Skip to Main Content

We have a new app!

Take the Access library with you wherever you go—easy access to books, videos, images, podcasts, personalized features, and more.

Download the Access App here: iOS and Android. Learn more here!


In the investigation of most clinical research questions, some form of quantitative data will be collected. Initially these data exist in raw form, which means that they are nothing more than a compilation of numbers representing empirical observations from a group of individuals. For these data to be useful as measures of group performance, they must be organized, summarized, and analyzed, so that their meaning can be communicated. These are the functions of the branch of mathematics called statistics.

Descriptive statistics are used to characterize the shape, central tendency, and variability within a set of data, often with the intent to describe a sample or population. Measures of population characteristics are called parameters. A descriptive index computed from sample data is called a statistic. When researchers generalize sample data to populations, they use statistics to estimate population parameters. In this chapter we introduce the basic elements of statistical analysis for describing quantitative data.

Frequency Distributions

Because the numerical data collected during a study exist in unanalyzed, unsorted form, a structure is needed that allows us to summarize trends or averages.


Consider a set of hypothetical scores for the Coin Rotation Test (CRT), an assessment of motor dexterity.1,2 Using a stop watch, a clinician determines the time it takes for the patient to rotate a nickel as rapidly as possible through consecutive 180° turns, using the thumb, index, and middle fingers for 20 rotations. A lower score (shorter time) indicates better dexterity.

Table 22-1A presents a set of hypothetical scores on the CRT for 32 patients with multiple sclerosis. The total set of scores for a particular variable is called a distribution. The total number of scores in the distribution is given the symbol N. In this sample, N = 32.

Table 22-1Distribution of Scores for the Coin Rotation Test (in seconds) (N= 32)

image An uppercase N is used to represent the total number of subjects in a sample. If the sample is divided into groups, a lowercase n is used to indicate the number of subjects in each group.

Although visual inspection of a distribution allows us to see all the scores, this list is long and unwieldy and inadequate for describing this group of patients or comparing them with any other group. We can begin to summarize the data by presenting them in a frequency distribution, a table of rank ordered scores that shows the number of times each value occurred, or its frequency (f).

The first two columns in Table 22-1B show the frequency distribution for the CRT scores. Now we can ...

Pop-up div Successfully Displayed

This div only appears when the trigger link is hovered over. Otherwise it is hidden from view.