# Describing Variation in Data

9 Describing Variation in Data

# II Statistics and Variables

## B Types of Variables

Information Content Variable Type Examples
Higher Ratio Temperature (Kelvin); blood pressure*
Continuous (dimensional) Temperature (Fahrenheit)*
Ordinal (ranked) Edema = 3+ out of 5
Perceived 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

### 2 Dichotomous (Binary) Variables

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.

### 4 Continuous (Dimensional) Variables

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).

### 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”).

## 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.

# III Frequency Distributions

## A Frequency Distributions of Continuous Variables

Observations on one variable may be shown visually by putting the variable’s values on one axis (usually the horizontal axis or x-axis) and putting the frequency with which that value appears on the other axis (usually the vertical axis or y-axis). This is known as a frequency distribution. Table 9-3 and Figure 9-2 show the distribution of the levels of total cholesterol among 71 professional persons. The figure is shown in addition to the table because the data are easier to interpret from the figure.