((

'i

CH

AP

TE

R

I

I NT

RO

DU

CT

I O

N

Education

r s goa I i s

improv i ng hum

an behavior. T

oday, this

formally involves tw

o mi I lion teachers and over sixty

nri I I iorn school-

aged ch i ldren (NE

A R

esearch B

u I leti n ,

1967) . lby can education do its

job more precisely, m

ore ef fectively, m

ore scientif ical ly? C

urrrently,

we dontt of ten ref er to the science of education.

And yet, to

improve

the behavior of ove: sixty m

i llion people six hours each day, nine

months each year for thirfeen years, education m

ust become a science.

That is,

educators must know

whaf to do and rhen to do it

in order to

rapidly and economically im

prove human behavior.

ln short, a science

of gducatlog must develop.

Today, educators are at the threshold, at the beginning of the

development of a -science o_f educatiolr.

The I lterature describes this

beginning. F

or example, W

helan ( 1966) provided examples of teachers

precisely demonstratlng the feasibility

of the development of this

science. Lindsley (1970a) described the scientif ic behaviors of

a

group of m

en who m

ay become contributors to this field--its

scientists.

Baer ( 1970) m

aintained that thi s developing science has "...the

essence of good and responsible science devoted to m

anrs benefit...

(p. 243-)n w

hile describing the moral responsibility of its scientists.

A science of e4ucation is feasible,

scientists are becoming avai lable

and it has the essence of a good and responsible science along w

ith an

awareness of

its m

oral responsibility. ln surrm

ary, a science of

education is developing.

PU

rpose

The purpose of this research E

s to evaluate a tool developedspecifically to help education reach lts goal of bm

lry a sclence.

The tool is the B

ehavior Chart, the foundation of the P

recise Behavioral

Managencnt S

ystar and its classrom application called P

recislon Teachlng.

Precise B

ehavioral ltlanagernent is a systerir of neasurlng, describlng, andpredictlng individual hum

n frequencies and ceterations. lt m

s

developed by Ogden Lindsley, xith the help of m

ny teachersr p€ersr

and students. The B

ehavior Chart is the forrm

t ln uhtch this systenpresents frequency and celeration m

oasures of lndividual behavlor.

lmD

ortance

Prediction is the ulttrnale crlterlon of effectlveness ln any

science. Ilhen a scierrce develops to the polnt of predlctlng'the

individual case, then the science has mtured (M

ltchell, 1969).

For educatlon to becone an effectlve and rnature sclence, lt

rnrst

have predictive capabllities for each lndlvidual student. Clearly,

and simply, accurate predictions about lndlvidual crinpanies have rm

de

buslnessnren successful, and accurate predlcttons about the rnovdnents

of individual celestial bodies helped land nren on the [Don.

ln the

flnal analysis, a science of education rlll be only as effectlve as

its predictive capabi I itles for each lndlvidual.T

he importance of evaluatlng the B

ehavior Chart as an educatlonal

tool is clear. lf

it aids ln predlctlng the behavior of indivldualhum

an belngs, then educators may be able to use It to m

ake nrore accurate

predictions and declsions about a chlldrs behavior and his future.1

ln fact, the chi ld m

ay be able to use this tool to m

ake his ow

n

predictions and decisions. lf

the Behavior C

hart helps predict hum

an

behavior, then it w

ill hetp advance the developing s-cience of

education

CH

AP

TE

R I I

RE

LAT

ED

RE

SE

AR

CH

Thls review

makes tw

o points direcfly relevant to this

research. T

he first descrlbes the use of frequency of behavior

as a measurem

ent dafum. T

he second descrlbes *he use of certdration

as the new m

easurement datum

of fhe Preclse E

lehavioral Managem

ent

System

. Appendlx A

provldes a list of up-to-date publlshed materials

for the reader interested in learning more about P

recise Behavioral

Managem

ent and its classroom appllcatlon, P

reclsion Teaching.

Frequency ls A

Universal B

ehavlor Measure

A behavior frequency ls defined as the num

ber of tlmes a

behavior occurs divided by the amount of tim

e during which thaf

behavior uas recorded. B. F

. Sklnner (1938; F

ersfer and Sklnner,

1957) was the first

scientist to systematlcal ly use frequency (S

kinner

cal led it .ra+

e. of resoonse) as a measure of an organlsm

rs behavior.

Lindsley (1956) found frequency a precise and sensltive measure of the

behaviors of lnstitutlonal lzed schizophrenic patlents.

l{it[ sim

ultaneous

frequency records of paclng, rorking (lever pul ling for consequences),.

and hallucinatlng, Lindsley

was able to predicf the effects of several

drugs upon human behavior.

Frequency appears to be a m

easuro applicable to all hum

an

behavior. Alm

ost by definltlon, the word behavlor lm

plles motlon or

opv€rnent. All rpvem

ents have a duration. S

ince movem

ent and

duration are sufficlent to produce frequency, and since al I hum

an

2

))

tl

behav lor has both movem

ents and durat lons, it appears that

frequency Is somethlng all

behaviors have in cormon. S

kinner rneant

this when he called rate a rrunlversal datum

fr (Llndsley, lg72).

At one tim

e a debate existed whether f requency or percent w

as

?he more useful m

easure of human behavlor. S

everal co-workers

even

col lected data aftempting to resolve the confuslon (C

aldwet l,

1966;

f-b I zschuh and Dobbs ,

1966, . W

hen I n doubt turn to a teacher. A

sk

a teacher what she w

ants to know about a childrs classroom

behavior.

The answ

er wl I I be spegd and ag_guracy. 0f course, the answ

er was

both frequency and percenf.

Later lt w

as discovered that by chartlng both frequency correct

and f requency wrong on a raf Io sca le, any ratlo sca le, the d i stance

befween these tw

o frequencles rlas in fact percent, Flgure I

shows a

ratlo scale, fhe Behavlor C

harf, on whlch the dlstance show

n between

frequency correct and frequency urrongr oo maffer w

here on the chart,

r€presents a ra.tlo of correct-to-wrong behavlor of 9:1.

This ratio

ls cornrnonly seen as a percentage, 90fr correct, or may be expressed as

a multlple, x9.

ln both cases the meanlng'lrs the sam

e: The behavior

occurred correctly nlne tlmes rnore often than lt

occurred incorrectly.

That ls, nlne correct per m

lnute and one wrong per m

inute Is g}ifi

correct or x9. Llkew

ise, 90 correct and l0 wrong per m

lnute is gO

fi

or X9, as Is 45 correct and 5 w

rong, ln other words, w

hen displayed

on the Behavlor C

hart, pairs of correct-wrong frequencles show

accuracy,

whether expressed as a m

ultiple, x9, a ratlor g:1, or a percentage,

90fr correct.

The adV

antages of ratlo charts have conmonly been recognized

by mathem

aticians (eg. Schm

id, lg54) and englneers (eg. Am

erican

Soclety of M

echanical Engineers, 1960). ln 1954, S

chmld w

rote:

The sem

i logarlthmic chart Is unequaled for m

anypurposes, especlal ly ln portraylng proporflonalald percentage relationshlps. ln com

parisonw

lth the arlthmetlc

I ine chart, lt possesses m

ostof the advantages

w I thout the d I sadvantages. T

h I stype of chart not on I y correct

I y represents re I at I vechanges but a lso Ind lcates absolute arpunts at thesam

e tlme.

...For the unlnlfiated, the term

ttsem i logar i thm

lc, tt as we I I as the character

t st I crul ing of the vertical axls, ffioy seem

formldable;

but actual ly the theoretical prlnclples on which this

chart ls based, and also lts construcilon and useare com

paratlvely slmple.

preJudlce and generalI ack of understand I ng unfortunate

I y have resu I tedin conslderable resistance fo the use of sem

l log-arlthm

lc charts. G

eneralfy, rates of change[called celeraf lon In P

recision Teachlng uni

dlscussed ln the next secttonl are more signlflcant

than abso l ute amounts of change l n stafl stica l

analysls and presentatlon. ln uslng the rafiochart, one can have confldence thaf ielatlve changes?re portrayed w

ithout dlstortlon and uncertalnty(p. 109).

ln 1967, Precision T

eachlng began to encourage feachers tocom

blne the advantages of frequency and percent measures w

lth theadvantages of ratlo charts by displaying accuracy palrs of Indlvldualstudent perform

ance on the Behavior C

hart.

ln summ

ary, then, for measuring lndlvldual hum

an behavior

frequency is a useful datum for at least three reasons. F

irst,frequencf has hlstorlcal precedents. S

econd, two frequencles charted

on a ratio scale show percent. T

hird, frequency appears to be am

easure applicable to all hurnan behavior--a universal m

easure of

behav I or.3 (

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Celeratlqn ls A

Universal B

ehavlor Chanse M

egfqfg

Users of the P

reclslon Teaching S

ystem and the B

ehavior Charf

notlced some rafher interestlng rela*lonshlps

arnong charted frequenclos.

