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Baseline Measurement of Running Away among Youth in Foster Care

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Permanent Link: http://ufdc.ufl.edu/UFE0012781/00001

Material Information

Title: Baseline Measurement of Running Away among Youth in Foster Care
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0012781:00001

Permanent Link: http://ufdc.ufl.edu/UFE0012781/00001

Material Information

Title: Baseline Measurement of Running Away among Youth in Foster Care
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0012781:00001

Full Text












BASELINE MEASUREMENT OF RUNNING AWAY AMONG YOUTH IN
FOSTER CARE
















By

LUANNE R. WITHERUP


A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005
















TABLE OF CONTENTS


LIST OF FIGURES .............. .. .. .................. ........iii
ABSTRACT................................................ iv
INTRODUCTION ........................................... ...... ... ................ 1
Incidence of Running Away .............. ............................. .............. 1
Prior Research on Running Away ................................... ....... .............. 3
Purpose of the Current Investigation ......................................................... ... ....... 6
M ETH OD ................................................................. 8
Inclusion Criteria and Demographics ................................... 8
Data Collection........................................ ........8
Data Analysis.......... ....................... 9
Observer-Panel Evaluation ................................................... 12
Inter-Observer Agreement ........................................................ ......... .. ...... 14
RESULTS ........................................... .... .............. 16
Single-Subject Interval-Based M measures ............................................................ 16
Single-Subject Episode-Based M measures ............................................................... 18
Observer-Panel Single-Subject Evaluation................. ....................................... ...... 25
Group-Size Analysis ................... .................. .......... ......... .. ....... 27
DISCUSSION ................... ................... ............................................. 31
REFERENCES ........................................ 37
APPENDIX A SINGLE-SUBJECT INTERVAL-BASED MEASURES ............ 41
B SINGLE-SUBJECT EPISODE-BASED MEASURES ................ 58
C GROUP INTERVAL-BASED MEASURES................................ 75
B IO G R A PH ICA L SK ETCH ....................................................................... 82















LIST OF FIGURES

Figure page
1 Example single-subject interval-based measures (Finding 1) ............................ 20
2 Example single-subject interval-based measures (Finding 2) ............................ 21
3 Example single-subject interval-based measures (Finding 3) ............................ 22
4 Example single-subject interval-based measures (Finding 4) ............................ 23
5 Example single-subject episode-based measures........... ................................... 24
6 Observer evaluation- baseline acceptance .................................. 26
7 Observer evaluation- measure type................... ..... .................... 26
8 Example group interval-based measures .................................. 28
9 Observer evaluation- group-size analysis........................... .......... ................ 30
10 M ultiple-baseline designs ......................................................... 35
11 Single-subject interval-based measures ....................... ................................... 41
12 Single-subject episode-based measures ....................... ................................... 58
13 Group interval-based m easures................................ ....................... ....... 75















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

BASELINE MEASUREMENT OF RUNNING AWAY AMONG YOUTH IN
FOSTER CARE

By

Luanne R. Witherup

December 2005

Chair: Timothy R. Vollmer
Major Department: Psychology

The primary purpose of this study was to demonstrate the usefulness of several

different behavioral measures of running away by evaluating various measurable

dimensions of running away for a sample of children in foster care. Participants included

84 runaways residing in one service district of the Florida Department of Children and

Families (FDCF). All data were obtained from existing databases managed by FDCF.

Seven baseline measures were calculated for each runner including (a) the number of run

initiations, (b) the proportion of opportunity days in which the child initiated a run, (c)

the number of days the child spent on the run, (d) the proportion of opportunity days that

the child spent on the run, (e) the duration of successive run episodes, (f) successive

episode inter-response times and (g) successive initiation inter-response times. In

addition, an observer-panel evaluation was conducted to identify baselines that would be

suitable for treatment evaluations. A group-size analysis was conducted by aggregating

data from the original sample. Results demonstrate the usefulness of evaluating several









measurable dimensions of running away, and highlight the benefits of including

duration-based measures and correcting for opportunity. However, results suggest that

treatment evaluations may only be possible via an analysis of groups of runners rather

than individual subjects. Several conceptual implications related to the assessment and

treatment of runaway youth are discussed.















INTRODUCTION

Running away is possibly one of the most severe forms of problem behavior

exhibited by adolescents (Biehal & Wade, 1999). Results of various studies indicate that

children who run away from home are more likely than other children to abuse drugs

(e.g., de Man, 2000; Edelbrock, 1980; Kennedy, 1991; Koopman, Rosario, & Rotheram-

Borus, 1994; Yates, MacKenzie, Pennbridge, & Cohen, 1988), commit crimes (e.g.,

Abbey, Nicholas, & Bieber, 1997; Powers, Eckenrode, & Jaklitsch, 1990), engage in

prostitution (e.g., Cohen, MacKenzie, & Yates, 1991; Yates, MacKenzie, Pennbridge, &

Swofford, 1991), contract sexually transmitted diseases (e.g., Cohen et al., 1991; Yates et

al., 1991), attempt suicide (e.g., Kennedy, 1991; Powers et al., 1990), join street gangs

(e.g., Yoder, Whitbeck, & Hoyt, 2003), skip school (e.g., de Man, 2000; Sullivan &

Knutson, 2000), and drop out of school (e.g., Yates et al, 1988). Research also indicates

that runaways are likely to be physically and sexually victimized while on the run (e.g.,

Abbey et al, 1997; Hoyt, Ryan, & Cauce, 1999; Yates et al., 1991).

Incidence of Running Away

Given the serious risks listed above, several government reports and research

studies have attempted to estimate the incidence of running away among youth in our

society. A study by Hammer, Finkelhor, and Sedlak (2002) estimated that in 1999

approximately 1,682,900 children, representing approximately 2.6% of all youth in the

United States, either ran away from home or were forced out by their caretakers (U. S.

Bureau of the Census, 2000). Although this figure is most likely an overestimate of









running away due to the inclusion of children forced out by caregivers, difficulties in

discriminating between such children have been noted by the researchers attempting to

produce such estimates (e.g., Hammer et al., 2002).

Running away among foster children has received considerable attention in recent

years due to the heightened publicity surrounding children missing from substitute care.

