Frequency represents a standard measurement that pervades all motion and movement. "Combining observation time with count yields one of the most widely use of measures in applied behavior analysis, rate (or frequency) or responding, defined as the number of responses per unit of time." (Cooper, et al., 2007, p.76) By providing the number of occurrences over time, a frequency measurement can precisely describe the dimensional quantity of a repeating event. A standard measurement must be applied precisely in all cases. Once the fundamental properties of the event are chosen, a standard measurement can be implemented and used across all cases without yielding faulty interpretation. For example, when instances of a repeating event are of interest, frequency offers precise measurements across any behavior topography such as typing, walking, running, and so on. The National Institute of Standards and Technology, or NIST, defines the time interval as "one of the four basic standards of measurement (the others are length, mass, and temperature). Of these four basic standards, the time interval (and frequency) can be measured with the most resolution and the least uncertainty (NIST, 2007).
A measurement remains standardized in any occurrence, which is especially true within natural science. NIST defines frequency as the time of a repetitive event. If T equals the period or time interval elapse for a repetitive event, then frequency, or f, is its reciprocal or f = 1/T (NIST, 2006a). An example of a special unit of measurement for frequency is the Hertz, named after Heinrich Hertz. A hertz represents 1 crest of a wavelength passing a given point per second (Hazen & Trefil, 1990). In other words, we want to measure the frequency of sound by capturing the number of repetitive crests of the wave moving per second. T equals one second. Frequency of one Hz is one cycle of wave moving per second. As an example of a Hertz measure, the musical note "A" corresponds to a frequency of 440 crests of the wave moving per second, known as 440Hz, and middle "C" on a piano equals 246 Hz. By using standardized measurement of sound frequency, we can identify and compare various musical notes. Frequency settings also play a vital role beyond science in technology mediums such as television and radio broadcasting. Although seconds are commonly used in frequency measurement, the passage of time can vary depending on the repeated events of interest. The frequency quantity may include units of waves per second, cycles per minute, responses per hour, or occurrences per given period of time.
Importance of Measuring Frequency in Behavior Science
In behavioral science, quantitative data of behaviors are collected and converted to units of measurement for purpose of comparison. Skinner had long maintained the importance of frequency when measuring behaviors. In Skinner's words: "It follows that the main datum to be measured in the study of the dynamic laws of an operant is the length of time elapsing between a response and the response immediately preceding it ..." (1938, p. 58). Visual inspection of the cumulative number of responses occurring in time, or the number of events over time, played a critical role in the discovery of basic principles of behavior. Ferster and Skinner (1957) explained how graphic displays of frequency and the manipulation of schedules of reinforcement demonstrated reliable changes in the likelihood of an organism's response. In Science and Human Behavior, Skinner (1953) described how frequency advanced the concept of the probability of a response: "When we come to refine the notion of probability of response for scientific use, we find that here, too, our data are frequencies and that the conditions under which they are observed must be specified" (p. 63).
On many occasions, Skinner also used the word "rate" referring to frequency. "Rate of responding" allowed Skinner to articulate patterns of behavior occurring as the number of events in a given time frame. …