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Dummy Variables

Why use dummies?

Regression analysis is used with numerical variables. Results only have a valid interpretation if it makes sense to assume that having a value of 2 on some variable is does indeed mean having twice as much of something as a 1, and having a 50 means 50 times as much as 1.

However, social scientists often need to work with categorical variables in which the different values have no real numerical relationship with each other. Examples include variables for race, political affiliation, or marital status. If you have a variable for political affiliation with possible responses including Democrat, Independent, and Republican, it obviously doesn't make sense to assign values of 1 - 3 and interpret that as meaning that a Republican is somehow three times as politically affiliated as a Democrat.

The solution is to use dummy variables - variables with only two values, zero and one. It does make sense to create a variable called "Republican" and interpret it as meaning that someone assigned a 1 on this varible is Republican and someone with an 0 is not.

Nominal variables with multiple levels

If you have a nominal variable that has more than two levels, you need to create multiple dummy variables to "take the place of" the original nominal variable. For example, imagine that you wanted to predict depression from year in school: freshman, sophomore, junior, or senior. Obviously, "year in school" has more than two levels.

What you need to do is to recode "year in school" into a set of dummy variables, each of which has two levels. The first step in this process is to decide the number of dummy variables. This is easy; it's simply k-1, where k is the number of levels of the original variable.

You could also create dummy variables for all levels in the original variable, and simply drop one from each analysis.

In this instance, we would need to create 4-1=3 dummy variables. In order to create these variables, we are going to take 3 of the levels of "year of school", and create a variable corresponding to each level, which will have the value of yes or no (i.e., 1 or 0). In this instance, we can create a variable called "sophomore," "junior," and "senior." Each instance of "year of school" would then be recoded into a value for "sophomore," "junior," and "senior." If a person were a junior, then "sophomore" would be equal to 0, "junior" would be equal to 1, and "senior" would be equal to 0.

Interpreting results

The decision as to which level is not coded is often arbitrary. The level which is not coded is the category to which all other categories will be compared. As such, often the biggest group will be the not- coded category. For example, often "Caucasian" will be the not-coded group if that is the race of the majority of participants in the sample. In that case, if you have a variable called "Asian", the coefficient on the "Asian" variable in your regression will show the effect being Asian rather than Caucasian has on your dependant variable.

In our example, "freshman" was not coded so that we could determine if being a sophomore, junior, or senior predicts a different depressive level than being a freshman. Consequently, if the variable, "junior" was significant in our regression, with a positive beta coefficient, this would mean that juniors are significantly more depressed than freshman. Alternatively, we could have decided to not code "senior," if we thought that being a senior is qualitatively different from being of another year.

Levels of Measurement

The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. What does that mean? Begin with the idea of the variable, in this example "party affiliation." That variable has a number of attributes. Let's assume that in this particular election context the only relevant attributes are "republican", "democrat", and "independent". For purposes of analyzing the results of this variable, we arbitrarily assign the values 1, 2 and 3 to the three attributes. The level of measurement describes the relationship among these three values. In this case, we simply are using the numbers as shorter placeholders for the lengthier text terms. We don't assume that higher values mean "more" of something and lower numbers signify "less". We don't assume the the value of 2 means that democrats are twice something that republicans are. We don't assume that republicans are in first place or have the highest priority just because they have the value of 1. In this case, we only use the values as a shorter name for the attribute. Here, we would describe the level of measurement as "nominal".

Why is Level of Measurement Important?

First, knowing the level of measurement helps you decide how to interpret the data from that variable. When you know that a measure is nominal (like the one just described), then you know that the numerical values are just short codes for the longer names. Second, knowing the level of measurement helps you decide what statistical analysis is appropriate on the values that were assigned. If a measure is nominal, then you know that you would never average the data values or do a t-test on the data.

There are typically four levels of measurement that are defined:

• Nominal
• Ordinal
• Interval
• Ratio

In nominal measurement the numerical values just "name" the attribute uniquely. No ordering of the cases is implied. For example, jersey numbers in basketball are measures at the nominal level. A player with number 30 is not more of anything than a player with number 15, and is certainly not twice whatever number 15 is.

In ordinal measurement the attributes can be rank-ordered. Here, distances between attributes do not have any meaning. For example, on a survey you might code Educational Attainment as 0=less than H.S.; 1=some H.S.; 2=H.S. degree; 3=some college; 4=college degree; 5=post college. In this measure, higher numbers mean more education. But is distance from 0 to 1 same as 3 to 4? Of course not. The interval between values is not interpretable in an ordinal measure.

In interval measurement the distance between attributes does have meaning. For example, when we measure temperature (in Fahrenheit), the distance from 30-40 is same as distance from 70-80. The interval between values is interpretable. Because of this, it makes sense to compute an average of an interval variable, where it doesn't make sense to do so for ordinal scales. But note that in interval measurement ratios don't make any sense - 80 degrees is not twice as hot as 40 degrees (although the attribute value is twice as large).

Finally, in ratio measurement there is always an absolute zero that is meaningful. This means that you can construct a meaningful fraction (or ratio) with a ratio variable. Weight is a ratio variable. In applied social research most "count" variables are ratio, for example, the number of clients in past six months. Why? Because you can have zero clients and because it is meaningful to say that "...we had twice as many clients in the past six months as we did in the previous six months."

It's important to recognize that there is a hierarchy implied in the level of measurement idea. At lower levels of measurement, assumptions tend to be less restrictive and data analyses tend to be less sensitive. At each level up the hierarchy, the current level includes all of the qualities of the one below it and adds something new. In general, it is desirable to have a higher level of measurement (e.g., interval or ratio) rather than a lower one (nominal or ordinal).