Agencies responsible for the well being of these children must abide by policies and

procedures designed to accurately track the whereabouts of missing children (Florida

Statutes, 937.022, 2004). For this reason, state agencies often require foster parents to

abide by strict reporting procedures for missing children. For example, Florida foster

parents are required by state law to immediately report to the Florida Department of

Children and Families (FDCF) when a child has run away from their home (Florida

Administrative Code, 65C-13.010(4)(k)3, 2004). Due to these legal mandates, estimates

of running away among foster children are potentially more accurate than estimates of

running in the general population. Even so, considerable variability exists among

estimates of foster children who run from care (Kaplan, 2004). According to the

Department of Health and Human Services (2001), 9,112 foster children were on the run

as of September 30, 2001. This value represents approximately 2% of the children in

care on that date. The National Survey of Child and Adolescent Well-Being reported that

11% of 700 children in care for one year had attempted to run away (Department of

Health and Human Services, 2003). Even higher estimates were obtained by Fasulo,

Cross, Mosley, and Leavey (2002) during a study of 147 adolescents residing in

specialized foster care. Results indicated that 44% of the children ran away at least once

during their stay in care and 22% of the children ran permanently. However, the high









incidence of running found in that particular study may be due to the specific

characteristics of children in specialized foster care. Several studies have also examined

the extent to which children exit the child welfare system via a run episode. Such

estimates range from as low as 2% to as high as 21% (Courtney & Barth, 1996;

Department of Health and Human Services, 2001).

Prior Research on Running Away

A considerable number of research studies have focused on identifying risk

factors associated with an increased likelihood of running away. Unfortunately, a

cohesive literature base on risk factors for running away does not exist due to

considerable variability in definitions and measurement procedures. Although mixed

results are a frequent occurrence, some factors found to be associated with an increased

risk of running away include a history of maltreatment (e.g., Famularo, Kinscherff,

Fenton, & Bolduc, 1990; Yoder, Whitbeck, & Hoyt, 2001), increased age (e.g., Courtney

& Wong, 1996; Yoder et al., 2001), being female (e.g., Courtney & Wong, 1996; Fasulo

et al., 2002), placement instability (e.g., Abbey et al, 1997; Kashubeck, Pottebaum, &

Read, 1994), placement in a group home (e.g., Courtney & Wong, 1996), a prior history

of running (e.g., Kashubeck et al., 1994; Siegel & Callesen, 1993), drug and alcohol use

(e.g., de Man, 2000; Edelbrock, 1980), emotional problems (e.g., Cohen et al., 1991; de

Man, 2000), attempted suicide (e.g., Cohen et al., 1991; Edelbrock, 1980), academic

problems (e.g., Rogers, Segal, & Graham, 1994; Sullivan & Knutson, 2000), and truancy

(e.g., Sullivan & Knutson, 2000; Yates et al, 1988).

It is surprising to note that no investigations to date have attempted to obtain

repeated measures of running away for individual children. Rather, researchers generally









categorize children as either runaways or non-runaways but make no attempt to the track

the occurrence of run episodes on an individual or even a group basis. This is

unfortunate given that an effective behavioral analysis of running away necessitates the

use of repeated measurement in order to properly evaluate behavior change. For

example, if one were to evaluate the efficacy of an individual or large-scale behavioral

intervention for running away, some type of baseline measure would be required.

The lack of research on repeated measurement of running away might be

explained by considering the methodology commonly used by behavior analysts

attempting to assess and treat problem behavior. Specifically, direct observation and

repeated measurement of behavior-environment relations are standard components of

traditional behavioral assessment procedures. Typical child problem behavior such as

verbal and physical aggression, noncompliance, and tantruming are readily suited for

such assessment procedures due to their relatively high rate (e.g., multiple times per day

or hour) and overt nature. Conversely, running away is very low rate (e.g., once in a

lifetime or multiple times per year) and is often initiated covertly, which makes direct

observation unlikely and reduces the opportunity to obtain repeated measures.

Additionally, difficulties often arise when attempting to evaluate treatment effects for

low-rate problem behavior. Specifically, the ability to produce a convincing behavior

change upon the introduction of a treatment program is difficult when the baseline rate of

problem behavior is very low. Modification of traditional assessment procedures and

treatment evaluation methods may be required if behavior analysts plan to address this

socially significant problem behavior.









Researchers attempting to study low-rate and covert problem behavior have

employed several useful strategies to date. Application of these strategies to the study of

running away may be a first step toward filling the existing research void. For example,

researchers attempting to study covert problem behavior often make use of permanent

behavior products (e.g., Grace, Thompson, & Fisher, 1996) or other naturally occurring

records of behavior (e.g., McSweeny, 1978). A similar strategy may prove useful when

attempting to study running away. More specifically, it may be possible to obtain

missing child reports that are filed to law enforcement when a child runs away from

home. Although such a report is not a direct product of the run episode, it is a direct

product of the caregivers' response and is presumably at least correlated with an actual

run episode.

In cases where low-rate baselines make treatment evaluation difficult, one method

that researchers have found to be effective is to alter the unit of interest by evaluating

groups of individuals rather than individual subjects. For example, using both reversal

(ABA) and multiple-baseline designs, several researchers have demonstrated behavior

change across entire groups rather than for individual subjects. A study by Agras, Jacob,

and Lebedeck (1980) demonstrated the effectiveness of a community-wide water

conservation intervention by using a multiple-baseline-across-cities design. Similarly, a

study by Kirchner (1980) evaluated the effectiveness of a helicopter patrol program at

reducing residential burglaries using a multiple-baseline-across-neighborhoods design.

Multiple-baseline designs have also been used across classrooms (e.g., Switzer, Deal, &

Bailey, 1977), coal mines (Fox, Hopkins, & Anger, 1987), intersections (Van Houten &

Retting, 2001), and highways (Van Houten & Nau, 1981). Reversal designs have also









been used to demonstrate behavior change for groups of individuals. For example, a

study by Cope and Allred (1991) used a reversal design to demonstrate the effectiveness

of a community wide intervention to deter illegal parking.

When attempting to study low-rate problem behavior, the use of duration

measures is another possible strategy for evaluating potential treatment effects. At times,

a change in the duration of problem behavior may be clinically significant even when the

rate of behavior remains unchanged. In such cases, the use of duration measures may be

more clinically relevant than rate measures by providing a more descriptive account of

the problem at hand. This is clearly the case with the problem of running away given that

children may be exposed to serious risks with each day spent on the run (Biehal & Wade,

1999). Surprisingly, government issued reports and research studies often focus only on

the number of children on the run at a given time (e.g., Department of Health and Human

Services, 2001) or the number of run episodes occurring over a specified period of time

(e.g., Hammer et al., 2002). Little attention has been given to producing reliable

estimates of the total amount of time children spend on the run.

Purpose of the Current Investigation

The primary purpose of the study was to demonstrate the usefulness of several

different behavioral measures of running away by evaluating several measurable

dimensions of running away for a sample of children in foster care. To accomplish this,

naturally occurring behavior records in the form of missing child reports were obtained.

