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Frequency and Celeration Definitions


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Definition of Frequency:
Frequency refers to "the number of cycles or completed alternations per unit of time." In general, frequency means some count per unit of time. In behavior analysis the most common measure of frequency has been responses per minute. In behavior analysis, frequency often gets renamed as "rate" or as "rate of response."
Definition of Celeration:
Celeration forms the root word of acceleration and deceleration. Celeration refers to number per unit of time per unit of time. In behavior analysis (Precision Teaching) the most common measure of celeration has been number per minute per week.

Frequency on a Standard Chart

On a Standard Celeration Chart, we show frequency in several ways. When you have only one pinpointed behavior, use a dot. When you chart an accuracy pair, use a dot for frequency correct, and an x for frequency error. When frequencies fall below the Record Floor, the convention is to use a question mark ("?") to show frequency.

As you chart frequencies over time, certain trends, patterns, or periodicities will emerge. In the example above, the frequencies of correct responding are increasing -- or accelerating -- over time. Likewise, the frequency of error responses is decreasing -- or decelerating over time. A "line of best fit" can be drawn through a set of frequencies. This line then becomes a "celeration" line. On the chart, we depict celeration with a line:

Frequency and Celeration Comparison
Frequency Celeration


speeding up & slowing down*





count per unit of time

count per unit of time per unit of time

Behavioral unit:

responses per minute

number per minute per week








Cumulative Record

Standard Celeration Chart


B.F. Skinner

O.R. Lindsley


Behavior of Organisms

Handbook of the

Standard Behavior Chart

* Dr. Henry S. Pennypacker suggested "speeding up" and "slowing down." (personal communication, March, 2000).

Frequency Defining Attributes:

Simply put, frequency denotes how often something happens. We use the word in that manner in our everyday language. The word "frequently" likewise connotes something that happens repeatedly, and often. So, to use a word that Dr. Ogden R. Lindsley once used to describe frequency, it denotes "oftenness."

Frequency has two dimensions: count, and time. The definition of frequency always denotes some count per unit of time. The counts themselves can run in a regular, evenly spaced manner, as with sine waves whose curve shapes do not change. Or the counts can run in an irregular manner within the specified unit of time. When the latter happens, the frequency would vary if one broke the time period down into smaller units of time.

Frequency has a scientific unit name, designated Hertz. This unit is named after Heinrich Rudolph Hertz (1857-1894), a German physicist. The scientific abbreviation for Hertz is Hz. The naming and abbreviations for frequency follow the metric system. Hence, 1000 Hz equals 1 kilohertz, or 1 kHz for short. Likewise, 1,000,000 Hz equals 1 megahertz, or 1 MHz for short.

One Hertz equals one cycle per second, or a count of one event per second. In physics 1 Hz often means one wave per second. In that usage, a frequency means the number of waves that pass a given point per unit of time. A frequency of 1 Hz means that one wave, or wave crest, passes a point in a second's worth of time. A frequency of 10 Hz means that 10 waves pass the same point in one second of time. For 1 megahertz, one million waves pass a point in a given second.

For the study of human behavior, however, the Hertz unit proves somewhat inconvenient. A frequency of 1 Hz, or 1 cycle per second, equals 60 per minute. In human behavioral terms, 60 per minute already means a behavior repeating very quickly. Moreover, 60 per minute exceeds the bulk of daily behavior. In addition, B.F. Skinner and other behavior scientists selected number per minute as their frequency measure of choice. So, casting behavioral frequencies in terms of number per minute may prove more convenient than using the Hertz scale directly. Note that one can always convert from a count per minute to a count per second and vice versa.

As noted, behavioral scientists such as B.F. Skinner, Ivan P. Pavlov, and Ogden R. Lindsley measured behavior frequencies as counts per minute. Skinner and Lindsley studied responses per minute, Pavlov cc's per minute. Such count per minute frequencies, however, have no unit name. Therefore, I propose either the "Skinner," or the "Lindsley" as the unit name for frequency as defined in terms of count per minute.

Frequency has played a critical and vital role in the development of a science and technology of behavior. To put it bluntly, without frequency we could not have had the science of human behavior that B.F. Skinner and his associates and successors built. Frequency formed the absolutely necessary measure of behavior, and dimension of behavior, used in B.F. Skinner's two primary research books, The Behavior of Organisms, and Schedules of Reinforcement (the latter written with C.B. Ferster, who is listed as first author). Skinner represented frequency with cumulative records in both of these books. Take out the cumulative records, and you remove virtually all of the data. Take away all of the inductions and conclusions based on the frequencies shown on the cumulative records, and both books would almost completely vanish. Remove all scientific publications that are based on the findings and implications in these two books, and almost all of the science that ensued from B.F. Skinner's work would disappear. Note, however, that neither applied behavior analysis nor behavior analysis in general would disappear, since both of these fields have origins in the works of individuals other than Skinner.

The best graphical depictions for frequency, for a science of human behavior, are (1) the cumulative record, and (2) the Standard Celeration Chart. B.F. Skinner devised the cumulative record, where the slope of a line equals frequency. O.R. Lindsley devised the Standard Celeration Chart, where a point equals frequency, and the slope of a line equals celeration. Lindsley has proposed the name "Standard Frequency Chart" in place of "cumulative record" for Skinner's charts. On both, the slopes form the standards.

Scientific Units

Hank Pennypacker (1976) stated that scientific units are absolute, standard and universal. What do these three defining properties mean? Well, going through some old notes I found some succinct definitions that Pennypacker came up with, and which others should find useful.

ABSOLUTE -- A scientific unit becomes absolute when its existence as a unit is independent of the number and frequency of its use.

STANDARD -- A standard unit remains invariant over time. Its definition does not vary.

UNIVERSAL -- A unit becomes universal when the physical objects or events being measured do not dictate the choice of the scientific unit.


Pennypacker, H.S. (1976). The role of direct measurement in the evolution of a complex educational system. In Vargas, E., & Fraley, L. (Eds.) Proceedings of the Third National Conference on Behavior Research and Technology in Higher Education. Gainesville, FL: Society for Behavior Technology and Engineering. pp. 259-266.

Note: Dr. Ogden R. Lindsley invented the Standard Celeration Chart, founded Behavior Research Company, and has been the main proponent and developer of both Precision Teaching and standard celeration charting.

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Copyright (c) 2000 by John W. Eshleman, Ed.D.




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