a family of standard event-frequency time series charts: o.r

A Family of Standard Event-Frequency Time Series Charts:O.R. Lindsley’s Powerful Method of Measuring Change

Wells Hively and Ann Dell Duncan-Hively 12

Duncan-Hively Psychological Services, St. Louis, MO, www.duncanhively.com

Running Head: A FAMILY OF STANDARD EVENT-‐FREQUENCY TIME SERIES CHARTS 1

1 Like Dr. O.R. Lindsley, Dr. Hively received his Ph.D. from Harvard University under B.F. Skinner. Dr. Duncan-Hively received her Ph.D. from the University of Kansas under Dr. Lindsley.

2 We thank the following people (in alphabetical order) for editorial consultation, while taking responsibility ourselves for the final manuscript.

Jack AumanScott BornDiane DeArmondNancy Hughes-LindsleyCarl KoenigRyan O’DonnellStu DormanMalcolm NeelyHank PennypackerIan SpenceClay Starlin

http://www.duncanhively.com

http://www.duncanhively.com

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Abstract

The late psychologist/educator, Ogden R. Lindsley, together with his students and colleagues, pioneered the development of a standard method for visual-perceptual analysis of event-frequency time series data, called the “Standard Celeration Chart.” Conceived in the context of applied behavior analysis in the field of psychology, this analytical technique has the potential to make important contributions to any area of study where frequency of event occurrence is the datum.

The purpose of this article is to describe the technique, trace its history of development, review its present uses and offer a web-site forum for its future evolution -- proposing that the general technique be known as Lindsley Standard Time Series Analysis.

A FAMILY OF STANDARD EVENT-‐FREQUENCY TIME SERIES CHARTS 2

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A Family of Event-Frequency Time Series Charts:O.R. Lindsley’s Powerful Method of Measuring Change

The Visual Analysis of Trends in Events Occurring Over Time

Figure 1 is a graph of corn production in the United States from 1866 to the present.

Figure 1

____ Corn Production, millions of bushelsSource: National Agricultural Statistics Service http://www.nass.usda.gov/Statistics_by_Subject/index.php?sector=CROPS

Since 1930 the increase in productivity has been amazing – from 2 billion to 13 billion bushels a year!


http://www.nass.usda.gov/Statistics_by_Subject/index.php?sector=CROPS




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Figure 2 is a graph of the acreage of corn plantation during the same period of time.

Figure 2

____ U.S. Corn Acreage, millions of acresSource: ibid

Roughly comparing these two graphs, we can see that from 1920 to 1970 farmers planted fewer and fewer acres of corn while production increased more and more. That’s somewhat counter-intuitive.


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Given the data for production and acreage, we can calculate yield, in bushels per acre, to see how that has changed over time. Figure 3 shows that graph.

Figure 3

___ U.S. Corn Yield, bushels per acre.Source: ibid

Like many charts in the recent history of science and technology, this graph looks like a hockey stick, documenting the amazing growth in productivity of U.S. agriculture under scientific, petrochemical management since 1930 (see Hively & Hively 2013).


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To better understand what has been going on, it would be helpful if we could put these three graphs into a single chart so we could examine in detail how acreage, production and yield have been related to each other over the years. That is difficult, but Figure 4 a serious attempt.

Figure 4

To make this chart, three scales were needed on the vertical axis, because acreage ranged from approximately 50 million to 110 million acres, while production ranged from approximately 1 billion to 13 billion bushels and yield ranged from approximately 14 to 170 bushels per acre. Allocating space to the scales decreased the space available for the chart so we could only show the time period from 1900 to the present, leaving out important data between 1866 and 1900.

It took considerable time to create this chart, and it is not easy to read. What conclusions do you draw from it?


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The Semi-Logarithmic Transformation

Now see what happens if we simply convert the vertical axes in Figures 1 through 3 from equal interval scales to (base-ten) logarithmic scales. We can put the entire range of all three graphs on the same chart, much of the variability disappears, and relationships among the three variables become much clearer (Figure 5).