They saw

that frequencles displayed on the Behavior C

hart were often

either acceleratlng or decelerating as tlme passed. C

eleratlon ls

th€ general term for these accelerating and decelerating relafionshipi.

The B

ehavior Chart users also noticed the goneral lineari.ty of their

accelerating or deceleratlng frequencies. Therefore, fhese precise

behavior managers (E

dwards, 1969; S

lezak, 1969; Johnson, l97l; Bafes,

l97l; Kyrklund, 1971) starfed uslng sfralght lines to represent thoir

celeratlng froquencles (See section A

of Figure 2).

Stralghf I lne represontatlon of celeratlng frequencles has

several advantagos for Behavior C

hart users. S

traight llnes are

certalnly oasler than curved llnes to draw, see, and understand.

Second, these sfralght lines provlde an opportunity for these users

to compare changlng or celerating behavior over a w

lde range of

posslble hum

an frequencles. Secflon B

of Flgure 2 show

s that behaviors

doubllng weekly, no m

atfer what their frequency, produce celeration

llnes that are parallel to one anofher. Thls m

eans that if !s easy

to conpare growfh In behaviors that have the sam

e or different

f requenc i es.

Since indlvldual celerations are m

easured over a comm

on

denominator of one w

eek, they can be used to comparo changing frequencies

covertng dlfferent periods of time.

Section C

of Figure 2 shoivs that

a on6 vreek cgleration of x2 ls parallel to a two or three w

eek celeration

of the same size.

Another advantage af celera-tions in describing changing

frequencierg is thatthey are sym

metrical (S

ee section D of F

igure 2).

Ttris m

elans tha-i"a weekiy doubling w

ill look sirnl lar to a w

eokly

halvlng and'*ill have the sam

e numerical value.

Only the directions

of 1'tre-two celerations w

ill be

cl ifferent.

Finally r:eleration is appticable to all

changing Individual

hurnan behav i or'" L" i nds ley m

ean t t'h is

vrhen he ce I lod ce lerat ion arfuniver$aI rneaslrr-e of behavior change" (Lindsley,

1970b).

Schm

icl ar^gued strorrgly in favor of using a ratio chart to

show ce I er;:1- ions er ra1'e:l of

charrqe,':

Because of lack of fam

i liarity wifh the ssnl logarithm

iccharf, a desire for sim

pliclty, or for sorne otherreason, a statistician m

ay prefer to use some technique

other than the semi logarlthm

ic chart to portray ratesof change. T

his can be done ln at least two w

ays,neither of w

hlch is entlrely satisfactory. T

hesem

ethods represent only a partial and frequentlyinadequate solutlon.

Moreover, lf

simpl iflcation Is

the objective, more problem

s ars actual ly created thanso I ved.

The f i rst m

ethod i s to portray rel ati ve

cha nges by mea ns of a percentage sca I e .

Mere rrercentages

fal I to provide any indication of the actual values thatare represented by the percentages on the curve.

The

semi logarithm

ic scale nof only porfrays relativechanges correctly but also exhibits accuratoly fhenum

er i ca I va I ues of the ser i es represented by thecurve.

Moreover, the ssm

i logarlthmic chart avoids the

inevltable confusion resultlng from fhe arbltrary selectlon

of the base year or base period. T

he second altornatesolution is to construct an arithm

etlc grld with tw

odifferent vertical scales.

Thls m

ethod Is satisfactoryif

the scales are drawn in proper proportion and ff

the va lues do not vary too rnarked ly f rom one another.

Otherw

ise, the changes Indlcated by the curves wlll

bedistorted and m

isleading (1954r pp. 131-132)"

5

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Stralght I ine celerations on the B

ehavior Chart have several

advantages for thelr users, and are the current behavior change record

of Prec i s ion T

each i ng. T

he purpose of th I s research was to eva I uate

celeratlon llnes dtsplayed on the Behavlor C

hart across a large sample

of Indivldual hum

an behaviors. This evaluation had tw

o parts. F

irst,

the goqdness-of-flt of these celeration I lnes w

as determined. S

econd,

thelr accuracy in predlctlng future behavior frequencies was m

easured.

CH

AP

TE

R I I I

ME

TH

OD

Hqr the B

ehavior Chart T

ransforms F

requencles

The B

ehavlor Chart used ln P

recls,lon Teachlng is a sem

l-

logarlthmlc scale (descrlbed to teachers and chlldren as a m

ultlply-

divlde scale). 0n the B

ehavlor Chart, the user can chart frequencles

of human behavlor ranglng from

one ln a waklng day to 1,000 ln a

mlnute on an 8 1/2ttx llfipage.

Houever, the userts eyes w

lll see theequal lnterval relaflonship of the logs of these charted frequencles.T

hat ls, equal dlfferences betw

een logs, correspondlng to equal multlples,

are represented by equal dlstances. ln other $ords, the Behavlor

Chart perform

s a logarlthmlc transform

atlon on the charted frequenctes.

Flgure 3 show

s thls transformatlon of charted frequenctes lnto equal

logar lthmlc

I nterva I s.

It ls very Important to rem

enrber that all the m

efhods

descrlbed ln thls research were applled to the logs.of frequencles.

The relatllonshlps that w

ere dlscovered are propertles of the dataas they are seen on the sem

i logarlthmlc

Behavior C

hart.

Popu latlon

The data for thls research cam

e from tw

o sources. O

ne source,

the Behavlor B

ank, delcrlbed in Appqndix B

, has been col lectlng and

computerizlng large num

bers of lndlvidual human frequencles for the

past flve years. C

ontrlbutions 1o the Behavlor B

ank have come fronr

educators and other professionals from 32 states (S

ee Appendix C

for7

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a llsf of D€posltors). T

helr deposlts are lndlvldual behavlor

projecfs, the charted frequencles of a personrs dai ly performance of

a plnpolnted behavlor.

The second source of lndlvldual

human behavlor frequencles

was four popular Journals: B

€havlour Research and T

heraov, tne Jgre1

of the Experlm

ental Analvsls of B

ehavior, the iggg! of A

pplled Behavlor

Analysls, and .f=

I99P@

L C

hl ldren. E

ach journal was screened from

lfs flrsf lssue through 1970 to obfaln addltlonal records of

human

f requenc I es.

Pooulatlon

Screenlno

The lndlvldual hum

an behavlor frequbncy proJects provlded by

the Behavlor B

ank and the Journals wero flrs* dlvlded lnto their

reported phases. A phas€ ls a perlod of tlm

e durlng whlch envlronm

ental

condlllons are reported to be relatlvely constant' A proJect

may

contaln any number of phases. T

o Illustrate, the flrst phase of

a proJect m

ay contaln several dal ly frequencies of words read corectly

by a student uslng the classroorn test' T

he second phase beglns when

the proJectrs author reports that the student began uslng a nett

currl,culum.

The frequencles rlthln elther phase can be vlew

ed as a

group, because fhey occurred durlng reportedly slnl lar environmental

condltlons. Thls research used the P

hase as the basic unlt for

.t.'screen

I ng.

The Indlvldual

phases of the Eanked and Journal projects

were

then screened accordlng to mlnlm

um and m

axlmum

number of frequencies'

and mlnlm

um celeratlon.

