Nominal

Objects or people are often placed in categories according to specific characteristics. If the categories have no rank or order, then the measurement is considered nominal. An example of a nominal measurement is the classification of patients with pulmonary disease into those with obstructive lung disease, restrictive lung disease, or a combination of obstructive and restrictive disease. The categories are mutually exclusive (i.e., all patients fit into one and only one category). Nominal categories are unranked, in that an individual with obstructive lung disease would not necessarily have a worse prognosis than an individual with restrictive lung disease.

The categories of a nominal measurement scale are defined using objective indicators that are universally understood. For example, the classification of patients with heart failure could be based on the primary cause for the development of the condition (Box 7-1). In each case, the cause would be determined by diagnostic testing such as angiography or echocardiography. Clear descriptions of the criteria for inclusion in each category are necessary to facilitate clinicians’ agreement on the assignment of patients to categories. A high percentage of agreement indicates high interrater reliability.

Ordinal

Ordinal measurements are similar to nominal measurements with the exception that the categories are ordered or ranked. The categories in an ordinal scale indicate more or less of a certain attribute. The scale for rating angina is an example of an ordinal scale (Table 7-2). Each category is defined, and a rating of grade 1 angina is less than a rating of grade 4. In an ordinal scale, the differences between consecutive ratings are not necessarily equal. The difference between grade 1 angina and grade 2 is not necessarily the same as between grade 3 and grade 4 angina. Consequently, if numbers are assigned to categories, they can be used to represent rank but cannot be subjected to mathematical operations. Averaging angina scores is incorrect because averaging assumes that there are equal intervals between categories. A group of ordinal data could be reported as a percentage of each response (i.e., 80% of clients reported exercise-induced angina as 3 before a cardiac rehabilitation program.)

Categorical measurements are considered ordinal if being assigned to a specific category is considered better than or worse than being in another category. For example, patients with angina could be classified as having either stable or unstable angina. This measurement would be considered ordinal, because stable angina is considered a better condition to have compared with unstable angina.³

Interval

Interval measurements have units on a scale with equal distance between consecutive measurements and are differentiated from ratio measurements because the zero point is arbitrary rather than absolute. An arbitrary zero point is one that does not mean an absence of the characteristic that is being measured. Temperature, for example, can be measured using either an interval or a ratio scale. The Celsius temperature scale (interval measurement) assigns the zero point to the temperature at which water freezes, whereas the Kelvin scale (ratio measurement) assigns the zero point to an absence of heat.

The original Borg Ratings of Perceived Exertion (RPE) scale is considered an interval level of measurement.⁴ This scale, ranging from 6 to 20, has been shown to be linear with oxygen consumption and heart rate.⁴

Measuring force production using an isokinetic dynamometer is an example of an interval measurement commonly used in physical therapy. Patients may generate muscle tension and move an extremity but register a score of zero because they cannot move as fast as the dynamometer. Interval measurements can have negative values and can be subjected to some arithmetic operations. Adding and subtracting values is logical. A patient who generates 10 ft-lb of torque at one session and 20 ft-lb at the following session increased her torque production by 10 ft-lb. However, interval values cannot be subjected to division or multiplication. It cannot be stated that the patient generated twice as much torque on the second session compared with the first session because it cannot be assumed that a reading of zero indicates no torque production.

Ratio

Ratio measurements have scales with units that are equal in size and have a zero point that indicates absence of the attribute being measured. Examples of ratio measurements that are used in cardiopulmonary physical therapy include heart rate, cardiac output, oxygen consumption, and 6-minute walk distance (6-MWD). Ratio measurements are always positive values and can be subjected to all arithmetic operations. For example, an aerobic capacity of 4 L/min is twice as great as an aerobic capacity of 2 L/min. The Borg CR10 scale and visual analogue scales are also examples of ratio level measurements.4,5 The zero point of these scales is “nothing at all” or no perception of exertion. The CR10 scale may be preferable for use with patients who experience strong symptoms during testing or training.⁶

When deciding whether a measurement is a ratio or interval, the attribute that is being measured is defined. If the zero point indicates absence of the attribute, then the scale would be considered ratio. For example, cardiac output can be defined as the amount of blood in liters ejected from the left ventricle over a 1-minute period. A measurement of zero cardiac output would be absence of the characteristic, or no blood ejected from the left ventricle.