Figure 5

____ U.S. Corn Production, millions of bushels____ U.S. Corn Acreage, millions of acres____ U.S. Corn Yield, bushels per acrex—x Slope Angle Anchor, times 2 every 10 years = 34 degrees

It was easy to construct this chart, and it is easier to see patterns and relationships in it than in the combination of the equal-interval graphs. One can see, for example, that prior to 1930 production mirrored acreage: the more (or less) farmers planted, the more (or less) they produced. But from 1938 to 1970 production increased at a steady rate (30% every 10 years) while acreage steadily decreased (20% every 10 years) -- a dramatic evolution due to the introduction of motorized farm machinery, hybrid seeds, petrochemical fertilizers, petrochemical pest control and cropland management. As a result, between 1938 and 1970, yield, which had been unchanging up to that


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point, began to increase at the amazing, constant rate of 50% every 10 years. (The overall pattern is interrupted by occasional “bad years” in which yield and production both dropped sharply: e.g. 1902, 1932, 1934, 1948.)

Why does this chart look so orderly? Here is the reasoning:• Most, if not all biological processes, including human behavior, evolve exponentially,

multiplying until they reach a limit (e.g. microbes in a medical culture, fluency of a child learning to read, farmers planting better hybrid corn). When these changes are plotted on equal-interval (Cartesian) coordinates they appear as the well-known “S” curve of population biology. But on a chart where time is displayed in equal intervals on the horizontal axis, but the counts (numbers of microbes, words read, bushels of corn) are displayed on a logarithmic scale on the vertical axis they appear as straight lines. The slopes of the lines on such “semi-logarithmic” charts show the rates of exponential growth.

• So wherever we study changes in frequencies of the occurrence of events over time -- in such fields as biology, psychology, education, economics, history or anthropology -- we may expect to see straight lines on a semi-log chart. These focus our attention on changes in the rates of change. In Figure 5, for example, you can clearly see the change in the rate of corn production around 1930 and the change in rate of acreage plantation around 1970. 1930 marked the beginning of scientific, petrochemical agriculture in the United States. 1970 marked the international oil shock, after which farmers began to plant more acreage to grow corn for ethanol fuel. (Synchronized departures from the overall trends again mark “bad years”: 1984, 1989, 1994 and 1996.)

• Variability in a semi-log chart is proportional to magnitude. A deviation of two from a count of 10 looks just as large as a deviation of 200 from a count of 1000. That makes sense when we focus our attention on relative changes rather than absolute values, and it is another reason the graphs in Figure 5 look more orderly than the graphs in the preceding figures.

So semi-log charts give us a powerful way to analyze time-series, event-frequency data.

The Perception of Time

There is great variability in the perception of time. On the way to your destination, time passes slowly. On the way back, the trip seems shorter. For a young person, 10 years is an eternity. For an octogenarian, it is yesterday. Time frames condition our perceptions of rates of change and affect our world views.


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Figures 6 and 7 illustrate how our perceptions of change can be affected by altering the dimensions of a time series chart.

Figure 6


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Figure 7

By lengthening and shortening the horizontal and vertical axes of the charts, growth in corn production can be made to seem quite substantial (Figure 6) or only modestly important (Figure 7). The numbers on the charts are the same, but the visual impression overpowers them.

Reporters of time-series data inevitably anchor their arguments to a preferred time scale (what will happen tomorrow v. what will happen fifty years from now), and they usually have a point to make (e.g. the belief that global warming will be disastrous), so they choose dimensions of their charts to emphasize their points. But for unbiased investigators there is an obvious drawback: it is difficult to make visual comparisons and evaluate effects unless we have some standard frame of reference.

If we wish to do a balanced analysis of a large domain of data by examining time series graphs, we need a standard visual context in which to make comparisons. Here’s a logical way to do it with the semi-log transformation:

• Begin with the dimensions of a sheet of paper we are all used to looking at, and on which the finished chart is likely to be printed (an 8 ½ by 11 inch visual field in English units of measure).

• Lay out the chart so as to accommodate as wide a variety of data as possible. About the best we can do without eyestrain is to put 200 units on the horizontal axis. (In the field of agricultural history that can give us a time span of 200 years.) On the vertical axis, 6 base-10 cycles, going from 1 to 1,000,000 makes about the longest easily visualized scale on which to plot the occurrence of events.

