since tables are rarely as balanced as this one, cell frequencies are always presented as percentages rather than raw numbers. Percentages permit one to draw precise conclusions about different rates of behavior among groups of different absolute size.

When we convert the frequencies into percentages there are two possibilities: 1) We can percentagize by the dependent variable so that the rows total up to 100 percent (Table 2); or 2) we can percentagize by the independent variable so that the columns add up to 100 percent (Table 3).

		Table 2
		Ideology by Troop Preference.
				Number of
Position on Issue:	Liberals	Conservatives	Total	Respondents
For Sending Troops	33.3%	66.7	100.0%	(300)
Against Sending Troops	57.1%	42.9	100.0%	(700)

	Table 3
Troop Preference by Ideology.
Position on Issue:	Liberals	Conservatives
For Sending Troops	20.0%	40.0%
Against Sending Troops	80.0	60.0
Total	100.0%	100.0%
(N)	(500)	(500)

The two ways of percentagizing give different figures and are read differently. Table 2 is read: Of those who are in favor of sending troops, 33.3 percent are liberals and 66.7 percent are conservatives. Of' those who are against sending troops, 57.1 percent are liberals and 42.8 percent are conservatives.

Table 3 is read: Of the liberals, 20 percent are in favor of sending troops into Canada and 80 percent are opposed to doing so. Of the conservatives, 40 percent are for sending troops into Canada and 60 percent are opposed to it. Table 3 shows the correct way to percentagize the table because we are interested in the effect of ideology on sending "troops in Canada." We hypothesize that ideology causes issue position so that ideology is the independent variable and issue position (troops to Canada) is the dependent variable. As ideology shifts from liberal to conservative, we anticipate greater support for sending troops into Canada.

A control variable can now be introduced to increase our understanding of the original two variable relationship. Suppose, for example, we think that a conservative respondent does not favor sending in troops (the hypothesized liberal response) because he prefers the use of nuclear weapons. We can control for, or hold constant, the respondents' position on nuclear weapons and then look at the effect of this third variable on the original two. In the following tables respondents have been separated according to whether they approve (Table 4) or disapprove (Table 5) of the use of nuclear weapons.

	Table 4
Troop Preference by Ideology among Those Who Approve Nuclear Weapons
Position on Issue:	Liberals	Conservatives
For Sending Troops	100.0%	66.7%
Against Sending Troops	0.0	33.3
Total	100.0%	100.0%
(N)	(50)	(150)

Only those respondents who are in favor of the use of nuclear weapons.

	Table 4
Troop Preference by Ideology among Those Who Disapprove Nuclear Weapons
Position on Issue:	Liberals	Conservatives
For Sending Troops	12.5%	28.5%
Against Sending Troops	87.5	71.5
Total	100.0%	100.0%
(N)	(450)	(350)

Only those respondents who are oppose to the use of nuclear weapons.

The data in Table 4 show that all of the liberals who were for the use of nuclear weapons also favored sending troops into Canada while two-thirds of the pro-nuclear weapons conservatives took such a position. This lends some support to the supposition that there were conservatives who made the hypothesized liberal response for the "wrong" reason--or at least a reason that was not expected when the initial relationship between the two variables was predicted.

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