Information Content	Variable Type	Examples
Higher	Ratio	Temperature (Kelvin); blood pressure*
	Continuous (dimensional)	Temperature (Fahrenheit)*
	Ordinal (ranked)	Edema = 3+ out of 5Perceived quality of care = good/fair/poor
	Binary (dichotomous)	Gender; heart murmur = present/absent
	Nominal	Blood type; color = cyanotic or jaundiced; taste = bitter or sweet
Lower

Note: Variables with higher information content may be collapsed into variables with less information content. For example, hypertension could be described as “165/95 mm Hg” (continuous data), “absent/mild/moderate/severe” (ordinal data), or “present/absent” (binary data). One cannot move in the other direction, however. Also, knowing the type of variables being analyzed is crucial for deciding which statistical test to use (see Table 11-1).

^*For most types of data analysis, the distinction between continuous data and ratio data is unimportant. Risks and proportions sometimes are analyzed using the statistical methods for continuous variables, and sometimes observed counts are analyzed in tables, using nonparametric methods (see Chapter 11).

1 Nominal Variables

Nominal variables are “naming” or categorical variables that have no measurement scales and no rank order. Examples are blood groups (O, A, B, and AB), occupations, food groups, and skin color. If skin color is the variable being examined, a different number can be assigned to each color (e.g., 1 is bluish purple, 2 is black, 3 is white, 4 is blue, 5 is tan) before the information is entered into a computer data system. Any number could be assigned to any color, and that would make no difference to the statistical analysis. This is because the number is merely a numerical name for a color, and size of the number used has no inherent meaning; the number given to a particular color has nothing to do with the quality, value, or importance of the color.

2 Dichotomous (Binary) Variables

If all skin colors were included in one nominal variable, there is a problem: the variable does not distinguish between normal and abnormal skin color, which is usually the most important aspect of skin color for clinical and research purposes. As discussed, abnormal skin color (e.g., pallor, jaundice, cyanosis) may be a sign of numerous health problems (e.g., anemia, liver disease, cardiac failure). Researchers might choose to create a variable with only two levels: normal skin color (coded as a 1) and abnormal skin color (coded as a 2). This new variable, which has only two levels, is said to be dichotomous (Greek, “cut into two”).

Many dichotomous variables, such as well/sick, living/dead, and normal/abnormal, have an implied direction that is favorable. Knowing that direction would be important for interpreting the data, but not for the statistical analysis. Other dichotomous variables, such as female/male and treatment/placebo, have no a priori qualitative direction.

Dichotomous variables, although common and important, often are inadequate by themselves to describe something fully. When analyzing cancer therapy, it is important to know not only whether the patient survives or dies (a dichotomous variable), but also how long the patient survives (time forms a continuous variable). A survival analysis or life table analysis, as described in Chapter 11, may be done. It is important to know the quality of patients’ lives while they are receiving the therapy; this might be measured with an ordinal variable, discussed next. Similarly, for a study of heart murmurs, various types of data may be needed, such as dichotomous data concerning a murmur’s timing (e.g., systolic or diastolic), nominal data on its location (e.g., aortic valve area) and character (e.g., rough), and ordinal data on its loudness (e.g., grade III). Dichotomous variables and nominal variables sometimes are called discrete variables because the different categories are completely separate from each other.

3 Ordinal (Ranked) Variables

Many types of medical data can be characterized in terms of three or more qualitative values that have a clearly implied direction from better to worse. An example might be “satisfaction with care” that could take on the values of “very satisfied,” “fairly satisfied,” or “not satisfied.” These data are not measured on a measurement scale. They form an ordinal (i.e., ordered or ranked) variable.

There are many clinical examples of ordinal variables. The amount of swelling in a patient’s legs is estimated by the clinician and is usually reported as “none” or 1+, 2+, 3+, or 4+ pitting edema (puffiness). A patient may have a systolic murmur ranging from 1+ to 6+. Respiratory distress is reported as being absent, mild, moderate, or severe. Although pain also may be reported as being absent, mild, moderate, or severe, in most cases, patients are asked to describe their pain on a scale from 0 to 10, with 0 being no pain and 10 the worst imaginable pain. The utility of such scales to quantify subjective assessments such as pain intensity is controversial and is the subject of ongoing research.