• It is important to fix the relative dimensions for the chart in a ratio that gives the best resolution for the data. Then if the size of the chart has to be changed to fit a particular publication, the relative dimensions, and the visual impression, will stay the same. The chart in Figure 5, above, has an aspect ratio (length of vertical axis divided by the length of horizontal axis) of approximately 5 by 7 = 0.7. On this chart a straight line that shows


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a doubling of the count every 10 years (shown as the “Chart Angle Anchor”) makes an angle of 34 degrees with the horizontal axis. The exact angle is not critical, so long as the aspect ratio of the chart shows the best resolution of the data being studied. What is critical is that the angle be standard – so that the eyes of the viewers can accommodate. You can check to make sure this aspect ratio is constant across all the charts you might want to examine by measuring their anchor angles with a protractor. When your eye becomes accustomed to looking at them, you will automatically notice if the aspect ratio of a standard chart has accidentally changed.

A standard time series chart makes it possible to compare trends in any quantity to the trends in any other quantity, against a constant visual–perceptual background: that’s the essence of this technology. Such a chart makes it possible to go beyond the simple presentation of data to the exploration of unknown/unexpected relationships among any chosen variables as they change over time.

Figure 8, another example from U.S. agricultural history, exemplifies the potential of this kind of analysis -- equally applicable in many other areas of investigation. It depicts the historical relationship between the productivity, and the acreage, of corn and wheat in the United States since 1866.


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Figure 8

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In order from top to bottom:_____ U.S. Corn Production, millions of bushels_____ U.S. Wheat Production, millions of bushels_____ U.S. Corn Acreage, millions of acres_____ U.S. Wheat Acreage, millions of acresx-----x Slope Angle Anchor, times 2 every 10 years = 34 degrees

The graphs of corn and wheat parallel each other to a surprising degree despite great differences between farms that grow wheat and farms that grow corn in their geographic locations, their climates, and their methods of cultivation. Detailed analysis of the correlated trends shown in this chart offers a wealth of information and raises many interesting questions. For example, after 40 years, from 1950 to 1990, during which the planted acreage of corn and wheat in the U.S. were almost exactly equal, why has wheat acreage (and production) substantially decreased over the last 20 years while corn acreage (and production) has increased?


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Conclusion

A standard semi-logarithmic time series chart can be powerful analytical tool, making it possible to go beyond simple presentation of research findings to exploration of unexpected/unknown relationships among related sets of data. It is surprising that it isn’t used more often in the social and biological sciences.

The Evolution of the Standard Event-Frequency Time Series Chart

These ideas originated in the work of the late psychologist/educator, O. R. Lindsley. For those who might be curious, here is a brief history of their development.

O. R. Lindsley (ORL), B. F. Skinner (BFS) and Rate of Response -- a Fundamental Measure of Human Behavior.

BFS, who did his original research on animals, established rate of responding as a basic measure of motivation and learning. He extended this work on “operant conditioning,” to human psychology in a landmark textbook, Science and Human Behavior (Skinner, 1953). At that time, ORL was a post-graduate fellow working under BFS and doing operant conditioning research with inmates of a Boston mental hospital – the first formal studies of operant conditioning of human beings.

The measurement technique that BFS invented and ORL used in his own initial research was a “cumulative record” in which each response by an experimental organism (a pigeon pecking a disk or a person pulling a plunger) was marked by a short upward movement of a pen drawing on a constantly moving strip of paper. This technique produced a graph showing rate-of-response as the slope of a line on a chart that measured cumulative responses on the vertical axis, and time on the horizontal axis. The rate of occurrence of any repeated events, e.g. cells dividing, seeds being planted, children being born, can be measured by such a cumulative record so long as the events can be continuously detected. Figure 9 is a schematic picture of a cumulative recorder.


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Figure 9

ORL and the Applied Science of Operant Conditioning

ORL was interested in applying the basic principles and experimental techniques of operant conditioning to improving the human condition. He was an applied scientist in the purest meaning of the term, holding firmly to the science while imaginatively pursuing its applications to practical problems.