Although any child or adolescent who runs away should be eligible for assessment and

treatment at the clinical level, it is possible that many would have baselines insufficient to

demonstrate experimental control of treatment effects due to the relatively low rate of






7


behavior. Therefore, a secondary purpose of this study was to examine (a) the likelihood

of obtaining single-subject baselines suitable for treatment evaluations, and (b) the role of

group size on the suitability of baselines for treatment evaluation. To quantify baseline

suitability, a panel of observers was polled to evaluate the acceptability of individual and

group baselines on the assumption that the baselines would eventually be used to evaluate

the efficacy of a treatment. However, note that no treatment was actually evaluated as

part of this investigation.















METHOD

Inclusion Criteria and Demographics

Data for all runaway foster children residing in one FDCF service district as of

10/12/04 were considered for inclusion in this study. A runaway was defined as a child

who engaged in one or more run episodes between 9/1/01 and 10/12/04. This time

interval was deemed by FDCF personnel to represent the most reliable period of data

collection with respect to the accurate documentation of run episodes by children in

foster care due to the implementation of a data system in September of 2001. Based on

these criteria, 86 children were identified for inclusion. Two children were excluded

from the analysis due to missing or insufficient information. Of the 84 runaways

included in the analysis, 42 were female and 42 were male. The median age was 16 years

(range 10-17 years), the median number of run episodes was 2 (range 1-19 episodes), the

median number of days spent on the run was 10 (range 1-441 days), and the median

number of years spent in foster care was 2 (range 0.12-15.6 years).

Data Collection

Data were obtained from two databases managed by FDCF. Data on run episodes

were obtained from the Missing Child Tracking System (MCTS). This database records

the initiation and recovery dates of all run episodes based on missing child reports that

are filed to the Florida Department of Law Enforcement (FDLE). Data were obtained for

all episodes initiated between 9/1/01 and 10/12/04. Demographic information including

gender, age, and time spent in foster care was also obtained from the MCTS.









The MCTS database contained only some of the information needed to carry out

this investigation. Therefore a second database called HomeSafenet (HSn) was used to

obtain additional information. Specifically, placement history reports were obtained for

each child from HSn. Such histories contain the placement and removal dates for each

placement episode a child experiences while in foster care. These histories also include

information about placements at lockdown facilities such as juvenile detention.

Data Analysis

Interval-Based Measures

The four interval-based baseline measures, described below, were calculated for

each child across 30-day intervals beginning with the child's first day in care or 9/1/01,

whichever was later, and ending with the last completed interval expiring on or before

10/12/04. The average number of intervals evaluated for each child was 25 (range 1-37

intervals). At times, researchers or clinicians may wish to evaluate the effect of a

particular intervention on groups rather than individuals (e.g., multiple-baseline-across-

groups design). Therefore, 80 of the 84 runners were randomly selected for inclusion in a

group-size analysis. A parametric group size analysis was accomplished by constructing

31 groups as follows: 16 groups of 5, 8 groups of 10, 4 groups of 20, 2 groups of 40, and

1 group of 80. For each group, the average value of each measure below was calculated

across successive 30-day intervals. All measures were put into graphical form to allow

for easy visual inspection.

Number of run initiations

The number of run initiations the child engaged in during each successive 30-day

interval was calculated.









Proportion of opportunity days initiating a run

Due to the fact that run initiations cannot occur when a child is already on the run

or when they are placed in a lockdown facility, the preceding measure may not provide

an accurate account if the behavior is frequently prevented from occurring. This concern

is warranted given that all of the children included in this analysis spent at least one day

on the run and 40% of the children spent at least one day in a lockdown facility (median 0

days, range 0-876 days). Therefore, the number of opportunity days was calculated for

each 30-day interval. For this measure, an opportunity day was defined as any day not

spent entirely on the run or in a lockdown facility. Days in which a child spent only a

portion of the day on the run or in a lockdown facility were considered to be opportunity

days. Given that the number of opportunity days in each interval can fluctuate, the

proportion (rather than the number) of opportunity days in which the child initiated a run

episode was calculated for each successive 30-day interval.

Number of days spent on the run

Measures related to the occurrence of run initiations provide little information

about the total amount of time a child spends on the run. Therefore, the total number of

days spent on the run was calculated for each 30-day interval. Days in which a child

spent at least some portion of the day on the run were considered to be a day spent on the

run.

Proportion of opportunity days spent on the run

Due to the fact that there is no opportunity to be on the run while a child is placed

in a lockdown facility, the preceding measure may not provide an accurate account for

children who spend time in lockdown facilities. Therefore, the number of opportunity









days was calculated for each 30-day interval. For this measure, an opportunity day was

defined as any day not entirely spent in a lockdown facility. Days in which a child spent

only a portion of the day in a lockdown facility were considered to be opportunity days.

Given that the number of opportunity days in each interval can fluctuate, the proportion

(rather than the number) of opportunity days that the child spent on the run was

calculated for each successive 30-day interval.

Episode-Based Measures

The following baseline measures were calculated based on an analysis of each

child's run episodes. These measures were not subject to the group size analysis. All

measures were put into graphical form to allow for easy visual inspection.

Run durations

The duration of each run episode was calculated in days. Run episodes that were

in progress on the date of data collection were indicated as such when displayed

graphically. Therefore, minimum durations are depicted for such episodes rather than

actual durations (i.e., final durations are unknown).

Episode inter-response times

The time elapsing between the end of each run episode and the beginning of the

next episode was calculated in days. This measure was omitted for 29 children with only

one run episode.

Initiation inter-response times

The time elapsing between successive run initiations was calculated in days. This

measure was omitted for 29 children with only one run episode.









Observer-Panel Evaluation

In order to evaluate the acceptability of each baseline measure for use during

treatment evaluations, a panel of five observers was constructed to evaluate the data.

Observer panels of this sort have been used by prior researchers to assist with data

interpretation for various purposes (e.g., Hagopian, Fisher, Thompson, & Owen-

DeSchryver, 1997; Kahng et al., 1998). Both the single-subject and group data sets were

subjected to observer evaluation. Initiation inter-response time was the only measure not

subjected to observer evaluation given that the direction of behavior change associated

with improvement is ambiguous. For example, an improvement in the rate of running

would produce an increase in this measure, but an improvement in the duration of run

episodes would produce no change in this measure. So although this measure may

provide useful information about temporal patterning of run initiations, such a measure

would not be appropriate for experimental evaluations of behavior change.

Observer-Panel Selection

Five individuals were selected for the observer panel based on their expertise in

the field of Applied Behavior Analysis and their experience working with runaway foster

children. Specifically, all observers possessed a doctorate degree, were Board Certified

Behavior Analysts (BCBA), had at least one first-author publication in the Journal of

Applied Behavior Analysis (JABA), and had work experience involving runaway foster

children.