Ordinal variables are not measured on an exact measurement scale, but more information is contained in them than in nominal variables. It is possible to see the relationship between two ordinal categories and know whether one category is more desirable than another. Because they contain more information than nominal variables, ordinal variables enable more informative conclusions to be drawn. As described in Chapter 11, ordinal variables often require special techniques of analysis.

4 Continuous (Dimensional) Variables

Many types of medically important data are measured on continuous (dimensional) measurement scales. Patients’ heights, weights, systolic and diastolic blood pressures, and serum glucose levels all are examples of data measured on continuous scales. Even more information is contained in continuous data than in ordinal data because continuous data not only show the position of the different observations relative to each other, but also show the extent to which one observation differs from another. Continuous data often enable investigators to make more detailed inferences than do ordinal or nominal data.

Relationships between continuous variables are not always linear (in a straight line). The relationship between the birth weight and the probability of survival of newborns is not linear.³ As shown in Figure 9-1, infants weighing less than 3000 g and infants weighing more than 4500 g are historically at greater risk for neonatal death than are infants weighing 3000 to 4500 g (~6.6-9.9 lb).

Figure 9-1 Histogram showing neonatal mortality rate by birth weight group, all races, United States, 1980.

(Data from Buehler JW et al: Public Health Rep 102:151–161, 1987.)

5 Ratio Variables

If a continuous scale has a true 0 point, the variables derived from it can be called ratio variables. The Kelvin temperature scale is a ratio scale because 0 degrees on this scale is absolute 0. The centigrade temperature scale is a continuous scale, but not a ratio scale because 0 degrees on this scale does not mean the absence of heat. For some purposes, it may be useful to know that 200 units of something is twice as large as 100 units, information provided only by a ratio scale. For most statistical analyses, however, including significance testing, the distinction between continuous and ratio variables is not important.

6 Risks and Proportions as Variables

As discussed in Chapter 2, a risk is the conditional probability of an event (e.g., death or disease) in a defined population in a defined period. Risks and proportions, which are two important types of measurement in medicine, share some characteristics of a discrete variable and some characteristics of a continuous variable. It makes no conceptual sense to say that a “fraction” of a death occurred or that a “fraction” of a person experienced an event. It does make sense, however, to say that a discrete event (e.g., death) or a discrete characteristic (e.g., presence of a murmur) occurred in a fraction of a population. Risks and proportions are variables created by the ratio of counts in the numerator to counts in the denominator. Risks and proportions sometimes are analyzed using the statistical methods for continuous variables (see Chapter 10), and sometimes observed counts are analyzed in tables, using statistical methods for analyzing discrete data (see Chapter 11).

C Counts and Units of Observation

The unit of observation is the person or thing from which the data originated. Common examples of units of observation in medical research are persons, animals, and cells. Units of observation may be arranged in a frequency table, with one characteristic on the x-axis, another characteristic on the y-axis, and the appropriate counts in the cells of the table. Table 9-2, which provides an example of this type of 2 × 2 table, shows that among 71 young professional persons studied, 63% of women and 57% of men previously had their cholesterol levels checked. Using these data and the chi-square test described in Chapter 11, one can determine whether or not the difference in the percentage of women and men with cholesterol checks was likely a result of chance variation (in this case the answer is “yes”).

Table 9-2 Standard 2 × 2 Table Showing Gender of 71 Participants and Whether or Not Serum Total Cholesterol Was Checked

D Combining Data

A continuous variable may be converted to an ordinal variable by grouping units with similar values together. For example, the individual birth weights of infants (a continuous variable) can be converted to ranges of birth weights (an ordinal variable), as shown in Figure 9-1. When the data are presented as categories or ranges (e.g., <500, 500-999, 1000-1499 g), information is lost because the individual weights of infants are no longer apparent. An infant weighing 501 g is in the same category as an infant weighing 999 g, but the infant weighing 999 g is in a different category from an infant weighing 1000 g, just 1 g more. The advantage is that now percentages can be created, and the relationship of birth weight to mortality is easier to show.

Three or more groups must be formed when converting a continuous variable to an ordinal variable. In the example of birth weight, the result of forming several groups is that it creates an ordinal variable that progresses from the heaviest to the lightest birth weight (or vice versa). If a continuous variable such as birth weight is divided into only two groups, however, a dichotomous variable is created. Infant birth weight often is divided into two groups, creating a dichotomous variable of infants weighing less than 2500 g (low birth weight) and infants weighing 2500 g or more (normal birth weight). The fewer the number of groups formed from a continuous variable, however, the greater is the amount of information that is lost.