ORL began his applied work at the University of Kansas Medical School, in the field of Special Education. His strategy was to teach graduate students the fundamentals of applied operant behavior analysis so that they, in turn, could teach teachers and parents to use those fundamentals to change the behaviors of their challenging children – by decreasing rates of undesired behaviors (e.g. self injury) or increasing rates desired behaviors (e.g. reading).ORL’s approach to graduate education was itself experimental. He seriously attempted to practice what he preached, applying the fundamentals of operant behavior analysis to manage his own behavior and the behavior of his students. So in the course of this long-term project, he and his students invented:

1. A simple, general procedure for carrying out applied behavior research known by the short hand “pinpoint, record, chart, change and try, try again” (Lindsley 1966).

2. A precise and immediately understandable (“is-did”) terminology for analyzing contingencies of reinforcement, solidly based on BFS’s basic operational definitions (Lindsley 1967).


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3. A technology for efficiently communicating the procedures and the results of this research to the community of advisors, teachers and parents who were engaged in the work – which came to be called “Chart Sharing” (Lindsley 1968).

Efficient, Convenient Communication in a Community of Researchers – the Birth of the Standard Behavior Chart

The central tool for chart sharing was the overhead projector, a fixture at that time in most U.S. classrooms, from elementary school to the university, in both special and regular education. ORL’s research teams gathered in laboratories and classrooms for meetings where they used the projectors to conveniently display the procedures and the results of their experiments, consult each other and plan future work.

Presentations at first were idiosyncratic. For practical purposes, research teams could not create cumulative records of children’s behaviors. Instead, they counted “movement cycles” in blocks of time (e.g. self injuries per day or words read aloud per minute) and they kept records of how the counts changed over these successive blocks of time, punctuated by interventions intended to increase or decrease the rates. They put their hand-made charts through a machine that turned them into transparencies for the overhead projector. The graphs, like those in most of the literature at that time (and now) were drawn on equal-interval coordinates, sized to fit the range of the researcher’s data and stretched to fit the presentation space. Consequently, it was difficult to easily see how substantial the outcomes of the experiments really were, and much time was taken up in explaining exactly what the graphs depicted.

ORL saw that stretching the graphs to fit the space often distorted the visual impression of the magnitude of the effects, and he understood that the researchers needed to standardize their presentations to facilitate communication, but the range of data, from self injury 20 times a day to reading words aloud 100 times a minute, made it impossible to put all projects on one standard equal-interval chart.

ORL of course realized that a wide range of data could be plotted on semi-log graph paper. More importantly, he saw the deep connection between the semi-log chart and BFS’s cumulative record: the slope of the line in the cumulative record measures the rate of occurrence of a “movement cycle” (e.g. lever press), while the slope of the line in the semi-log chart measures the rate of change of this rate of occurrence (the “first derivative” in a mathematical analysis.)

ORL understood that researchers didn’t need to be concerned primarily with absolute rates. Instead, they needed to focus on relative changes: decelerating the rates of undesired behavior and accelerating the rates of desired behavior no matter what the level of the overall rates. These relative changes were exactly what the semi-log chart directly measured. This was the birth of the “Standard Behavior Chart.”


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For mathematical specialists it is important to note that, in a characteristically detailed and scholarly essay (Lindsley 1994) ORL persuasively argued that the proper historical ancestor of the vertical axis of the Standard Chart is not Napier’s logarithms, but rather it is “Gunter’s Line,” a graphical method of multiplication that was a precursor of the slide rule. So the vertical axis of the chart should not be called a “logarithmic scale.” It should be called a “multiply-divide scale” instead. Common usage seems to be overpowering this very logical argument, so in this review we will continue to use the term semi-logarithmic (base 10).