Observer-Panel Materials

Participation was requested from each observer selected and evaluation materials

were provided upon acceptance. Observers were allowed to complete the evaluation









independently and were asked return materials upon completion. In addition to a basic

description of each measure as described above in the Data Analysis section, observers

were provided with the following written instructions:

The field of Applied Behavior Analysis has traditionally focused on the
assessment and treatment of high rate problem behavior such as self-injury
or aggression, which can occur multiple times per minute. In contrast,
behavior such as rape, murder, suicide and running away from home can
be extremely low rate. For this reason, research-based treatment
evaluations of such behavior may prove difficult if adequate baseline
measures cannot be obtained. In order to assess this difficulty with respect
to running away from home, we have compiled several relevant baseline
measures using a sample of 84 foster children who have run away at least
once. The data have been presented in both single-subject and group
formats. You have been selected to evaluate these data based on both your
expertise in the field of Applied Behavior Analysis and your experience
working with children who run away. Please evaluate the following data
sets under the assumption that you are a behavior analyst planning to
evaluate an intervention designed to address running away among
children. The assumption is that all children who run away could receive
interventions, but only a portion of those would be eligible for a proper
experimental evaluation (e.g., a multiple-baseline evaluation). After
reviewing the descriptions for each section of graphs (below), circle all
graphs that you feel represent adequate baselines by which to evaluate the
intervention.

Graphs packets were organized by type of measure rather than by individual

runner or group of runners. For instance, each page included baselines of a single

type (e.g., number of run initiations) for several of the individual runners or

groups of runners. A total of 599 graphs were presented. Interval-based single-

subject measures were presented first (336 graphs), episode-based single-subject

measures second (139 graphs), and interval-based group measures third (124

graphs). Participant and group numbers were not included, however group sizes


were denoted next to each group baseline.









Observer-Panel Data Analysis

To evaluate the likelihood of baseline acceptance, the total number of baselines

designated as acceptable by a majority of the observer panel (i.e., at least 3 out of 5

observers) was calculated for each runner individually. Note that runners could attain a

maximum of six acceptable baselines (i.e., all measures except for initiation inter-

response times).

To evaluate possible differences in the likelihood of baseline acceptance based on

type of measure and group size, the average proportion of observer acceptance was

calculated for each interval-based and episode-based measure individually (excluding

initiation inter-response times). Episode inter-response times that were omitted for

runners with only one run episode were automatically designated as inadequate (i.e.,

proportion observer acceptance = 0). The proportion of observers designating the

baseline as acceptable was first calculated for each of the baseline graphs individually.

The average of these values was then calculated according to group size (interval-based

measures only) and type of measure (e.g., number run initiations, days spent on the run).

Inter-Observer Agreement

Inter-observer agreement with respect to the calculation of all baseline measures

was evaluated for 27 of the 84 children in this analysis (32%). A second observer

calculated both the interval and episode-based measures for each child. An exact

agreement measure was employed across all types of measures. For example, a

disagreement was scored if Observer A counted two run episodes in a given interval and

Observer B counted only one run episode. Average agreement was then calculated for

each type of measure by dividing the total number of agreements by the total number of









agreements plus disagreements, then dividing by 100. Average agreement across all

seven baseline measures was 99% (range 98% -100%).

Inter-observer agreement was also calculated with respect to ratings of

acceptability among the observer panel. A pairwise exact agreement comparison was

used to identify the extent to which each observer concurred with every other observer.

A total of 599 acceptability ratings were obtained for each observer. Individual pairwise

agreement scores were obtained by comparing each observer's ratings (i.e., acceptable or

not acceptable) with the ratings of each other observer (5 observers = 10 pairings). The

average pairwise agreement score across all 10 pairings was 81% (range 68% -90%). An

average pairwise agreement score was also obtained for each observer. For example, if

Observer 1 agreed with Observer 2 on 100% of the graphs rated, but agreed with the

remaining observers (i.e., 3, 4, and 5) on only 70% of graphs, the resulting average

pairwise agreement score for Observer 1 would be 77.5%. Average pairwise agreement

scores for the 5 observers were 72%, 82%, 82%, 84%, and 85%.















RESULTS

Single-Subject Interval-Based Measures

The utility of the four interval-based measures varied across children due to

differences in run and lockdown histories. However, four potentially useful findings

emerged when evaluating the measures obtained for individual children. Example

datasets highlighting each of these four findings are presented in Figures 1-4. Interval-

based measures for all 84 runners can be found in Appendix A. For Figures 1-4, each

row depicts all four interval-based measures for a given runner. All measures are

displayed across successive 30-day intervals along the x-axis. The number of data points

displayed for each child will vary based on the amount of time spent in foster care. The

first column depicts the number of run initiations, the second column depicts the

proportion of opportunity days in which the child initiated a run, the third column depicts

the number of days the child spent on the run (maximum 30 days), and the fourth column

depicts the proportion of opportunity days that the child spent on the run. Missing data

points (i.e., no data point between successive x-axis tick marks) will result for any

intervals containing no opportunity days. Y-axis scales were adjusted on an individual

basis to allow for proper analysis of trends. Baselines judged as acceptable for treatment

evaluation by a majority of the observer panel (i.e., at least 3 out of 5 observers) are

designated by light gray shading.

The first general finding that emerged from this analysis was that a majority of the

children engaged in very few run episodes of minimal duration (51% of children ran less









than 3 times and spent less than 16 days on the run). Figure 1 depicts the interval-based

measures for three such runners. With respect to behavioral trends, similar information is

provided across all four measures for these children. In addition, these baselines were

typically judged as unacceptable for treatment evaluation by the observer panel.

The second general finding was that baseline data for children with frequent run

initiations was often times variable or on a downward trend across all interval-based

measures. Figure 2 depicts the interval-based measures for three such runners. Data such

as these were also viewed as unacceptable for treatment evaluation.

The third finding that emerged concerns the utility of duration measures and

correcting for initiation opportunity. Given that children cannot initiate run episodes

while on the run, improvements in the rate of run initiations were often accompanied by

an increase in the amount of time spent on the run. In other words, spending time on the

run artificially suppressed the rate of run initiations for several runners. In general, the

utility of duration measures and correcting for initiation opportunity increased as time

spent on the run increased for a given runner. Figure 3 depicts the interval-based

measures for three runners who spent a substantial amount of time on the run (range 253-

437 days). The advantages of using duration measures and correcting for initiation

opportunity were apparent for these children. Note that although all runners showed a

recent decline in number of run initiations (column 1), it became clear that these declines

did not represent desirable outcomes once we corrected for initiation opportunity (column

2). Additionally, number of days spent on the run (column 3) and proportion of

opportunity days spent on the run (column 4) were both high and stable for these









children. In these cases, the duration measures were most informative given the

substantial amount of time these runners spent on the run, yielding high, stable, baselines.