Screenlnq .tgr_P

has€s. wlth 20 or M

ore Frequencles

Each phase w

as screened and accepted only lf lt

contalned 20

or more frequencles. E

xgrerience wlth m

any Behavlor C

harts has ln-

dlcat€d that a representatlve stralght llne can usually be drarn fhrough

l0 to 14 data polnts. P

hases wlth a m

lnlmum

of 20 data polnts provlded

l0 frequencles through whlch a stralght llne could be flf

and fhen

extended, hopeful ly, to projecf the next l0 frequencles. ln otherw

ords, 20 frequencies provlded a mlnlm

um of dafa w

lth whlch to fest

the predlctlvs accuracy of straight line projecflons.S

creenlnq for Phases w

lth Celeratlons >

l.t

. N

ext, phases were screoned on the slze of thelr average

reekly change. Phases shonlng a m

lnlmum

weekly celeratlon of at least

I t.t, or about tO

i weekly Increase or decrease, nere accepted.

Because of the posslble range of hum

an frequencles, from

one por

day tq 1000 per mlnute, tt ls necessary to use a relatlve m

easure of

change. Thls relatlve m

easure of change must not be affected by the

slze of the frequencies, and lt m

ust be extrapolated to a comrorl tim

e

base lf lt

ls to be useful for comparlson

across proJects. Such a

measure ls called ueeklv celeratlon. and lt tclls

hoyl much a behaulor

frequency is changlng (multlpllng or dlvldlng) w

lthln one reek.

To flnd out w

hether or not a phase of frequencles was celeratlng

at least l.l (x or *) w

eekly, the followlng steps w

ere taken. F

lrst,

a quarter-lntersect stralght llne was flt

to the frequencles (See the

next sectlon for a detailed descrlp*lon). Thls line then w

as measured

to find the average weekly change or celeration.

Sectlon A

of Flgure

2 shows w

hat dlfferent reekly celeratlons look llke on the Behavlor

Chart, and F

lgure 4 shows fhe range of celeratlons lncluded in thls research.

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(Weekly celeration indlcates hou m

uch the frequencies within

a

phase change wlthin one w

eek. ln this research, phases confaining

frequencies that were changing w

eekly at leas+ jlO

X, or {1.1, w

ere

accepted. U

sing fhls criterlon would require the techniques described

later to project changing frequencies rather than static behavior.

These celeraflng frequencies

would certainly provide a m

ore rigorous

fest of the accuracy of straight I ine projection techniques.

Screening for C

eleratioq Phases w

tth 20 to 29 Frequencies

The first

two screening procedures selected from

+he B

anked and

Journal projecfs all phases that contained 20 or m

ore frequencies celer-

aflng af least 1.1 (x or t) weekly. T

he final screening criterion

fixed the upper limit of frequencies w

lfhin a phase a+ 29.

This criterion

was applied to decrease the posslbility of effects fhaf m

ight be

lntroduced by tOo w

ide a range in the number of frequencies w

ithin the

selected phases.. This screening procedure; then, guaranteed that all

phases would be approxim

afely the sane length.

To sum

marlze, the hum

an behavior. frequency projects provided by

the Behavior B

ank and the Journals were first

dlvided into their

lndlvidual phases. These phases w

ere then scresned (a) by minim

um -U

mber

of freqqelcies, to provlde enough data points to draw a represenfative

straight line, and check fhe accuracy of straight line projectlon;(b) by m

inimum

cdlerdtlon,to include only dynamlc or changing frequencies;

and (c) by m

axlmum

number of frequencies, to guarantee fhat all

phases

were about the sam

e length. T

he resultlng screened phases were then

used to test the goodness-of-fif of stralght lines and fhe accuracy

of their projections.

I i.'tlfqg. St"ra iqht.

l,.!_nes. fo. Ce I erat i ng

Frequenc I es

Tw

o techniques were used to fit

sfraight I ines to the screened

population of frequencies. T

he lqaFt*S

;qlfqre.s techniq.ug (F

erguson, lg5g)

was selected because of

its historical

acceptance and because it

minirnizes the variance of the data around the line it

produces, U

sing

the least-squares method a straight

I ine was fit

to the logs of the

f requerlc i es of each phase. T

he equat ion of th i s stra ight I i ne i s

derived using the fol lowing form

ulation:

Xi =

days

Yi =

logs of frequencies

N

= num

ber of frequencies,Yi =

estimated log of frequency along straight

s =

slope

a =

estimated log of frequency at X

=0

line

S=

^EX

iYi -sxiA

i&

Exi

fx-,,'&

a=

lyi - E.zxtr

The equation for the least-squares straight

I ine is

then :

Yi =

s'Xi *

a

2

N

11

(

The quarter-intersect technique, developed by Lindsley and

Koenig, w

as selected because of the ease with w

hich it can be perform

ed

on the Behavior C

hart. T

his technique of I ine fitting

is i I lustrated

and explained in Figure 5.

Goodness-of -F

i t C

r i terion

The purpose of this research w

as to compare the usefulness of

a tradltional and u{6ll-documented straight line technique fhaf requires

mathem

atlcal calculations ( least-squares) w

ifh a fechnique that is

graphic and easier to do in the classroom but not yet w

el l-documented

(quarfer-lntersect). O

ne comparison evaluafed how

accurately lines

drawn by both techniqu6s represented the frequencies to w

hich they were

flf. T

wo m

easures would show

how w

ell a straight line represented a

series of celerating frequencies, while com

paring the two line-fitting

techniques. T

hese were (a)

how w

el I the line bisects the frequencies;

and (b) how w

ell the line bisects the variance sf the frequencies.

How

Wel I S

traiqht Lines Bisect F

requencies

This criterion

assum€s that the m

ore closely the straight I ine

bisects fhe frequencies, the more representative if

is of those frequencies.

That is, if the line is a good fit,

it will

have as many frequencies

above it as below

it. F

or each straight line, a counf was

made of the num

ber of frequencles above and below it.

!:low W

el I Stra i q!'rt, Lj nqs

Bi sect V

ar i ance

Th i s cr i ter i on assum

es that the more equa I the var i ance around

the straight Iine,

the better its fit.

The m

easure of variance used

was the relative

!a,nqe of the frequencies around the straight line.

This m

easure was the sim

plest, statistically the least ef f icient,

and

for our purposes the most rigorous.

To m

easure how w

ell a straight

line bisected the total variance on fhe Behavior C

hart, the variance

above the line was com

pared to the variance below the line.

First, the distances of the frequency farthest above and the

frequency farthest below the straighf line w

ere measured. T

hen the

distance of the frequency farthesf above the straight llne, or up

bounce, was com

pared to the distance of the frequency farthest below

the straight I ine, or dow

n bounce. These distances w

ere compared

as

ratios of one another, with the up bounce in the num

erator (Flgure

6

i I lustrates).

lf the straight line bisects the variance, so fhat the up bounce

equals the down bounce, then their relafionship is 1: I (xl.b).

lf

+he up bounce is tw

ice the down bounce, then thelr relationship is

2:1 k2.0. lf the up bounce is half the dow

n bounce, then the

relationship is 1:2 (92.0).

Again, it

is assumed that a representatlve straight line w

i I I

bisect the variance of its frequencies, producing equal up and down

bounce, or non-skewed variance around it.

The closer the ratlo of

+he up and dow

n bounce is to x1.0, the beffer the straight line fit.

To surunarize, tw

o measures w

ere used to evaluate the goodness-of-

fif of straight I ines to celeratlng hum

an frequencies. T

he firs* m

easure

assumed that a representative straight line w

ould bisect the frequencies,

so that there would be as m

any frequencles above i+ as below

it. T

he

second assumed that a representatlve stralghi line w

ould bisect the

variance of the frequencies around it, so that the up bounce equalled

fhe down bounce.

12

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Pro.iecf ion

ln fhe current sfate of the sclence of behavlor, *he probabl I ity

of predlctlng exact human frequenc6es ls lov.

Af the present tim

e, a

more reasonable goal m

ay be to predlct the area or envelope ln which

future frequencles w

l I I occur. T

hls research used stralght I ine

projectlon on a seml logarithm

lc charf to center or locate an envelope

conta lnlng fufurs f requencles.

At thls polnt, one im

portant questlon had to be answered:

D,oes

the slze of the proJection envelope change, get larger or smal ler, as

behavlors celerafe? ln other uords, as hum

an behavlor changes frequency,

golng from a louer frequency to a higher frequency, or vlce versa, ls the

varlance addltlve? lf

the answer to thls questlon ls that the varlance

does change, fhen lt w

ould be necessary to lnclude some factor to adjust

fhe slzo of the proJectlon onvelope in order to lmprove projec*ion accuracy.