A Family of Standard Charts, Each Tailored to a Specific Purpose

At first, the semi-log charts presented in the Chart Shares varied idiosyncratically, depending on the researcher’s choice of time scale, but ORL soon saw that the standard charts could be grouped into sets depending on the general rates of occurrence of different types of behavior being studied. (Just as different, standard gear settings on the cumulative recorder drove the paper at different speeds depending on the type of animal – rat, pigeon or human -- being studied.) Researchers interested in things like reading aloud needed charts that showed “movements per minute,” (measured in timed trials) changing over a scale of days. Researchers interested in managing problem behaviors like self-injury needed charts that tracked movements per day. Researchers interested in bedwetting needed charts that tracked movements per week, and so on. To meet these needs ORL developed a set of special-purpose Standard Behavior Charts with time scales ranging from days to years.

A Standard Visual-Perceptual Context

At this point each researcher could conveniently present data using a chart that fit the time scale of her/his chosen research topic. But ORL added one more refinement in the communication process. Schooled in psychophysics (the study of perception) he felt that the visual perception of rate of change should be constant across all members of his family of standard charts. So he set the following requirement: All charts must contain exactly 20 major time intervals spaced equally along the horizontal axis, although within each major interval minor intervals may vary. For example, in the standard daily chart, the horizontal axis is divided into 20 major intervals, each seven days (one week) long, for a total of 140 days. Similarly, the horizontal axis of the weekly chart is divided into 20 major intervals, each five weeks (about one month) long, for a total of 100 weeks. But the measured distance between the lines marking the major intervals on both the charts must be exactly the same. That way, a line showing a count that doubled each week on the daily chart would have the same slope as a line showing a count that doubled each month on a weekly chart and so on -- all these lines make a 34 degree angle with the horizontal axis.

At this point, the basic features of the Standard Behavior Chart were established, and the stage was set (within the community of researchers who became familiar with the technology) for rapid, intuitive, unbiased visual analysis of virtually the entire range of event-frequency data that could be subjected to time series analysis.


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The Standard Chart and the associated Chart Sharing technology became the basis for a program that came to be widely known as Precision Teaching, and subsequently ORL moved into the Department of Educational Administration at the University of Kansas. Around that time, the Standard Behavior Charts were renamed Standard Celeration Charts. The new name emphasized the fact that the charts were designed so that lines showing a given “acceleration” or “deceleration” across the major time segments on all the charts all looked the same. A handy “Celeration Finder” (special-purpose protractor) could be used to measure the rate at which the counts on any of the charts multiplied or divided. And a common descriptive language evolved, e.g.: “This chart shows that from June 17 to July 24 words-read-aloud-per-minute accelerated x1.2 (times 1.2 or 20%) per week.”

The overhead-projector-based, chart sharing technology evolved to become quite elaborate, utilizing not only precisely printed paper charts, but also precisely matching overhead transparencies on which graphs could be drawn in erasable ink, blank transparent mylar sheets die-cut to exactly match the dimensions of the overhead transparencies, which could be laid over a projected master chart making it possible to quickly display a series of graphs for comparison, and a chart frame attached to the overhead projector to keep the transparencies accurately registered on top of one another. All these things are presently available (along with celeration finders and many other useful things) from the Behavior Research Company. http://www.behaviorresearchcompany.com

Equipped with this technology, ORL and his students set out to measure, explore and influence a wide range of human behavior. Figure 10 is a particularly interesting example from the early work.

Diane DeArmond, then a professor at the University of Missouri in Kansas City, monitored a class taught by ORL and taken by her husband, Joe Edwards in 1968. At the time she was pregnant with their son, Scott. For four hours each day she counted the infant’s movements as she felt them in her womb. Dividing the number of movements by the number of minutes she counted each day, she produced this pioneering chart of fetal movement per minute during the 19 weeks preceding Scott’s birth.

After hovering around one movement every two hours or so for the first five weeks of her study, the infant’s movements accelerated smoothly for the next six weeks to about 1 every three minutes. The activity became quite variable over the following four weeks and then decelerated sharply over the last four weeks before birth.


http://www.behaviorresearchcompany.com




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Figure 10

Studies like this might make a considerable contribution to behavioral medicine. It is easy to imagine the development of a normative curve of infant fetal movements against which an individual mother could compare her own child’s activity and from which departures might suggest consultation with her obstetrician. Although the Edwards team published a follow-up study (Edwards & Edwards 1970) according to Joe the idea received little support from the medical community. Perhaps its time may still come.