The fourth general finding that emerged was the need to correct for opportunity to

run for children who spent time in lockdown facilities. More specifically, we noted that

when evaluating time spent on the run, the utility of correcting for opportunity increased

as time spent in lockdown increased. Figure 4 depicts the interval-based measures for

three runners who spent a substantial amount of time in lockdown facilities (range 229-

402 days). Note that although all runners showed a recent decline in the number of days

spent on the run (column 3), correcting for opportunity (column 4) indicates that these

were forced improvements due to time spent in lockdown.


Single-Subject Episode-Based Measures

The episode-based measures provided a different way to evaluate behavior

patterns by allowing for an explicit analysis of response duration and inter-response times

that was not possible using interval-based measures. However, we found that the

usefulness of such measures varied among children based on the total number of run

episodes. More specifically, an analysis of trend in run duration was only possible for

children engaging in two or more run episodes. Similarly, inter-response time trend

analyses were only possible for children engaging in three or more run episodes.

Figure 5 contains the episode-based measures for 5 of the 84 runners in this

analysis. Episode-based measures for all 84 runners can be found in Appendix B. Each

row depicts all three episode-based measures for a given runner. All measures are

displayed across successive run episodes along the x-axis. The number of data points

displayed for each child will vary based on the total number of run episodes. The first









column depicts the duration of each run episode in days, the second column depicts

successive episode inter-response times in days, and the third column depicts successive

initiation inter-response times in days. Y-axis scales were adjusted on an individual basis

to allow for proper analysis of trends. If a child was on the run as of the date of data

collection, the associated run duration is designated as being in progress (IP) and

represents only the minimum duration of the episode (i.e., final duration is unknown).

Inter-response time measures were omitted for children who engaged in only one run

episode. Baselines judged as acceptable for treatment evaluation by a majority of the

observer panel are designated by light gray shading.

Data for runners RI 1, R43, and R83 in the top three rows are typical for children

with few run episodes. Although data such as these provided limited information, it is

important to note that with respect to run duration limited information may still prove

useful. For example, the fact the runner R 11 only remained on the run for 2 days

suggests the possibility that she may be incapable of obtaining the basic needs required to

maintain long absences from care (i.e., food, shelter). Such information could have

important implications for treatment. Episode-based measures for children who engaged

in many run episodes were inherently more informative. For example, data for runners

R70 and R56 are much more descriptive due to the high number of run episodes.

In general, differences between episode inter-response time (column 2) and

initiation inter-response time (column 3) were observed for runners with relatively long

run episodes. For example, note the similarity in these two measures for runner R83 who

had a maximum run duration of 9 days. In contrast, these measures differed substantially

(note y-axes) for runner R56, who had a larger maximum run duration of 139 days.















# Run Initiations














]* pp ,, ,01 ,


Proportion Opp Days
Initiating Run
.04




.04-


____[


# Days on Run


Proportion Opp Days
Spent on Run

I A B


.2 -


-~~~~~iiiiiii A ~~~ ~


Successive 30-day


Intervals


Example single-subject interval-based measures (Finding 1). Each row represents data for one runner. Data for all 84
runners can be found in Appendix A.


Figure 1.


1,777 " "777 _7 7r",Vl












# Run Initiations



L owhu...i.40i0.44ioft


Proportion Opp Days
Initiating Run
.6







.15
151-


# Days on Run


15 -



4 -


1_L


Proportion Opp Days
Spent on Run

1 A z E


15-


.15-


Successive 30-day Intervals


Example single-subject interval-based measures (Finding 2). Each row represents data for one runner. Data for all 84
runners can be found in Appendix A.


Figure 2.













# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


30


WN .014,44000...


4


1.MAiW'i~~iiiii~~~~


30 1 -



an 1 vue FeHVA 1 I


2


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Successive 30-day Intervals


Example single-subject interval-based measures (Finding 3). Each row represents data for one runner. Data for all 84
runners can be found in Appendix A.


E R5


Figure 3.


.6


-~~~~~~~~~~~~~~yy --Y Y --------


AA AA












# Run Initiations
3


Proportion Opp Day!
Initiating Run


.15 -


5
# Days on Run
30 -


Proportion Opp Days
Spent on Run


Lf.


30 -

:. ,, ,, ,,, ,, ,


C0=1 .


Successive 30-day Intervals


Example single-subject interval-based measures (Finding 4). Each row represents data for one runner. Data for all 84
runners can be found in Appendix A.


Figure 4.


k









Run Durations


20 -



60


30


150- 60


:^,t. I I


150 L



150 R56

131aA4


Successive Run Episodes

Example single-subject episode-based measures. Each row depicts data for one runner. Data for all 84 runners can be
found in Appendix B.


60



10


Figure 5.





Episode IRTs


Initiation IRTs









Observer-Panel Single-Subject Evaluation

The shaded baselines contained in Figures 1-5 provide specific examples of

individual graphs judged as acceptable for treatment evaluations by a majority of the

observer panel. Additional data analyses were also conducted to answer specific

questions concerning the acceptability of baseline measures. One question of interest is

the likelihood that a given runner would have one or more baselines judged as acceptable.

Figure 6 depicts the percentage of runners attaining various degrees of baseline

acceptance. The number of baselines judged as acceptable by a majority of the observer

panel is displayed along the x-axis, with the percentage of runners along the y-axis.

Given that initiation inter-response time was not subjected to observer evaluation, a

maximum of six acceptable baselines was attainable. Results indicate that a large

percentage of runners (62%) had no baselines judged as acceptable according to the

majority criteria. The remaining 38% of the runners had at least one acceptable baseline

and none of the runners had all six baseline measures judged as acceptable.

A second question of interest is was whether the likelihood of baseline acceptance

would vary according to the type of baseline measure selected. Figure 7 depicts the

average proportion of observer acceptance for all six baseline measures. A majority

criterion was not employed, but rather the actual proportion of observers accepting each

baseline graph was determined and then the average of these values was calculated for

each type of measure. Recall that episode inter-response time baselines that were omitted

for children with only one run episode were automatically considered unacceptable.

Results for the interval-based measures (left side of graph) indicate that number of run

initiations was the least accepted type of baseline measure (0.17), followed by the










80% -
8b-



60% -


40% -


20%


62%


38%

26%
19%
14%
8%
0%


0 1 or> 2or> 3or> 4or> 5or>


# Acceptable Baselines


Observer evaluation- baseline acceptance. Baselines approved by a
majority of the observer panel were considered acceptable.


Observer evaluation- measure type. Average proportion observer
acceptance for all single-subject baseline measures


Figure 6.








O
C U

0Q
0 a.
M


0)


Figure 7.