But lf the varlance is addltlve, lf It

does not change as behaviors celerate,

then adJusfments.of fhe slze of the proJectlon envelope w

ould nof be

n€c€ssary and fhe proJectlon technlques would be less com

pl lcated.

Chanoe ln V

arlance around Stralqh+

Line.as Frequencles C

elerate

To m

easure change In the varlance around celeratlon I lnes on

the Behavlor C

hart, the range, or lgtll bounce, of the flrst

quarter

of a phase was com

pared to fhe total bounce of the fourth quarter of

that phase. To flnd the total bounce, a llne w

as drawn parallel to

fhe coleraflon llne through the frequency farthest above it. T

hen a

llne was draw

n parallel fo the celoratlon llne through the frequency

farthest belorv lt. T

he dlstance between these tw

o outer lines, expressed

as a ratlo, deflnes the total bounce around the celeratlon line (See F

igure

6).

To m

easure change ln the total bounce of celeratlng frequencles,

each phase was dlvlded lnto four equal parts, or quarfers. N

ext the

total bounce of fhe flrsf

quarter was com

parod to the tofal bounce of fhefourth quarter, as show

n ln Flgure 7.

lf the ratio of these total bounces

ls 1:l (xI.0), then the varlance around the stralght llne remains relatlvely

constant.The rssults roported In the next sectlon shored that the

proportional varlance around the stralght llne of celerating frequencles

usual ly remalns consfant. T

hls means that th6 varlance of celeratlng

human frequencles ls addiflve.

Therefore, the proJectlon technlgues

descrlbed next did nof need to,lnclude an adJustrnent factor to'change

the slze of the proJectlon envetope.

Pro.iectlon T

echnlques and Pro.iectlon A

ccuracy

To proJect future freguencles, the follorlng nrcthod, Illustrated

ln Flgure 8, w

as used. Flrst a llne, elther least-equares or quartar-

lntersect, was fif

to a serles of frequencles. T

hen two llnes w

ere

drawn parallel to this celeratlon llne, one through the freguency

farthest above lt, and one through the frequency farthest below

lt.

These tw

o outer llnes forred an envelope, whlch w

as proJectod beyond

the serles of frequencles to +ry to predlcf the area ln w

hlch future

frequencles w

ou ld occur.

ln fhls research, the flrst l0 to 14 frequencles of each phase

formed tho proj€ctlon envelope.

The envelope w

as extended to proJect

the next l0 to 14 frequencles. T

he percentage of fufur€ frequencies

contalned in this projected envelope was the m

easure of the accuracy

of the projecflon technlque (See F

igure 8).15

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17

Sim

i larities:R

eliabi I itv, Generality, V

al_i ditv

According to S

ldman (1960) the m

aturity of a science can be

judged by the extent to whlch new

information is related to the exlsting

body of knowledge of that science.

This m

eans that comparlson Is a

n€cessary part of a growlng science.

This research used tw

o nethods,

the least-squares and the quarfer-lntersecf techniques, for com

paring

lndivldual hum

an behavior frequencles ob*ained from tw

o sources' Banked

phases and Journal phases. A new

ly-obtained body of information,

the

Banked frequencies, w

as compared fo an exlstlng body of inform

ation, the

Journal frequencles. Also, a new

technique for describing col lectlons

of changlng frequencles, the quarter-intersect, w

as compared to an

existtng technlque, the least-squares. The m

easures used to make

these cornparlsons have been called lndlces of reliabillty, generallty,

and val ldltY.

lndlces of rellabilltv shou how

conslstenfly behavlor has been

measured (C

ronbach, 1960).. To the extent lt

is shown that certain data

are rellable, then dlfferences amohg those data can m

ore confidently be

attrlbuted to the variables belng studied rafher than to inconslstencies

of measurem

ent. Accordlng fo S

idman, ilthe soundest em

plrical fest of

fhe reliability of data Is provided by replication (1960, p. 70)r'. A

sophlstlcated tesf of rel iabl I ity ls intersubject systematic repl ication,

ln which the sam

e measures are obtained from

indlviduals (rather fhan

groups) ln different (rrither than the same) settings.

This iesearch com

pared the behavior frequency records of more

fhan 11000 differenf lndlvlduals. S

ome of fhese records w

ere observer-

checked, sotne ttere Journal-edlfed, some w

ere self-recorded' M

ore than

1,200 different behaviors were recorded in nearly as m

any different

settings. A

ll of these individual records of human behavior

were

compared

us i ng two d i f ferent m

easurement

techn i ques, the I east-squares

and the quarter-intersect. T

hese comparisons m

ay be viewed as inter-

subject systematic replication.

The degree of sim

ilarity among the

records may be view

ed as an index of the rel iabi I ity of these measures

of human behav i or.

Sidm

an states that systematic repl ication is also a m

easure

of the qene,ra I i ty of the re lat i onsh i ps that have been d i scovered .

The m

ore consistent the findings am

ong data that vary on many dlfferent

d i mens ions, the greater the genera I i ty of those f i nd i ngs.

The degree

of simi larity

between m

easures of the two sources of hum

an frequencies,

and the degree of simi larity am

ong measures of al I the individual

f requency records within the tw

o sources may be v iew

ed as dernonstrations

of the general ity of the relationships show

n by this research'

lndices of val iditv show how

useful a measure is in m

aking

decisions (Cronbach, 1960). V

alidity is often determined by com

paring

a measure to som

e criterion measure that has already been proven

useful. T

he best criterion is a direct measure of the inform

ation

needed to make the decision (C

ronbach, 1960; Lindsley, 1964).

Concurrent val idity show

s how useful ly a m

easure describes a

current situation (Cronbach, 1960).

The nevv m

easure is compared to

a

criterion, preferably a direct descriptlon of the situation. ln this

research, Banked frequencles (the new

measure) w

ere compared to Journal

frequencies (the criterion rneasure) as descriptors of individual

human behavior. T

his comparison m

ay be viewed as a test

of

the concurrent validity of the Banked frequencies. ln additlon, the

\I

18

)

comparlson of the new

quarter-lnfersect results to the establlshed

least-squares resulfs may be view

ed as an lndex of the concurrent

valldlty of fhe guarter-intersect technlque.

Predlctlvo val ldlfy show

s how usefully a m

easure predlcts

a future sl+uation (C

ronbach, 1960; Suchm

an,1967). 0n fhe basis of a

measure, a predlctlon about the future ls m

ade. This predlcflon is

tafer compared fo the acfual future outcom

e. ln this research, fheleast-squares and quarter-intersect

technlques were used fo predict the

envelope ln whlch future frequencies w

ould occur. T

he percentage of

frequencies actually occurrlng rvlthin the projected envelope was later

found. T

his percenfage m

ay be vlewed as a m

easure of the predictive

valldlty of the two llne-flfting

technlques.

ln summ

ary, fhe results obtalned In this res€arch may be seen

as lndlces of the rel'iablllty ot fhe Banked and Journal frequencies as

m€asures of hum

an behavlor, as lndices of the gonerality of the'''l

relattonshlps dlscovered am

ong the frequencles, as lndices of the

concurrent valldlty of the Banked frequencles and the quarter-intersect

fechnlque, and as Indices of the predictlve validity of *he two line-

flttlng techniques. A

l I of +he m

ethods used ln ihis research provide

data compartisons producing m

easures of slmllarities.

Whether any one

comparative

measure of sim

ilarlty ls seen as more an index of reliability

than valldity, or more an index of valldlty than generality, is left to

each reader and his statistical preferences.

For this reason, the results sec+

ion contains measures of the

slml larltles betw

een techniques, the leasf-squares and quarter-intersect,

and between sets of dafa, Journal frequencles and B

anked frequencies,

The im

portance and implications of these sim

i larities must be

eva I uated by the reader, os S

i dman adv i sed:

The exerc i se of m

ature judgement i n eva I uati ng

the re I iab i I i ty and genera I i ty of exper im

enta I

data is seldom discussed in textbooks on

experimental m

ethod. Y

et it plays a basic

role in the evaluation of data. A

thoroughaw

areness of this general fact w

i I I prove more

valuable than any of the individual evaluativetechniques that are described in the follow

ingchapters (1960, p 43).

