One of the major contributions Precision Teaching (PT) has made lies in a standard measurement unit called celeration. It makes sense a measurement unit would rise to the top of the achievement list because Precision Teaching itself is a measurement system. (Lindsley, 1997, 1999). And the measurements have centered on human behavior. If you read this blog and find yourself measuring the behavior of other people (e.g., clients, students, yourself), celeration takes center stage as part of the scientific analysis of time series data.

We can compare trend lines on a nonstandard linear chart and celeration lines on a Standard Celeration Chart. Trend lines, also referred to *lines of progress* or *celeration lines* have three functions: 1. describing the performance patterns in a series of data; 2. predicting the future performance of a series of data; and 3. describing the effects of an intervention on a series of data (White, 2005). The trend or celeration line directly informs the chart reader when it comes to making judgements about progress and the degree of change. Two options exist for representing how much change has occurred – using words or using numbers.

**Measurement**

Taking a step back, let’s first examine a measurement unit or unit of measurement (same term but some people order their coffee black while others order black coffee). A measurement unit refers to a specific amount of a physical quantity that becomes the standard for all other similar physical quantities. As an example, length refers to a measure of something from one end to the other. Your friendly blogger has a body length measured from my feet to the top of my head. How do we describe my bodily length? We call it height if I stand up and we measure from the bottom of my body to the top.

To answer how we have come to measure parts of our physical universe we could examine the history and development of measurement. The short answer; a group of people, scientists mostly, developed standard units to precisely define the measures we use in everyday life. You can access the standard measures from different sources (discussed later).

We rely on standardized measures so we do not get cheated when buy products. If you go to your local grocery store and buy milk for $2.99 (€2.16 for all of those readers in Europe), how much should you get? The enterprising clerk might give you “a lot of milk” for your money. The next time you purchase milk from the farmers market a kindly Amish salesperson might also give you “a lot of milk” for your $2.99. The Amish salesperson has a different idea what “a lot of milk” means and you receive more this time than the last. Imagine the worldwide chaos that would ensue? Everywhere you go you never know how much milk your $2.99 will procure.

In the United State we know what $2.99 gets us, a gallon of milk. The rest of the world uses liters but the upside remains the same – because we have standard units of measurement commerce doesn’t look like the wild west where everyone makes up stuff and measures differ from one person to the next. Ask yourself, do you want to live in a world where no standard units of measurement reign supreme? Stated differently, do you want to live in the 10th century where the King of England had to declare that people do not use “false weights and wrongful measures” under pain of intense corporal punishment or death?

**Standards**

The International System of Units http://physics.nist.gov/cuu/Units/ or SI (abbreviated from French Le Système international d’unités) encompasses a set of measures used almost universally in trade and science. The table below shows dimensions people may like to measure (under the Measurement column). For example, we all keep track of time. Eating meals, showing up for work, watching our favorite TV shows, and figuring out how much we owe for our monthly cell phone bill all represent facets of time. We can do all of the previous activities because we measure time a Physical quantity or Unit (second column in the table below). A second represents a universal unit for capturing time. We have 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 7 days in week, 4 weeks in a month, 12 months in a year, 10 years in a decade, 10 decades in a century, and 10 centuries in a millennium. The sequence of time strikes us as wonderful order!

First, we recognize everything starts with the second. People who have adopted the second as a standard unit of measurement have a sense of scale. We understand the difference between 30 minute television show and a three hour lecture. We perceive the lifetime of a person measured in years (maximum lifespan = 120 years) versus the staggering immensity of time involved with the lifetime of our Sun (maximum lifespan = 10,000,000,000 years).

Standards give us a sense of scale by imposing order within our measurements.

Take a moment and closely examine the first two columns. You will quickly come to appreciate standard units of measurement because the spectacular growth of our technological culture rests with the common language of units. If we didn’t have the standard units try and imagine the present state of our society by using the the third column for doing science, trade, and commerce. Just open a book and look at life in 10 century and before.

Standard units of measurement make your life run smoothly. Standard units of measures (and their derivatives) touch you when you go to the doctors, fill up you car with gasoline or diesel, buy Starbucks, drive to work, and stand on your scale (and smile because your healthy life style shows up in numbers). Does anyone want to live in world where everything previously mentioned goes away and in their place we have to use adjectives and more subjective impressions of nature? When you ask someone how to dress they say “It be warm outside.” Of course asking your friend Norway instead of your friend from Florida will influence how you dress and what warm means to your friends. Likewise, imagine going to your doctor prescribes a medicine and says take a little of it each day. Does a little mean a teaspoon (5 milliliters), a table spoon (15 milliliters), a fluid ounce (34 milliliters), or a cup (240 milliliters)?

You get the picture. The world, and your life, would function very differently without standard units of measurement. We don’t want to move from an age of technological splendor back to the dark ages. Standards make life better.

**Stand Units of Measurement on the Standard Celeration Chart**

Back to trend and celeration lines. Take a look at the figure below. The same data appear on a section of a nonstandard linear graph and a portion of the Standard Celeration Chart. The dimensions of both figures have the same physical and numerical scaling. Each data display clearly portrays the dataset and allows line fitting. For each figure I used the split middle technique to fit the celeration and trend line line respectively. When looking at the lines, both have two distinct features which directly factor into analysis of the meaning of the line.