Resources

In the general field of Behavior Management, alongside the special area of Precision Teaching, applications of the Standard Celeration Charts and the Chart Share Technology have diversified into a variety of areas. See Appendix A (thanks to Malcolm Neeley) for a list of agencies that significantly utilize the charts in their activities today, and see Appendix B (thanks to Clay Starlin) for a list of university programs in which the use of the charts is taught.


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Several handbooks and articles are available explaining the properties and the uses of the Standard Charts, describing techniques for plotting of trend lines, estimating significance of the effects of interventions, and illustrating various applications. See Appendix C (again thanks to Malcolm Neeley) for a currently available list of these publications.

For ORL’s unique perspective on issues surrounding the above-described evolution of the Standard Celeration Charts, see Lindsley (2013 Revised).

Graphical Excellence

Lindsley Standard Celeration Charts (as represented, for example, by Figure 8) have many of the characteristics of “graphical excellence” proposed by Edward Tufte (1983, p. 51):

• Graphical excellence is the well-designed presentation of interesting data – a matter of substance, of statistics, and of design.

• Graphical excellence consists of complex ideas communicated with clarity, precision and efficiency.

• Graphical efficiency is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space.

• Graphical excellence is nearly always multivariate.• And graphical excellence requires telling the truth about the data.

Curiously, Tufte does not discuss the need to standardize graphic displays for use by a community of investigators with a common purpose, although elegant graphics like Marey’s Graphical Train Schedule (p. 31) clearly were developed for this reason. Standardization of visual displays for effective communication in a collaborative research setting is the central idea behind the present essay.

Beyond Precision Teaching: Lindsley Standard Time-Series Analysis.

The point of this review has been that although the family of Standard Celeration Charts and the associated overhead-projector-based communication technology arose in the context of psycho-educational research and development, this basic visual-perceptual analytical technique can make a fundamental contribution to the analysis of any time series data whatsoever.

The late Stephen Graf was a pioneer in extending the technique beyond the field of behavior analysis. Thanks to Jack Auman, who preserved the original, Figure 11 shows one of Steve’s paper charts created in 1983 -- offering a nice insight into the history of American agriculture.


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Figure 11

According to this chart, the population of people living on American farms decreased steadily from 30 million in 1940 to 700,000 in 1980, while the number for farms followed a parallel decline from 6,000,000 to 2,500,000. At the same time, the size of the average farm increased from 175 acres to 450 acres – a picture of industrial farming replacing the traditional family farm.

One more example may further illustrate the general applicability of Lindsley’s technique. Figure 12 shows population growth for four selected countries and the world as a whole.


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Figure 12

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___ Germany ___ Japan ___ Nigeria ___ Venezuela ___ WorldPopulation, millions of people

Sources:http://www.census.gov/population/international/data/idb/informationGateway.phphttp://www.populstat.info The population of Germany has grown very slowly since World War I, and it essentially stopped around 1975. The population of Japan grew more rapidly, but it essentially stopped as well around 1990: two examples drawn from a number of relatively rich, industrialized countries where population is now stabilizing or decreasing. The populations of Nigeria and Venezuela, two examples drawn from a larger number of non-industrialized and “emerging” countries, grew at about the same rates as Japan up to 1950. But since then they have been growing at the amazing rate of 40% every 10 years. The growth of world population follows the general pattern of growth in Nigeria and Venezuela, because such countries currently contain a majority of the world’s population.

Nigeria and Venezuela have been selling oil to the industrialized nations and in return they have been able to purchase the world’s surplus food. Figure 13 shows a very interesting correlation.


http://www.census.gov/population/international/data/idb/informationGateway.php

http://www.census.gov/population/international/data/idb/informationGateway.php

http://www.populstat.info

http://www.populstat.info

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Figure 13

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1820"1830"1840"1850"1860"1870"1880"1890"1900"1910"1920"1930"1940"1950"1960"1970"1980"1990"2000"2010"2020"

____ U.S. Corn Production, Millions of Bushels____ Population of Nigeria, Millions of People____ Population of Venezuela, Millions of People

Correlation is not causation, and the variables are complex, but, taking U.S. corn production as a proxy for world grain production, what conclusions might you draw? In The Population Bomb (1968) Paul Erlich predicted a global disaster. What we have today, instead, are population land mines scattered throughout the non-industrialized countries. These rates of growth simply cannot continue. Something has to give. This Lindsley Standard Time Series Chart forces that conclusion on any rational viewer, without bias, without exaggeration, and without ambiguity. What will give (or is already beginning to give), and what should we get ready to do (or what are we already doing) about it?