O # Run Initiations
* Prop Opp Days Initiating Run

E # Days Spent on Run
M Prop Opp Days Spent on Run


* Episode Inter-Response Times

* Run Durations









proportion of opportunity days initiating a run (0.20), the number of days spent on the run

(0.23), and the proportion of opportunity days spent on the run (0.25). Therefore,

initiation measures (i.e., number of run initiations and proportion of opportunity days

initiating a run) were less accepted than duration measures (i.e., number of days spent on

the run and proportion of opportunity days spent on the run), and correcting for

opportunity increased average acceptance for both types of measures. Episode-based

measures are depicted on the right side of the graph. Episode inter-response times

attained an average acceptance similar to that of the interval-based measures (0.20), and

run durations attained the highest acceptance overall (0.30).

Group-Size Analysis

In general, the same considerations discussed previously regarding the utility of

correcting for opportunity and using duration measures apply to the group data sets. In

addition, the relative variability observed in the data for all measures was negatively

correlated with group size, in that smaller groups generally demonstrated more variability

than larger groups. This result was predictable given that the aggregation of single-

subject data will necessarily capture more behavior and reduce variability. Nonetheless,

this result is potentially informative because it suggests that studying runaway behavior

may be best accomplished using groups of runners.

Figure 8 contains the interval-based measures for 5 of the 31 groups constructed

for the group analysis (one group of each size is displayed). Data for all 31 groups can be

found in Appendix C. Each row depicts all four interval-based measures for a given

group of runners. The group average of each measure across successive 30-day intervals

is displayed on the y-axis. Although the number of intervals completed for each child












Avg. # Run Initiations

.4 -


Avg. Proportion Opp
Days Initiating Run

.06-


.1





.3-


1 -1





.6-




1M M


Avg. # Days on Run

6-


Avg. Proportion Opp
Days Spent on Run

.2G1-80





.2- G2-40





.2- G4-20

,,,,,,,, ^


6-


- ------------------ I ---r


30-day Intervals


Example group interval-based measures. Each row represents data for one group. Group sizes are in bold next to each
group number. Data for all 31 groups can be found in Appendix C.


Figure 8.


---------- 11111 1 1 iTrrrrrrrrri I I I I I I I


' ' ' ' ' '


G21-5
I G21-5 I









varied, the last interval for each group represents the last completed interval for all

children in the group. Baselines judged as acceptable for treatment evaluation by a

majority of the observer panel are designated by light gray shading.

Although the shaded graphs in Figure 8 provide examples of acceptable group

baselines, a more detailed parametric analysis of degree to which group size would

increase baseline acceptance was also conducted. Figure 9 depicts the average proportion

of observer acceptance according to both type of measure (legend) and group size (x-

axis). Single-subject results were included for comparison (interval-based measures

only).

Not surprisingly, results indicated that average acceptance increased as the size of

the group increased. In addition, consistent with the single-subject analysis, duration

measures fared better than or equal to initiation measures across all group sizes.

Although maximum acceptance was reached by group size 20 for duration measures,

initiation measures did not reach maximum acceptance until group size 80. One

unexpected finding is worth noting as well. Correcting for initiation opportunity (i.e.,

proportion of opportunity days initiating a run) did not produce any increases in

acceptance as was observed in the single-subject analysis. In fact, correcting for

initiation opportunity actually decreased acceptance for group sizes 5, 10, and 20.












1



> 0.8-
I-


co 0.6-
o0.




Wu -D-# Run Initiations
0)
-- *Prop Opp Days Initiating Run
-A--# Days Spent on Run A
-A- Prop Opp Days Spent on Run

0 1 1 I I
80 40 20 10 5 SS
Group Size

Figure 9. Observer evaluation- group-size analysis. Average proportion observer
acceptance is depicted according to both by group size (x-axis) and type of
measure (legend).















DISCUSSION

Given the lack of behavioral research targeted at the problem of running away,

even the most basic issue of measurement has yet to be thoroughly addressed.

Difficulties surrounding how and what to measure with respect to running away must be

resolved before more complex issues such as the identification of behavioral function can

be addressed. The current investigation demonstrated the usefulness of several different

behavioral measures of running away and examined their suitability for use during

treatment evaluation.

In general, results indicate that runaway behavior can be quantified along several

measurable dimensions, but that the usefulness of a particular type of measure will vary

across children. More specifically, the utility of using duration measures (in addition to

rate measures) and of correcting for opportunity was most apparent for children with

extensive run and lockdown histories. Similarly, episode-based measures including run

durations and inter-response times were more descriptive for children with a higher

number of run episodes. Results of the observer-panel evaluation suggest that single-

subject baselines may often be unacceptable for treatment evaluations, with 62% of

runners in this sample having no baseline measures viewed as acceptable. However,

results also indicate that using duration-based measures, correcting for opportunity, and

evaluating groups of runners may allow for successful treatment evaluations by capturing

the occurrence of more behavior and reducing variability in the data.









For the clinical assessment and treatment of running away, virtually all types of

baseline measures have the potential to provide useful information. Even baselines

similar to those in Figure 1, which were judged as unacceptable for use during treatment

evaluations, have the potential to provide extremely useful information when used in

conjunction with other assessment procedures. For example, assume that subsequent

assessment by a behavior analyst revealed that runner R28 (see Figure 1) was separated

from her siblings during the same interval containing her only run episode. This

information may lead to an effective preventive intervention based on the possibility that

separation from siblings serves as the primary establishing operation.

Although all baseline measures may prove informative in some respect, results of

this study highlight the need for both clinicians and researchers to carefully consider the

possible implications of the type of baseline measure they choose to use (or not use).

Arbitrary selection of a baseline measure could obscure pertinent information and

ultimately hinder treatment effectiveness or undermine the detection of important

treatment outcomes. Although the use of various types of baseline measures would

ensure the most thorough analysis possible in all cases, results of this study suggest that

certain types of measures may be especially useful for children with high run durations

and substantial lockdown histories. For example, the utility of duration measures was

apparent for children with lengthy run durations given that associated changes could not

be observed through the use of rate measures alone. This point is especially important for

agencies emphasizing recovery efforts for children already on the run, given that the

effect of such efforts may be reflected largely through the use of duration-based

measures.









Another consideration suggested by the results of this study is the need to correct

for a lack of opportunity when measuring running away. For example, certain

environmental circumstances may prevent the occurrence of run episodes (e.g., time

spent in lockdown facilities), and failure to correct for this lack of opportunity may

distort baseline data and alter interpretations regarding behavior change. The utility of

correcting for opportunity was most apparent for children with high run durations and

substantial lockdown histories. However, it is important to correct for opportunity in all

cases in order to ensure the most accurate account of each child's run history. Childcare

agencies should carefully consider the above implications when establishing data

collection requirements and performance standards related to runaways.

Based on the results of the observer-panel evaluation, treatment evaluation is

clearly an area in which both clinicians and researchers will face the most difficulties.

