Introduction to Statistics
Variables and Descriptive Statistics
Figure 1331 –
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Statistics provide a way of dealing with numbers. Before leaping headlong into statistical tests, it is necessary to get an idea of how these numbers come about, what they represent, and the various forms they can take.
Let’s begin by examining a simple experiment. Suppose an investigator has a hunch that clam juice is an effective treatment for the misery of psoriasis. He assembles a group of patients, randomizes them to a treatment and control group, and gives clam juice to the treatment group and something that looks, smells, and tastes like clam juice (but isn’t) to the control group. After a few weeks, he measures the extent of psoriasis on the patients, perhaps by estimating the percent of body involvement or by looking at the change in size of a particular lesion. He then does some number crunching to determine if clam juice is as good a treatment as he hopes it is.
Let’s have a closer look at the data from this experiment. To begin with, there are at least two variables. A definition of the term variable is a little hard to come up with, but basically it relates to anything that is measured or manipulated in a study. The most obvious variable in this experiment is the measurement of the extent of psoriasis. It is evident that this is something that can be measured. A less obvious variable is the nature of treatment—drug or placebo. Although it is less evident how you might convert this to a number, it is still clearly something that is varied in the course of the experiment.
A few more definitions are in order. Statisticians frequently speak of independent and dependent variables. In an experiment, the independent variables are those that are varied by and under the control of the experimenter; the dependent variables are those that respond to experimental manipulation. In the current example, the independent variable is the type of therapy—clam juice or placebo—and the dependent variable is the size of lesions or body involvement. Although in this example the identification of independent and dependent variables is straightforward, the distinction is not always so obvious. Frequently, researchers must rely on natural variation in both types of variables and look for a relationship between the two. For example, if an investigator was looking for a relationship between smoking and lung cancer, an ethics committee would probably take a dim view of ordering 1,000 children to smoke a pack of cigarettes a day for 20 years. Instead, the investigator must look for a relationship between smoking and lung cancer in the general adult population and must assume that smoking is the independent variable and that lung cancer is the dependent variable; that is, the extent of lung cancer depends on variations in smoking.
There are other ways of defining types of variables that turn out to be essential in determining the ways the numbers will be analyzed. Variables are frequently classified as nominal, ordinal, interval, or ratio ( Fig.1099). A nominal variable is simply a named category. Our clam juice versus placebo is one such variable, as is the sex of the patient, or the diagnosis given to a group of patients.
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| 5343. | Norman GR, Streiner DL. PDQ Statistics . 3rd ed. Hamilton, Ontario: BC Decker Inc.; 2003. |
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