Reliability

Reliability is defined as the consistency or reproducibility of a measurement. Ideally, when attempting to measure a specific attribute, the value of the measurement should change only when the attribute changes. All measures, however, have some element of error that contributes to the variability of the measurement. When the error is relatively high, the value of the measurement can change even when the attribute does not change. Believing that a change has occurred when it has not can result in an inaccurate clinical decision related to intervention planning or progression.

Many factors contribute to measurement variability. The characteristic being measured may demonstrate a certain degree of variability. Blood pressure and heart rate vary depending on mental and physical factors such as body position, hydration level, anxiety, and time of day. For these attributes, multiple measurements often are used to provide the best estimate of the patient’s true heart rate and blood pressure.

Another factor that contributes to the variability of a measurement is a change in the testing instrument. Testing instruments may vary in their readings because of changes in environmental conditions or malfunction of instrument parts. Instruments should be calibrated (i.e., compared with a known standard) on a regular basis to assure accuracy of the readings. Some instruments are relatively easy to calibrate. For example, values obtained using aneroid blood pressure devices can easily be compared with values obtained using mercury manometers. Values obtained using either palpation or a heart rate monitor can be compared with values obtained from electrocardiograph (ECG) recordings. The mercury manometer and the ECG would be considered the instruments that provided the best estimates of the characteristic being measured. Other devices, such as cycle ergometers, are more difficult to calibrate, and the usual approach is to rely on the manufacturer’s specifications regarding the accuracy of the work rate readings.

A third factor contributing to measurement variability is the difference in the methods therapists use to obtain measurements. If a measurement is consistent when the same therapist repeats a test, then the measurement is said to have high intrarater reliability. Measurements that are consistent when multiple therapists perform the test under the same conditions are said to have high interrater reliability. Often, measurements have high intrarater reliability but lower interrater reliability because of variations in the specific methods used by therapists to attain the same measurement. Auscultation of breath sounds, a commonly used method of assessing patients in cardiopulmonary settings, has been shown to have only poor to fair interrater reliability.⁸ Interrater reliability is important in clinical settings in which a patient may be evaluated and treated by more than one therapist. If the interrater reliability of a measurement is low, changes in the patient over time may not be accurately reflected. Interrater reliability for auscultation of breath sounds can be improved through education of the persons performing the measurements.⁸

Validity

Valid measurements are those that provide meaningful information and accurately reflect the characteristic for which the measure is intended. For a measure to be useful in a clinical setting, it must possess a certain degree of validity. Measurements can be reliable but not valid. For example, the ankle-brachial index (ABI) is reliable but not necessarily valid in all populations.⁹

There are various types of validity. Of importance in clinical practice are concurrent, predictive, and prescriptive validity. Concurrent validity is when a measurement accurately reflects measurements made with an accepted standard. Comparing a measurement made with a heart rate monitor with an ECG recording is an example of determining concurrent validity. In this example, the ECG recording would be considered the gold or accepted standard. Another example is using pulse oximetry during exercise testing. Yamaya and colleagues (2002)¹⁰ compared pulse oximetry versus directly measured arterial oxygen saturation (the gold standard) and reported that a forehead sensor was more valid than a finger sensor. Measurements with predictive validity can be used to estimate the probability of occurrence of a future event. Screening tests often involve measurements that are used to predict future events. For example, identifying people with risk factors for coronary artery disease (CAD) leads to a prediction that their likelihood of developing CAD is higher than normal. Measures with prescriptive validity provide guidance to the direction of treatment. The categorical measurement of determining a person’s risk for a future coronary event is a measurement that would need to have prescriptive validity. By classifying patients into high- versus low-risk categories on the basis of results of a diagnostic exercise test, the intensity and rate of progression of treatment is determined.