The reader m

ust exercise his basic judgement in evaluating the

simi larity m

easures reported in the results section.

ln Chapter V

, rel iabi I ity, generat ity,

and:val idity wi I I again

be discussed. There, an attem

pt wi I I be m

ade to put the results ofthis research into perspective relative to the topics of rel iabl I ity,general ity,

and val idity.

19

CH

AP

TE

R

I V

RE

SU

LTS

Population S

izes andS

imilarities

Table I

summ

arizes the sizes of the two data sources for this

resea rch. I n f i ve years, contr i butors f rom

32 states shared 13 ,g4l

behav ior im

provement projects

i n the Behav ior B

ank. F

our journa ls,

B-ehay-lgur R

esearch and Therapv, the Journa I of the E

xper imenta

I

Analvsis of B

ehavior, the Journal of Applied B

.ehavior Analvsis,

and

Except i ona

IC

h i I dren, each screened from

i ts f i rst i ssue through

l97O (totalling 6l journal-years), and covering j6 calendar years,

prov i ded 5 1 t hum

an frequency proj ects.

Phases per P

ro.iect

The B

anked projects averaged about two phases P

er proiect,

whi le the Journal projects averaged just under three.

The B

anked

projects prov i ded 26 1678 phases for screen i ng, and the Journa I s

provided 1,456.

Resu

I tS_ of S

c[een i [g Jgr Phases

w i th: 2A

or More

tes

For this criterion the B

anked proiects provided richer returns-

The B

anked projects produced 41180 phases with 20 or m

ore frequencies,

wh i I e the Journa

I s prov lded 63. T

hat i s, about 16fi of the Banked

phases and about 4fi of the Journa I phases urere 2A or m

ore f requenc ies

long. C

ompared to the Journal projects, the B

anked proiects produced

67 times m

ore phases and were 4 tim

es richer in phases with 20 or m

ore

f requenc i es .

With W

eekly Celerafion: l.l.

Both B

anked and Journal phases of 20 or

more frequencies produced abouf equal proportions (566. and 32fi respectively)

of phases rrifh weekly celerations of at least I.l

(x or i), T

he Bank

provided 1,507 phases, and the Journals, 20. ln other w

ords, about l/3

of all phases w

ith 20 or more frequencies yere increasing or decreaslrrg

10tr or more each w

eek for both Banked and Journal sources.

20 to 29 Fr_equenc

i es. T

he f i na I screen

i ng procedu re narrowed

the group to 1,186. F

or both the Banked and Journal phases, about 5/4

of all phases w

ith 20 or more frequencles and a w

eekly celerafion of at

least 1.1 (10, weekly change) had few

er than 30 frequencies. That is,

about f/4 of these screened phases had between 20 and 29 frequencies.

How

similar vere the B

anked and Journal projecfs? ln general,

the Journal projects had more phases but few

er frequencies per j:hase.

But m

ore imporfant, both groups show

ed weekly celerations of af least

1.1 about 33$ of the time for those phases w

i*h 20 or more frequencles.

For both groups, about 75$ of those phases had betw

een 20 and 29

frequencies. The B

ehatior Bank and the Journals provlded slm

i lar

proportions of data meeting the last tw

o screening criteria of this

research.

Goodness of S

traiqht LIne Fit

Tw

o measures show

ed hov nel I least-squares and quarter-lntersect

straight lines represent celeratlng hum

an frequencles. T

he first m

easured

how closely the line bisects the frequencies. lf

was slm

ply a counf of

the number of frequencies above and below

the line, assumlng that a

representative I lne w

ould bisect lts frequencies evenly.

And W

ith

a

))

((

(

Tab le

I

PO

PU

LAT

IOH

S IZ

ES

AN

D S

Ilvl I LAR

ITI E

S

OR

IGIN

AL

PU

BLIC

AT

ION

J OU

RN

AL

B E

HA

V I O

R

BA

N K

TO

TA

L4,243

,7

1

J

PR

OJ E

CT

SP

HA

S E

Sir''

PH

AS

ES

t^l ITH

20 OR

MO

RE

FR

EO

UE

NC

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i,

20 TO

29 FR

EO

S

5111,456

63

L3,gq126,678

4,180

2015

L,5A7

1,171

28,73414,t152

1,186

21

The second m

easured how closely the I ine blsects the varlance

of the frequencles lt represenfs. lf

compared the variance of the

frequencles abov€ the llne and the variance of the frequencies belon

the I lne, assuming that a representative

I ine would blsecf fhe varlance

of lts frequencies.

Straiqht Lines B

isectl no Frequencies

l-trw evenly do the tw

o stralghf lines, the least-squares llne

and the quarter-lntersect I ine, blsect the frequencies they represen*?

Figure 9 show

s that the least-squares line bisected all of the 20 or

more polnts ln a B

anked phase 29f, of the time, all

but one point 36tr

of the tlme, and all

but tvo polnts 19tr of the time.

This m

eans that

84fi of the time, the largest num

ber of polnts the least-squares line

did not blsect was tw

o. T

he quarter-intersect line dld this well 79tr

of the flme.

Further,

9t41 ot the time, the largest num

ber of points

the least-squares I lne dld g!

bisect was thrbe.

The quarter-intersect

line dld this wel I 91fi ot the tim

e.

Table 2 and F

lgure 9 show that the general pattern of goodness-

of-fit of these tw

o stralght lines for the Journal phases is similar

fo the Banked phases. F

or Journal phases with 20 or m

ore frequencies,

fhe least-squares llne blsected all but tw

o frequencies 85tr of the time,

while the quarter-lntersect did the sam

e 751 ol the time.

Table

2

Percent of C

elerating Phases inrtilhich Line B

isects All, A

ll but One,

or Al I but T

wo F

requencies

Least-Squa res

Li nesQ

uarter- I ntersectLines

Banked P

hases:

Journa I P

hases

Stralqht Lines B

isectinq Varlance

How

evenly does a stralght line bisect the range of the celeratlng

frequencies lt represents? Doas the varlance above the celeration

I ine

equal fhe variance below the celeraflon line?

Figure l0 show

s that for the Banked phases, the average up bounce or

varlance above the least-squares and quarter-lntersect stralghf I lnes w

as

about x2.5 (x2.4 and x2.5 respoctively), whlle the averag€ dow

o bounce or

variance below the sam

e sfraight lines was about i2.9 112.8 and 95.0

respectively). This m

eans that the highest frequency was usually 2.5 tlm

es

larger than the frequency esfimated by the strallht line, and that the low

est

frequency was usually 2.9 tim

es smaller than the frequency estlm

ated by the

straight line. T

hese data show that across all

phases, the average up

bounce was about equal to the average dow

n bounce, using elther the leasf-

squares or the quarfer-lntersect stralght line.

Flgure l0 also shous thaf the Journal phases produced resulls slm

llar

to the Banked phases, w

lth both the up bounce and the down bounce averaglng

x2.5 k2.6 and x2.3) and i2.5 (i2.4 and i2.6r, respectlvely 7efi

75fr

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does fhs varlance above fhe stralght llne compare to fhe

varlance below the stralght llne w

lthln each phase? Flgure ll

shows

fhe dls*rlbution of the relatlonshlp.befreen the up and down bounce

ylthln the same phase, for al I the B

anked phas€s. Thls relatlonshlp

averages 31.1, meanlng that on the av6rage, the dow

n bounce, the

lanlance below the best flt

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he

nearly'€qual up and down bounce of the Journal frequencles around

elther of the fwo best flt

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or non-skewed dlstrlbutlon of logged frequencles.

Surm

arv of Goodness of S

traloht Llne Flt

According to tw

o measures of goodness-of-flt, blsecting fre-

quencles and blsectlng varlance, the least-squares and quarfer-lntersect

sfralght llnes dld a good job of representlng Banked and Journal phases.

These stralght lines, flt

to logs of celoratlng human frequencles,

blsected at l6ast 90, of fhese frequencles 80i of *he time.