Specifically, the evaluation of treatment effects necessitates the use of individual

baselines that are capable of demonstrating convincing behavior change. This applies to

both clinical evaluations of single cases and research-based evaluations using multiple-

baseline designs. However, as results of this study suggest, such baseline measures may

be difficult or impossible to obtain for a majority of individual runaways. Therefore,

clinicians and researchers attempting to conduct treatment evaluations will face a difficult

challenge. One strategy suggested by the results of this study is the use of duration-based

measures (e.g., number of days spent on the run) rather than initiation-based measures

(e.g., number of run initiations). In the current study, duration-based measures were

more likely than initiation-based measures to be judged as acceptable for use during a

treatment evaluation. Results of the observer-panel evaluation also suggest that grouping









runaways in the context of single-subject methodology logic (i.e., multiple-baseline-

across-groups) may prove to be an effective strategy. Baseline acceptability in the

present study increased over that of single subjects for all group sizes, including as few as

five runaways per group. Using groups of 20 or greater may almost guarantee acceptable

baselines depending on the type of measure selected. These strategies will allow

behavioral researchers to conduct treatment evaluations for running away without

abandoning single-subject research design logic or being forced to rely on anecdotal

report of treatment effectiveness. Obviously, the use of reversal designs or intentional

baseline extensions during a multiple-baseline design would be too dangerous. Thus, the

use of naturally occurring baselines appears to be the most promising approach to

treatment evaluation. Figure 10 demonstrates how a multiple-baseline evaluation might

be conducted using either a single-subject or group format. Individual runners (left

column) or groups of runners (right column) with acceptable baselines were arbitrarily

selected for the purpose of this demonstration.

One limitation of the current study is that the reliability of the data contained in

the FDCF databases was not explicitly examined. Although reporting and data-entry

errors are almost inevitable, the rate and magnitude of such errors has not yet been

determined. Evaluations aimed at the identification and correction of such errors will be

necessary to ensure that FDCF databases are a reliable source of information. For

example, it may be possible to identify errors by cross checking multiple databases for

conflicting information or by comparing database records to a secondary source of

information such as foster parent report. The mechanisms needed to effectively carry out








Multiple Baseline Designs


Group


I R48 4 G5-201

|R31 G6-20


SR39 G7-20


Successive 30-day Intervals


Figure 10. Multiple-baseline designs across runners (left column) and groups (right
column). Runners and groups with acceptable baselines were selected for
the purpose of this demonstration.

such evaluations are not yet in place, therefore the retrospective nature of this analysis

made it difficult to assess database reliability.

The current investigation was also limited in scope, in that it focused solely on the

measurement of running away and did not directly evaluate any specific assessment or

treatment procedures. However, given the critical role of measurement in behavioral

methodology, this study was designed to serve as a catalyst for such endeavors. Future

research in this area should seek to develop and test behaviorally-based assessment and

treatment methods. Some investigations currently being conducted by our own research

team include (a) analysis of various foster child characteristics associated with running

away, (b) assessment of maintaining variables for running based on child and caregiver


Single-subject


[R16

-m


vll


'It"ic~

'l(lh~kl


'~Jd









verbal report and (c) assessment of run probability by placement type (e.g., group homes)

and individual caregiver (e.g., a particular foster caregiver).

Behavioral researchers should also begin to consider the issue of prevention when

attempting to address severe problem behavior such as running away. Given that even a

single episode of running away can pose serious risks (Biehal & Wade, 1999), the

prevention of running among children who do not yet exhibit such behavior is a top

priority (Kaplan, 2004). Unfortunately, traditional single-subject research methods are

not readily suited for an analysis of preventive interventions. Therefore behavioral

researchers will ultimately face yet another methodological challenge in their effort to

address this socially significant problem behavior.















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Biehal, N., & Wade, J. (1999). Taking a chance? The risks associated with going missing
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Cohen, E., MacKenzie, R. G., & Yates, G. L. (1991). HEADSS, a psychosocial risk
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Courtney, M. E., & Barth, R. P. (1996). Pathways of older adolescents out of foster care:
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Courtney, M. E., & Wong, Y.-L. I. (1996). Comparing the timing of exits from substitute
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de Man, A. F. (2000). Predictors of adolescent running away behavior. Social Behavior &
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# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


a-----------------------I-I -I I-


2-


---- -I

2-




2-

/-V% 04


.04 3




.04- 3




.3- 30-




.04 6-





1 30-




Successive 30-day Intervals


C

w
C-
n







cr
C
____ 0


Figure 11. Single-subject interval-based measures. Each row represents data for one runner.


. .i..








# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


l-J-h


Proportion Opp Days
Spent on Run


C- -- -- - -- .


~A44hA


30*


30


A0 i


**" i^ii ii ri

Successive 30-day Intervals


Figure 11. Continued


C---------------------------- --- 7


.041 6

A \\\||||||||||| *9 V V^^^^^^^^^









# Run Initiations
2


2 .. A .
2],


Proportion Opp Days
Initiating Run


Days on Run


A


Proportion Opp Days
Spent on Run


I I I I I I



]lm n.


.2 1


30-


----------- a ---------


-a-9


Successive 30-day


Intervals


Figure 11. Continued


------ ---- l M M -M


30


..i











# Run Initiations

2-


Proportion Opp Days
Initiating Run


.01-


Days on Run


Proportion Opp Days
Spent on Run


30-





3,


.1 4


-------------------------------i i i n l


10i





6

-- -- - -----


Successive 30-day Intervals

Figure 11. Continued


.1z









# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


.06.

LAAA.


30 -



30-

.. .. -- -


.15 30



.04 2



.6- 4
:^1~


Successive 30-day Intervals


Figure 11. Continued


.15 --


i hA


I ----~~~-~----rrrr---------7 77 77


I ------------------ 77777777=


:----------------------- -----------










# Run Initiations


a


aaa~


Proportion Opp Days
Initiating Run
.04-





.041


.04-





.04


------------------------------ --


# Days on Run


Proportion Opp Days
Spent on Run


I~I~I~I~I~I~I~I~I~I~I I-I-I-I-I


Ip.p.p.p.p-p-p.p.p.p.p.p.p.p.p.p.


.04



I ___IAW




*L A...........