When contrasting the two lines above the first determination made concerns the slope. Clearly both lines have an upward slant. A difference will never exist between trend lines on a nonstandard linear graph and celeration lines on a Standard Celeration Chart. If one line has an upward slope so too will the other.

The magnitude of the trend requires a judgement. The individual assessment yields a qualitative value. In the graph above I estimate the trend as medium. With the SCC we do not need to rely on a subjective impression. We can measure the line and express the magnitude of growth with a number. The figure below shows how a finder reveals the celeration value. Note when we extend the line it goes through the hatch mark labeled with a 2. Therefore, the celeration value of the line = x2.0. The x2.0 means the behavior has doubled or increased by 100%. Looking at the figure you see the first data point starts at 10 and the last data point ends at 20. Doubling 10, or 10 x 2, equals 20.

Celeration, then, refers to a unit of behavior change everyone can use. The unit of change expresses the quantified magnitude of growth or decay. For different situations celeration precisely tells the chart reader the speed at which behavior has changed. The table below lists a few examples of behaviors and celeration values.

With celeration the standard unit of change maximizes judgment of the effect through quantification. The celeration values states exactly fast the change occurred. The symbol (x or ÷) shows the direction of the change. Multiply symbol will denote growth or an upward slant of the line while a division symbol signifies decay or a downward inclination of the line.

As mentioned previously, trends lines describes the performance patterns in a series of data and communicate the effects of an intervention on a series of data. Examine the previous table above but without celeration.

*Or rapidly increasing? What rule determines the difference between moderate and rapid?

The judgement made for the trend line on a nonstandard linear graph provides information. The information, however, does not compare with the precision imparted by the celeration line on a Standard Celeration Chart. If someone ever tells you data on a linear graph doesn’t differ from data on a Standard Celeration Chart you will know otherwise. Stark difference start with the trend line and the subsequent effects of judgement.

The social sciences have used nonstandard linear graphs and trend lines for a long time. Researchers had made discoveries and helped many people change their behavior. The point of this blog is not to disparage trend lines and suggest they have no positive purpose, clearly the data say otherwise. The main point lies in what we might aspire to as a science and to recognize our present limitations. The scope and depth of analysis and judgement of change dramatically improves with celeration. If one argues against celeration as a standard unit of behavior change then that person argues for nonstandardization and less precision. As an applied scientist or a concerned citizen of behavior change, ask yourself what world do you prefer to live in, one with standard units of measurement or one without? We can start celeration.

References

Lindsley, O. R. (1997b). Precise instructional design: Guidelines from Precision Teaching. In C. R. Dills & A. J. Romiszowski, (Eds). *Instructional development paradigms* (pp. 537-554). Englewood Cliffs, NJ: Educational Technology Publications.

Lindsley, O. R. (1999). From training evaluation to performance tracking. In H. Stolovitch & E. Keeps (Eds.). *The handbook of human performance technology* (2nd ed.). (pp. 210-236). San Francisco, CA: Pfeiffer, Jossey-Bass.

White, O. R. (2005). Trend lines. In M. Hersen, G. Sugai, & R. Horner (Eds.), *Encyclopedia of behavior modification and cognitive behavior therapy. Volume III: Education applications* (pp. 1589–1593). Thousand Oaks, CA: Sage.

Hi Rick,

Good points.

Some added points:

(1) In Europe back in the 1700s every little principality had its OWN measure of a “foot.” That meant that in one town a “foot” as a unit of measurement might be, and was almost certainly, somewhat longer or somewhat shorter than a “foot” in the next town or city-state over. Consequently, there were dozens of measures of a “foot.” This made commerce more difficult.

(2) ALL charts and graphs that have any kind of rate measure up the left axis, or even a simple count measure up the left axis, and any kind of time measure across the bottom, WILL, in fact, have celeration in the data charted. This is obvious on a cumulative record, of course, where, for example, in an FI schedule there are “scallops.” A “scallop” shows acceleration. It is less obvious in various rate graphs (e.g., such as those published in JABA or AVB or other behavioral journals), but celeration’s still there nonetheless. Now, on such rate graphs, celeration is likely very difficult for one even to see it. Moreover, it will be very difficult to put in a line of best fit, which would likely be a curved line. And it will be very difficult to compute a celeration value for such a trend line, even if the trend line could be drawn in the first place. What would they use for units of measurement? This is WHY they resort to adjectives to describe trends. Finally, of course, it’s near impossible to compare celerations from one add-subtract chart to the next add-subtract chart. There’s no common basis for comparison. It’s little wonder, then, that celeration — EVEN THOUGH IT IS RIGHT THERE IN THE DATA — isn’t even considered for usage, much less used. Often, in fact, it gets denigrated, and we’re asked “to prove” celeration has value or is meaningful or is worthy of discussion — this often coming from researchers who don’t use it or who may not ever have even attempted to use it. — JE

Even as recent as the 1700s we still had measurement issues, good point.

I didn’t make the point that the SCC shows the data differently than nonstandard linear charts. So that means people have two reasons to chart: all of the benefits afforded by a ratio chart and the use of standard units of measurement. One day John we will see more people charting because the information has started to become more prominent and not as easy to just brush aside.