They

usually produc€d equal or non-skewed varlance around them

by bisectlng

the frequencies so that the varlance above the line approxlmafely

equalled the variance below fhe line.

The above data show

that the least-squares and quarter-intersect

stralght I lnes usual ly represent celeraflng

human frequencies accurately.

Further, these data apply only to about 1/5 of the hum

an frequency phases

wlth 20 or m

ore dafa poin*s thaf are changing 10tr or more w

eekly. T

he

other 2/3 of these phases change less fhan 10tr weekly. A

quarter-

lntersect strdlght ltne will atnost alw

ays blsect all the frequenciesin fhese statlc phases. T

herefore, yhen considerlng all hum

an

frequency phases of 20 or more frequencles, a s+

ralghf llne would

probabty produce goodness-of-fif percentages even hlgher than fhose

shown above.

Pro.lectlon

The least-squares and quarter-lntersect stralght llnes onlthe

Behavlor C

hart are representatlve ol Z

O to 29 hum

an frequencles celeratlng

af least lOi w

eekly. The variance around these llnes ls usually not

skewed. yiha+

happens to the varlance around these celeraflon I lnes

as behavlor changes frequency?

Chanqe in V

arlance around Sfraloht Line.eg F

requencles Celerate

Does the range of

human frequencles change as behavlor accelerafes

or decelerates? The range of the flrst

quarter was com

pared to *herange of the fourth quarter ln order to m

aximlze the size of the absolute

change. ln frequency. Flgure t2 show

s the dlstrlbutlon of these comparlsons.

For B

anked phases, the range of the fourth quarter usual ly equal led therange of fhe flrst quarter.

On the average, fhen, the range or total

bounce rernalned relatlvely constant as human frequencles celerated.

Flgure 12 also show

s that fhe Journal phases produced results

simllar to the B

anked phases. tlhlle the total bounce, or varlance,of celerating frequencles rem

ained relaflvely constant for the Banked

phases, the Journal phases showed only a sllght decrease ln varlance

from the flrst

to the fourth quarter, averaglng about il.4. C

ondlderlng

the relatlvely small num

ber of Journal phases and the slmllarlty of

distrlbution patterns b€tween the tw

o populations, both sourcesB

I

Behovior R

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Box 3351 K

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Konsos 66103

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of ce I erat i ng f requenc

i es.

This fact,

the additivity of variance in the logs of

celerating frequencies, means that

it is real istic

to base the size

or range of a projection envelope on the range of the m

easured

frequencies, since according to these data, the measured range

remains relatively

constanf for celerating frequencies.

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traiqht Line Pro.iections

Flow

accurate ly do the least-squares and quarter- i ntersect

stralght I ines project human behavior frequencies? F

or each,

:, -:

phase a projectlon envelope was developed, using the first

l0

to 14 frequencies to predict the next l0 to 14 frequencies.F

i gure 13 shows that the least-squares projection enve lope

contained 70fi gr more of the projected frequencies

42fi cf the time.

The quarter-intersect projecfion contained 7A

fi or more of the

fufure frequencies 38fr of the time.

About 21fi of the tim

e

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Figure 13 and T

able 3 show that the Journal phases produced

results I ike the B

anked phases, providing another measure of

simi ldrity betw

een Journal and Banked frequencies.

Table 3

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Frequenc i es are 7A

fi or more A

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Least-Squares

Proj ect

i onQ

uarter- I ntersect

Project

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Banked P

hases:

Journa I P

hases:

4zfr

47fr

31fr

47fr

Projecting only the next quarter, containlng f lve to seven

frequencies, improved the accuracy of both projection techniques.

Figure 14 and T

able 4 show that both projection techniques w

ere 70fi

or more accurate about 50fi of the tim

e (f rom 47 to

60fi of the time).

Both projection

techn iques were gO

fi or more accurate 25fr of the tim

e

for Banked phases and betw

een 33 and 40fi of the time for Journal

phases. Again, the data show

simi larity of results for B

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phases and for Journal phases.

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CH

AP

TE

R V

DIS

CU

SS

ION

The purpose of *his research w

as fo evaluate fhe baslc tool of

fhe Precise B

ehavior Managem

ent System

and Precision T

eaching, the Behavlor

Chart.

This tool w

as evaluated two w

ays. First, the goodness-of-flt

of straight celeration lines representing changing frequencies on the

Behavior C

hart was evaluafed. S

econd, the accuracy of stralght llne

projections of future frequencies on the Behavior C

hart was m

easured.

Tw

o sources provided the human frequencies upon w

hlch

stralght llne representatlon and projection accuracy w

ere measured.

One w

as fhe Behavior B

ank and the ofher, four popular Journals.T

ro technlques of flttlng stra.ight lines to celeratlng frequencles

and projecting future frequencies wer6 com

pared. One w

as the famlliar

and trel l-documenfed least-squares technlque, and the other w

as an easler

to use but less adequafely docum

ented method, the quarter-intersect

techn i que.

Sum

marv of R

esults

The resulfs clebrly show

ed that on the Behavlor C

hart, straight

lines adequately represent celerating frequencies. ln phases oi 2Q or

more frequencies celerating at leasf l0! w

eekly, ,a stralgh+

I ine bi'sects

al I but two of its frequencies about 80tr of the tim

e. T

he varlance

of frequencles around this sfraight line ls usually symetrical or non-

skewed. T

ha* Is, on the Behavlor C

hart tho up bounce usual ly equals

the down bounce. A

s frequencies celerate, their varlance or total

Least-Squares

Proj ect i on

Quarter-

I ntersectP

roj ect i on

Banked P

hases!

Journa I P

hases

53fi

60fr

47fr

47fi

Surm

ary of Pro.iection A

ccuracv

The least-squares envelope and the quarter-intersect envelope

projecfed future frequencies with sim

i lar accuracy. Developing the

projection envelope from the first

l0 to 14 frequencies,. these

techhlques pre<llcted 7O

i or more of th€ fu+

ure l0 to 14 frequencies about

4Ol of the flm

e. T

hey predicfed the future five to seven frequencies

about 50f of the time.

Projections of B

ankad frequencies were about

as accurate as projecflons of Journal frequencies.

31

t

bounce around this straight

I ine on the Behavior C

hart usual ly

remains relatively

constant. T

his means that the variance of

frequencies multipl ies, or is additive on the sem

i logarithmic B

ehavlor

Cha rt.

The results also show

ed that straight I ine projection envelopes

drawn on the B

ehavior Chart and based upon l0 to

14 frequencies contain

7|fi or more of the next five to seven frequencies about 50f, of the

time.

The projection envelope can eas i ly be draw

n on the Behavior

Chart,

because the techniques were not com

plicated with special

adjustment factors attem

pting to increase projection accuracy.

ln

other words, the m

ethods were kept as s im

p I e as poss i b I e. W

hether

or not the degree of accuracy demonstrated m

akes these projection

techniques useful remains to be show

n. C

ronbach clarified this

po i nt w

hen he sa i d:

Although w

e would like higher coefficients,

any positive correlation indicates that

predictions f rom the test w

ill be rnore

accurate than guesses. W

hether a val iditycoefficient

is high enough to warrant use

of the test as a predictor depends on suchpract i ca I

cons i derat i ons as the

u rgency ofthe im

proved pred i ct i on, the cost of testi ng,and the cost and val idity

of the selecfionm

ethods already in use. ..,1f

a criterioncan be predicted only

with validity

.20, thetest

may sti I I m

ake an appreciable practicalcontribution.

Natural ly a greater contribution

is reguired to justify an expensive, inconvenient

procedure than an i nexpens i ve one ( 1 960, pp.

115-ll6).

Prec i s i on T

each i ng has used the same strategy.

I nexpens i ve

and conven i ent stra i ght

I i ne project ion techn i ques are easy for

pract it ioners to use. W

hen more accurate projections "are needed, then

the projection techniques will

be refined. C

onsidering the fact that

the projection accuracy percentages dernonstrated apply only to dynamic

frequencies, frequencies celerating at teast lO

fi weekly, these straight

I ine projection techniques certainly provide an excel lent beginning for

accurate projections of hum

an growth.

