Frequency Jumps and Celeration Turns

One of the neat things about the Standard Celeration Chart resides in its ability to clearly show two basic types of changes to behavior that can occur when you change an independent variable.  We refer to the point in time when you make a change as a “phase change.”  A phase change takes place, for instance, between a baseline period of behavior recording and an intervention period.  In an intervention you change the values of at least one independent variable, and then monitor its effects to determine whether it changes behavior over time.

As noted, two basic changes to behavior can occur (there are more, but for now we will restrict the discussion to these two basic changes): 

 1. The frequency of the behavior can change abruptly.

 2. The celeration of the behavior can change over time.  We consider the celeration changes to consist of more “gradual” changes, though if the celeration runs steep enough, the change over time may seem anything but gradual.

We call the abrupt changes to frequency “jumps.”  For example, if you make a phase change and the frequency goes from 10 per minute on Monday to 20 per minute on Tuesday, we would say that that change describes a “frequency jump up.”  In this example, the jump up would have a value of x2 (“times two”) on the Standard Celeration Chart.  In charting terminology mathematicians used the older term “step function” for jumps.   The Precision Teaching term “jumps” runs more in line with the plain English emphasis of this field.

We call the more gradual changes to frequency over time “celeration turns.”  On the Standard Celeration Chart we depict frequency with a dot and celeration with a line of best fit drawn through a set of daily frequencies.  You can draw a celeration line for a baseline phase, and then draw a separate celeration line for the subsequent intervention phase.  If the angle of the celeration line changes across phases, then we say that the celeration has “turned.”  For example, if the celeration preceding a phase change ran at x1.0 (“times one”) and then after the intervention it shifted to a x2.0 per minute per week slope, then we would describe the celeration turn as a x2 (“times two”) change.

To recap, the frequency can “jump” and the celeration can “turn” when you put into effect some change to some independent variable.

There are many combinations of frequency jumps and celeration turns.  Note that “no jump” and “no turn” also represent possible outcomes of making an intervention.  Moreover, note that any jump or turn on the Standard Celeration Chart can be up or down.  If the frequency or celeration increases, then the change, as shown on the chart, is “up.”  Likewise, if the frequency or celeration decreases, then the change is “down.”

The basic jump and turn combination, therefore are:

* Frequency jump up, celeration turn up.

* Frequency jump up, celeration no turn.

* Frequency jump up, celeration turn down. (A counter-turn).

* Frequency no jump, celeration turn up.

* Frequency no jump, celeration no turn.

* Frequency no jump, celeration turn down.

* Frequency jump down, celeration turn up (A counter-turn).

* Frequency jump down, celeration no turn.

* Frequency jump down, celeration turn down.

Lindsley and his students identified two cases of “counter-turns.”  A counter turn occurs when you find a frequency jump in one direction followed by a celeration turn in the opposite direction. The two cases are frequency jump up followed by a celeration turn down, and a frequency jump down followed by a celeration turn up.  In both cases, the celeration trend will take the frequencies back to their starting point, suggesting that the changes made to the behavior by the manipulation of the independent variables produced only a temporary effect at best.  Lindsley and his students discovered that a fairly substantial proportion of the published behavior analysis literature contained such counter-turns.  Moreover, they found that the charts and graphs used in the published literature tended to obscure the illustration that counter-turns occurred.  You can make a counter-turn seemingly go away by using stretch-to-fill and fill-the-frame charts.  Of course, in the real life of the student or research participant, the counter-turn has not gone away.

The Figure associated with this essay illustrates the 9 basic frequency jump and celeration turn combinations.  However, you should know that many more combinations are possible.  For instance, while the Figure has the baseline phases running flat across the little charts, you could find situations where the baseline frequencies were already accelerating or decelerating.  Given that, the potential number of jump and turn combinations rises dramatically.  Of course, the total possible number of combinations becomes infinite when you consider all of the possible values that jumps and turns can take.

We use x2 (“times two”) as a useful rule-of-thumb to mark when we have a jump or a turn.  Any change having a value of x2 will clearly show up.  Any change having a value greater than x2 will show even more clearly.  Changes less than x2 can occur, but their distinction becomes somewhat harder to discern. For instance, a frequency change of x1.1 would not show up very clearly no matter what type of chart you used.

You can use a frequency finder and/or a celeration finder to determine the actual, precise values of the change to behavior over time.

  — John Eshleman, Ed.D., BCBA  (August 20, 2007)

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 Click on the Figure below to bring up a readable copy:

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