Experienced sailors learn to distinguish between wind waves that emanate from nearby sources and ground swells that arise from distant events. Recent happenings in Syria, for example, are wind waves. Population growth in the non-industrialized countries is a ground swell. Lindsley’s Standard Charts can help us to identify ground swells. We should add them to our tool kit, because preparing for distant future events is humankind’s greatest challenge.


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Technical Conclusion

Since Lindsley’s Standard Charts can be powerful tools for analyzing event-frequency time series data in any field, to make the technology more transparent and acceptable to scientists in general the name should morph again from “Standard Celeration Charts” to “Lindsley Standard Time Series Charts.” And to fully realize their potential, Lindsley’s Standard Charts need to be brought into the digital age, available to electronic communication. This is not especially difficult: Figures 5, 8, 12 and 13 -- simple, readable charts that meet all of Lindsley’s basic criteria -- were easily generated by Wells Hively from Excel spreadsheets. Figure 14 is an example of much more sophisticated charts generated from templates currently being designed by Stuart Harder, Jack Auman and others.

Figure 14

1920% 1930% 1940% 1950% 1960% 1970% 1980% 1990% 2000% 2010% 2020%

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•%>%Cimarron%USGS%Site%07156960%

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We hope to construct a web site to promote/facilitate the use of Lindsley Standard Time Series Charts in the analysis of general social-science data. The site is intended to do three things: 1. Provide templates to use in making Lindsley Standard Time Series Charts.

2. Provide a searchable archive of essays and reports based on the charts. 3. Eventually provide a data bank of graphs – e.g. country populations, CO2 emissions, tornado occurrences, pesticide sales, autism diagnoses, etc. – that can be retrieved in open-access for comparative analysis.. We look forward to the growth of a multi-disciplinary, Lindsley Standard Time Series Analysis Community on the Internet. Interested participants contact [email protected].


mailto:[email protected]

mailto:[email protected]

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References

Edwards, D, DeA. & Edwards, J. S. (July 3, 1970) Fetal movement development and time course, Science, 95-97

Erlich, P. (1968) The population bomb, Ballentine Books

Hively, W. & Hively, W. D. (2013) A perilous journey to abundance: looking for sustainability in agricultural history, Amazon Kindle

Lindsley, O.R. (December 1966). An Experiment with parents handling behavior at home, Talk Given at Johnstown Training Center, Bordentown, NJ

Lindsley, O.R. (May 1967). Operant behavior management: background and procedures, Talk Given at Breksville Institute, Brecksville, OH

Lindsley, O.R. (March 1968). Training parents and teachers to precisely manage children’s behavior, Talk Given at the C.S. Mott Foundation Children’s Health Center, Flint MI

Lindsley, O. R. (1994). Gunter's line: standard celeration chart ancestor, not Napier's logs or bones. Journal of Precision Teaching, 12, 97-104.

Lindsley, O.R. (2013 Revised). Skinner on measurement, Behavior Research Company

Tufte, E. (1983) The visual display of quantitative information, Graphics Press

Illustration Credits

Figure 9: http://web.mnstate.edu/malonech/images/Operan5.jpg Figure 10: traced from a copy of the original with permission of Dr.Diane DeArmond Figure 11: photocopy provided by Dr. Jack Aumon Figure 14: produced from a template by Stuart Harder Other figures created by Wells Hively


http://web.mnstate.edu/malonech/images/Operan5.jpg

http://web.mnstate.edu/malonech/images/Operan5.jpg

a family of standard event-frequency time series charts: o.r

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