Finally all

distributions w

ere almost identical for both the

least-squares and quarter-intersect techniques. S

ince it is easier

to draw the quarter- i ntersect I i ne than to

ca I cu I ate the I east-squares

equat lon of charted f requenc i es, and s i nce they produce near I y equa I

results, the quarter-intersect method is preferred, especially for

pract i t i oners. A

I though the Behav

i or Bank does not have enough

cases to com

puter-summ

a ri ze yet, f reehand lines of best f i t

drawn

by most chi ldren and teachers appears to be alm

ost as accurate as

the quarter- i ntersect I i ne.

Sim

i larities: R

eliabi ljtv, G

eneral ity, V

a I idity

The nearly identical data distributions of the B

ehavior Bank

and the Journals prove the functional or product simi larity

of these

two sources of

human behavioral inform

ation. T

his means that for

our practica I purposes, behavior projects recorded and deposited

directly in the B

ehavior Bank by chi ldren and teachers are as useful

and as product ive as those projects prof ess i ona.l I y recorded, summ

ar i zed,

edited and published in popular journals.

The sim

i larities betw

een fhe distributions from

the two data

sou rces used by th i s research have strong imp I icat ions

f or rna k i ng

9,

))I

,t

(

the collectlon of indivldual hum

an behavioral lnformation easier,

more sharing, and m

ore personally helpful. T

he future of education

and Precision T

eaching wlll

not be greatly affecfed by the labels

(rel labl I lfy, general lfy, or val idity) w

hlch are given to fhe

slmllarlties

shown by this research.

These futures can be changed

in important w

ays if fhe sim

ilarifies described in fhis paper are

found usefu I .

Functlonal V

a I iditv: U

sefulness

The m

osf senslble criterion for evaluating m

easures of and

technlques used with hum

an behavior is +heir usefulness.

Are they

usable by a large number of people? A

re *hey useful ln decision

maklng?

Do they help people? lt

ls against this crlterion, usefulness,

that the tools of Precision T

eaching, the Behavlor C

hart and straight

llne fittlng and predlctlng techniques, m

ust be evaluated. How

useful

are the flndlngs.reported in this research?

For fhe researcher planning to perform

parametric statistical

analysls on human frequency data, these results show

that the frequencies

must first

be logged. Logging frequencles increases the probabi I ily

that the researcherrs dafa will

meet tw

o of the requlrements of

parametric statlstical techniques: non-skew

od distributions, and

addltlvlty of variance.

'Stralght line descriptlons of celerating behavior are useful

to the Dracfltloner.

First, they provide a universal m

easure of

changlng behavior. S

econd, fhey make lt

easy to compare changing

behaViors of dlfferent form

, of dlfferent frequencies and covering

dlfferent perlods of time.

Third, straight llnes are easier than

curved I ines fo draw

, measure and com

pare. Therefore, younger, less

experlenced people can use *hem. A

lthough yet to be formally tested,

equal up and down bounce and a constant fofal bounce appear fo m

ake iteasier fo draw

freehand stralght lines simllar ln accuracy to least-

squares and quarter-lntersect stralght I ines.

Straight line proJecflons of behavior are useful.

For exam

ple,

they permit each indlvidual behaver to predict the date w

hen a

previously specifled goal will

be reached. The m

any uses of predictingindividual hum

an behavlor frequencies are only beglnning to be recognlzedby planners and decision m

akers.

Stralght I ine descriptions and projections of celerating behavior

are useful ln research design. For exanple, lf

ls no longer necessaryfo w

ait for a rstable basellner. T

he effects of procedures can bem

easured on celeratlng behaviors. 0r, by dividlng the daily recordingperlod into several parts and recording the behavior as [t occursin each perlod under dlfferenf conditlons, a dlrect com

parlson of theeffect of a treatm

ent or dlfferenf treatment procedures can be m

ade.

Thls m

eans that treatment can begin sooner. N

o longer must teachers

and parents, who have objected on m

oral grounds,be asked to delaytreatm

ent.

A R

econmendation

Wheh m

easurlng human T

requencles lf is to your advanfage to

log them. T

he Behavior C

hart performs thls transform

atlon for you.

You chart frequencies but your ey6s see the relatlonshlps --llnearlty,

synrmefry, and additivlty-- of *helr logs.

Seelng these relationships

will

help you to make m

ore accurate chart-based proJectlons and

33

(

declsions. U

sing the Behavior C

hart will

help advance the

deve I op i ng sc i ence of educat

i on .

Am

erican Society of M

echanical Engineers. A

merican standqr!- tim

e-series

char:ts (AS

A X

15.2). New

York, 1960.

Baer, D

. M.

A case

f or the selective reinforcement of punishm

ent.

ln C. N

euringer & J. L, M

ichael (Eds.), B

ehaviorm

odification

and cl inical psycholoqy. New

York: A

ppleton-Century-C

rofts,

1970,243-249.

Bates, D

. F.

School-w

ide im

plementation of precision teaching. U

npublished

doctoral dissertation, Unlversity of K

ansas, 1971.

Behaviour R

esearch and Therapv. N

ew Y

ork: Paragon P

ress, I963-1970, l-8.

Caldw

ell, T. E

. Com

parison of classroom m

easures: Percent, num

ber, and

rafe. U

npublished manuscript, U

niversity of Kansas, 1966.

Cronbach, L. J.

Essentlals of osycholoqical *estinq. N

ew Y

ork: Harper

& R

ow, 1960.

Diedrich, V

l. C

ountinq and chartlnq target ohonemes in conversafion.

t6rm color sound f i lm

, lGnsas C

lty, lGnsas: U

niversity of

lGnsas M

edical Center, S

peech and Hearing D

epartment, 1972.

Edw

ards, J. S.

Precisely teachlng children labled learning disabled.

Unpublished doctoral dissertation, U

nlverslty of Kansas, 1969.

Exceptional C

hi ldren. W

ashington: C

ounci I for Exceptional

Chl ldren,

1934 - 1970, !-31 ,

Ferguson, G

. A.

Sfafistlcal analvsls ln psycholoqy and education.

New

York: M

cGraw

-Hill,

1959.

Ferster, C

. 8., and Sklnner, B

. F.

Schedules of reinforcenent.

New

York: A

pplefon-Century-C

rofts, 1957.

Holzschuh, R

. D., and D

obbs, D.

Rate correct versus percenlage corect.

Unpublished m

anuscrlpt, Unlversity of K

ansas, 1966.

34))

)

(II

Johnson, N.

Acceleration of lnner-clty school pupilst reading perform

ances.

'Unpubllshed doctoral dlssertaflon, U

nlverslty of Kansas, 1971.

Jordon, J. B. &

Robblns, L. S

. (Eds.) Letrs lgy dolng sonethlnq else klnd

of thlnq. W

ashington: Councll for E

xceptional Chlldren, lgj7.

Journal of Applled B

ehavlor Analvsls.

Lawrence, K

ansas: Society for

the Experlm

ental Analysls of B

ehavior, lnc., l968-1970, L-3.Journal of the E

xperimental A

nalvsis of Behavlor. B

loomington, lndlana:

Soclety for the E

xperimenfal A

nalysis of Behavior, lnc., 1958-

t970, l-14.

Koenlg, C

, H. T

he behavior bank: Asystem

for sharing preclse lnformaflon.

TE

AC

HIN

G E

xceptlondl Children, lg7l, L

157.

Kyrklund, S

. J. A

year of school-wide preclslon teaching w

ith mentally

' retarded studetrts af Johnny A

ppleseed School. U

npublished

masferts fhesls, U

nlversity of Kansas, 1971.

Llndsley, Oi R

. O

perant condifionlng methods applied to research In

chronlc schlzophrenla. P

svchlatrlc Research R

eporfs, 1956,

I, ll8-t39.

LIndsley, 0. R.

Dlrect m

easurement

and prosthesis of retarded behavior.

Jgu rna I gf_ E{ucat i ory; 1964 , L

147 .

indsl"y, 0. R.

Procedures In com

mon descrlbed by a com

mon language.

ln C. N

euringer & J. L. M

ichael (Eds.),

Behavior m

odif ication

and cl inica I psvcholgqv. N

err, York: A

ppleton-Century-C

rof ts,,

1970a, 221-236.

Llndsley, O. R

. P

ersonal cornmunlcation,

1970b.

Llndsley, 0. R.

