Scale of Measurement

Once we have identified the independent and dependent variables, our next step in choosing a statistical test is to identify the scale of measurement of the variables. All of the parametric tests that we have learned to date require an interval or ratio scale of measurement for the dependent variable. Many psychologists also apply parametric tests to variables with an approximately interval scale of measurement. It is your decision whether to consider approximately interval or "scale" scores as suitable for parametric tests of means. If you are working with a dependent variable that has a nominal or ordinal scale of measurement, then you must choose a nonparametric statistic to test your hypothesis.

The scale of measurement of the dependent variable helps us to choose the broad category of statistical procedures appropriate for our hypothesis (nonparametric vs. parametric). The scale of measurement of the independent variable helps us to determine which statistical procedure within the broad category is appropriate.

Type of Statistic		Scale of Measurement
Nonparametric	-	Nominal
Nonparametric	-	Ordinal
Nonparametric	Parametric	Approximately Interval
-	Parametric	Interval
-	Parametric	Ratio

Let us now return to our study example and determine the scale of measurement in our study.

Study

It has been traditional for the man rather than the woman to receive the check when a couple dines out. A researcher wondered whether this would be true if the woman was clearly in charge, asking for the wine list, questioning the waiter about dishes on the menu, etc. A large random sample of restaurants was selected. One couple was used in all restaurants, but in half the man assumed the traditional in-charge role, and in the other half the woman was in charge. At each restaurant, the couple recorded whether the check was presented to the man or to the woman.

Test the research hypothesis that the check will be presented to the person showing in-charge behavior.

Analysis

The independent variable in the study is in-charge behavior and the dependent variable is the presentation of the check. The wait staff has only two options for the dependent variable -- to present the check to the man or to the woman. These options are categorical and discrete, thus, the dependent variable is measured on a nominal scale of measurement. Similarly, the in-charge behavior is categorical and discrete (male vs. female) and is also measured on a nominal scale of measurement. Since the dependent variable is nominal, we know that we must use a nonparametric technique. The independent variable is also nominal; think about statistical procedures for two nominal variables.

Let's review the nonparametric and parametric options that are available.

Once we have reviewed our options, the next step is to consider the study design.

 

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