Chirr+

ing behavior: New

scast tiO.

t6nm color sound fllm

,

lGnsas C

lty, Kansas: F

l lm F

und, I970c.

Llndsley, 0. R.

From

Skinner to precislon teachlng: T

he chi ld knows

best. ln J. B

. Jordan & L. S

. Robblns (E

ds.), Letts fgdoinq som

ethlnq else kind of thlnq, Arllngfon, V

lrgtnla:

The C

ounci I for Exceptlonal C

hi ldren, 1972,

Mitchell, J. V

. Jr. E

ducatlonrs challenge to psychology: The predlcflon

of behavior fron person-envlronment lnteracflons. R

eview of

educational research, Washington: A

ER

A, 1967, Z

r 695-721,.N

EA

research bulletin. W

ashington:.Research

Dlvislon, N

EA

, t967, !2,70.P

recise behavlor f acJg. lG

nsas City: precision M

edla, 1971, 7l J.

Schm

id, C. F

. H

andbook of graphic presentafions. New

york: The R

onald

Press C

o., 1954.

Sidm

an, M.

Tactics of sclentiflc Ieseqtch-. N

ew york: B

asic Books, lnc.,

I 960.

Skinner, B

. F.

The behavior of orqanlsm

s. New

york: Appleton-C

entury-

Crofts,1958.

Slezak, S

. T

wo years of preclsely teachlng orthopedlcally

handlcapped

pupils. U

npubllshed nasterts thesls, Unlverslty of K

ansas,

1969.

Suchm

an, E. A

. E

valuative research. N

ew york: R

ussell Sage F

oundatlon,

1967.

TE

AC

HIN

G E

xceotlonal Children W

ashlngton: Councll for E

xceptional

Children, 1971, L

3,

Whelan, R

. J. T

he relevance of behavlor modlflcatlon procedures for

teachers of emotlonally disturbed chlldren.

ln p. Knoblock

(Ed.), lntervention approaches in educatinq enrotlonal lv

dlsturbed chlldren. S

yracuse: Syracuse U

nlverslty press, I966,

35-78.36

Ir,{

AP

PE

ND

IX A

Publ ished P

recision Teaching R

esources

Several publ ished w

ritten and audio-vlsual resources are avai lable

for fhe reader lnterested in learning more about P

recision Teaching.

A

few of the m

ost current are listed below.

Teachinq E

xceotional Children, V

ol 3, No. 5, M

ay 71 contains

twelve artlcles on P

recislon Teaching w

ritten by people ranglng from

a

klndergarten student to a professor of Education. lf

is available from

the Council for E

xceptlonal Children, 14ll S

Jeff Oavis H

ighway, S

uite

900, Arlington,

YA

22202.

Another publication available from

the Councll for E

xceptlonal

Chlldren at the sam

e address is titled Letrs T

rv Doinq S

omethinq E

lse

Klnd of Iti!S

, publlshed 1n 1972. lt contains nine artlcles about

Precision T

eaching whlch are a part of a report from

the lnvisible

College C

onference on the Application of B

ehavior Principles

in

Exceptlonal C

hi ld Education.

Precise B

ehavlor Facts confains tabular and graphic sum

maries of

the entire content of the Behavior B

ank through June of 1971. lnform

ation

and this publication may be obtalned from

Precision M

edia, Box 3222,

KC

, KS

.66105.

Tw

o l6rm color sound film

s about Precislon T

eaching and lts

appl icatlon are:

Chartlnq B

ehavior: New

scast r70

f rom: F

llm F

.undB

ox 5026K

C, K

S 66103

Chart i no and . C

ount i nq Tarqet P

lonemes i n C

onversat ion

from: D

r. W. D

iedrichS

peech and Hear i ng

Un i vers i ty of K

ansas Med i ca I C

enterK

C ,

KS

66105

Both f i lm

s are excel lent introductions to the uses of Precision

Teach i ng and the B

ehav i or C

hart.

$

,IiI

.' ,'l

I(

AP

PE

ND

IX

B

The B

ehavior Bank: A

System

for Sharing

Precise lnform

ation cA

RL K

otNtc

Carl K

oenig is the Director of S

ystems,

Behavior R

esearch Com

pany in Kansas C

ity,f(ansas.

I T

he Behavior B

ank, an international com

puter bank, contains information

on precise measurem

ent projects. Projects deposited are reported on five data

bank forms. T

he forms report: individuals involved in projects, behaviors re-

corded and their frequencies, situations in whidt proiects took place, im

prove-rnents in perform

ances, and procedures used in projects. T

he forms and B

ehaviorC

harts are deposited together. In reporting a project, behavers are identified bysocid security

numbers and/or their initials or full nam

es. If anonymity

is desired,arbitrary num

bers are used.

Over tr.,ooo projects are stored in the B

ank from the fields of education, psy-

chology, psychiatry, social w

ork, medicine, and nursing. (5o to 7tl percent of the

projects stored deal with special education).

The B

ank's following capabilities have value for all.

r.. The B

ank provides precise comm

unications benueen professionals

and

the parents and children they serve.z. T

he Bank stores any approach to im

proving human behavior, be it educa-

tional, operant conditioning, psychoptherapy, counseling, drug therapy, special

nursing, love, or prayer. The B

ank provides project managers w

ith data on thew

ide variety of procedures used in their field and their effectiveness.

3. The large file of basic obs€rvations provide detailed answ

ers to detailedquestions, elim

inating the need for generalizations. Thus, the predictive

narure

of the data stored can answer tom

orrow's questions from

yesterday's data.q. T

he Bank provides sum

maries of proiects

across children, schools, districts,and states. E

ach depositor can get a summ

ary of all of his own.

S. M

anagemerit team

mem

bers who deposit a project can becom

e eligible forcertification as qualified precise behavior m

anagers. In this way the B

ank pro-vides quality crcntrol of precise m

anagement

proccdures, and names and loca-

tions of trainers, advisors, and managers. T

hus, if you're interested in trainingand/or supervision, you can locate qualified personnel.

6. The B

ehavior Bank perm

its rapid storage and retrieval of information

about precise behavior managem

ent.

Banh projects provide a broad base on w

hich depositors can compare charts

for under $ro per child per year. Data can be deposited for less than $r.oo

per proiect. The B

ank does not sell access to its data, To share you m

ust contri-bute. T

hrough the Bank, teachers of today and tom

orrow can share their joys

of helping children grow.

To share in the B

ehavior Bank or to obtain further inform

ation, contact Carl

Koenig, B

ehavior Bank, B

ox 3rr3, Kansas C

ity, Kansas 66rq.

TE

AC

HIN

C E

xceptional Children

157

AP

PE

ND

IX C

ALP

HA

BE

TIC

AL LIS

T O

F P

ER

SO

NS

DE

PO

S

I T I N

G B

EH

AV

I O

R P

RO

J EC

TS

0ver the past f i ve years, these peop I e have contr I buted what

they have learned about human behavior and grow

th to the Behavior

Bank, T

ogether they have produced 13,941 behavior lmprovem

ent

projects. T

heir trust and sharing made thls research posslble.

Aqu i zdp, R

B

Calkin, A

Cauf [e ld,

HD

Condon,

BS

Cund itl ,

M

Cund llf ,

R

Dean,

D

De i tz,

SM

Duncan, A

Easton, E

N

Ed i nger, D

Freund,

J

Gaasholt,

MG

Gal low

ay, C

Hasterock, J

Haughton, E

Ho I zschuh,

RD

Houston,

S

Johnson, Ct

Johnson, Ni

Li nds ley, 0RL i pton,

M

Lov ltt, T

Marti n,

M

Morrow

, W

R

New

mark,

ZM

Pennypacker, H

S

Porter,

SA

Sharp, F

Skyper, G

Soko love,

H

Spang

I er, R

S

Starl in,

AS

tarl In, C

Tel lez,

Y

l,'laechter, M

Com

pi led by:

0R Li nds I ey

CH

Koen i g

JB N

icholD

B K

anterN

A Y

oung

Strafeg

I esS

ystem D

es i gn

Qua I i ty C

ontro I

Prograrrn i ng

Cod i ng

Reproduced from

: Teachino E

xceptional Children,

|,97 1,3,157.gl

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