Successive 30-day Intervals
Figure 11. Continued


C -------------------------------- T-1









# Run Initiations


Proportion Opp Days # Days on Run
Initiating Run


Proportion Opp Days
Spent on Run


.04-



.15,


.04] 6



.04- 3


___ -


/% A II


a --------------- -----------------


Successive 30-day Intervals


Figure 11. Continued


r- -- -- i Ai-i-iAi ------i~ i~



L ,,,,,,,A,


1'1'1'1'1'1 1~1~1~1~1~1~1~1~1~1~I


I --~---~----------------~---------- -


- I










# Run Initiations


Proportion Opp Days
Initiating Run
.04- 6


w__


# Days on Run


Proportion Opp Days
Spent on Run
.2-R36


- -


'.1I -30-


.04


X*-A64"


30-




2-


14


Successive 30-day Intervals


Figure 11. Continued


E ----------------------------- TrY7


I ----------------------------- r-7


1 n dh









# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


15


4


Pd


4-



30


.1 20-



Successive 30-day Intervals
Figure 11. Continued


4


2-
L~--~---~~--~--~---------- -- ----


.04-



.4



.04


1 R43

--------------


JL_


C-------------------- = 'T-------


1 -n-- -


II


L











# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run
15


------------------------- .-w~rr

6]




30


21




10-


Successive 30-day Intervals


Figure 11. Continued


------------------------------


.04-




.06-


*1111111111


ib


--------------------- ~--


' '


FL









# Run Initiations


r


Proportion Opp Days
Initiating Run
.04-




.04-




.04-


]ml.;mlml:l.mlmm~m.mm:.mmT1


# Days on Run


Proportion Opp Days
Spent on Run


.06


1111


30- I *

:J7 ....
1 1 1 1 i1i1i i i i1*i ~~~~~


.06- 10 -




Successive 30-day Intervals

Figure 11. Continued


2


n -------------------


C----------------------------------- 1


:----------------------------------- 1


~-------------------


i _r









# Run Initiations

3-


t:.AAfl..A,


Proportion Opp Days
Initiating Run


A 1 1 1 1 1 1 1 1 1


# Days on Run


Proportion Opp Days
Spent on Run


30-


I------------------ --------


2 .1


-W------I-- 0-2 --


I .........----


2-


Successive 30-day Intervals


Figure 11. Continued


*ftttMMMMWMMMMM~f -----


M @ -----









# Run Initiations

2-


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


.06-


10 I .3


i i i .-


30


tJ, ,Z1-1,,.,,l


.p p181p181p1p181p1p1p p


C --------------A------------ 7


Successive 30-day Intervals


Figure 11. Continued


4-


.04-

A iio~~ i^ ii^


1M l


.04 R64




15 -R


2 -


-A










# Run Initiations


Proportion Opp Days
Initiating Run
.04-


.06-




.041


# Days on Run


3




30




10 -


Proportion Opp Days
Spent on Run

.1-


.15w


30-


1 __tti~ti~~llf-tl..I W


-. +r


Successive 30-day Intervals


Figure 11. Continued


~---------------~ ~---------


R70
I R70 I


4-


.Www









# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run
61 *


I1t 1$ I1 a1*t1 1


LY-MnY-un-Y--Y-~


3-L


:, A.,


4A,


.04




.06.




.06 -




1


't~fiiiiiiii


2 -


-PONMM MIM No_


2.


'-TT*r


.06


AT*T


10




30


R73


flr-1flrI


.3


R74A


i


1 h
^ W--F p R5


Successive 30-day Intervals


Figure 11. Continued


AVAVAVAVAkM 111


10101010


I I









# Run Initiations


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


.06-


I. I I 1* 1 1


10-


20I I *
20, -


2


I


Successive 30-day Intervals


Figure 11. Continued


NI


.04-

.-- A *ii6i ili 16i AAi A6i16i














# Run Initiations

2-




2-1


Proportion Opp Days
Initiating Run


# Days on Run


Proportion Opp Days
Spent on Run


30 .041




2-1 .04-1


.1 -

.04 1


15




6-


------- A ---------


Successive 30-day Intervals


Figure 11. Continued


:------------- -V- ------------------









Run Durations


Episode IRTs


Initiation IRTs


100

00


400


S1300-


I I I


~R2~




Mj
m

R3 w
--^ sm


m/ r


150 150


I I


.ei.*


150


Successive Run Episodes


Figure 12. Single-subject episode-based measures. Each row represents data for one runner.


/%-A








Run Durations


Episode IRTs


Initiation IRTs


150


I II I I I- -I


Successive Run Episodes


Figure 12. Continued


15



6-



100


L,


150-

1111


10


I l l








Run Durations


401 30-

1 1 1 / ,


I I I


Successive Run Episodes
Figure 12. Continued


C/


Episode IRTs


Initiation IRTs








Run Durations
IP


Episode IRTs


Initiation IRTs


150


60


150


I


Successive Run Episodes


Figure 12. Continued


10-


vI.I


- I


Z:/-











Run Durations


300


300-


-I-


Successive Run Episodes
Figure 12. Continued


100


1~


IRfl


__


_ _


,--r


Episode IRTs


Initiation IRTs









Run Durations


Episode IRTs


Initiation IRTs


15 100


:v^_-. *I


I I I a 6-


Successive Run Episodes


Figure 12. Continued


100


---













Run Durations


200 60





21


Episode IRTs


Initiation IRTs


15





63





3-


200 200





60- 1 60,-1


Successive Run Episodes


Figure 12. Continued










Run Durations


Episode IRTs


Initiation IRTs


10





200





100





2-

1* I


400- 400-



1\11


150





200 1


150





200 R401


Successive Run Episodes


Figure 12. Continued





wl










Run Durations


10 100





41


20- 100 150





Successive Run Episodes

Figure 12. Continued


100-


*^-A^


IP
I I





I I


Episode IRTs


Initiation IRTs










Run Durations

3 60-





6,


Episode IRTs


Initiation IRTs

60R

I .,A.


10


-e


Successive Run Episodes

Figure 12. Continued


300-





2





10









Run Durations


300


Successive Run Episodes


Figure 12. Continued


Episode IRTs


Initiation IRTs









Run Durations


Episode IRTs


Initiation IRTs


150 60 150 R56
T*Torol


30j


20-




2-1


200.


100 I p

] 4,k


600 *


Successive Run Episodes


Figure 12. Continued








Run Durations


Episode IRTs


Initiation IRTs


200-


Successive Run Episodes


Figure 12. Continued


300-


1


.,. _.


MW .









Run Durations


Episode IRTs


400 -


Initiation IRTs


400-


iJII


10 -



2-II I
30 150


30- 150 150




Successive Run Episodes


Figure 12. Continued


60


1


I ~A









Run Durations


Episode IRTs


Initiation IRTs


30


300


11111


Successive Run Episodes


Figure 12. Continued


10




200




1001









Run Durations


10


20 100 -




3




2


150-


A


Successive Run Episodes

Figure 12. Continued





Episode IRTs


Initiation IRTs


150













Run Durations

300
'P "y


10


61


Episode IRTs


150


Initiation IRTs


200.


60




100


Successive Run Episodes
Figure 12. Continued









Avg. # Run Initiations
.4



.6



.6
-4 : ^JW
IMMfinniwffiiiitiii


Avg. Proportion Opp
Days Initiating Run
.06 -



.1 -

:--------

.1 L







.15


Avg. # Days on Run
6



6



6



6



6
'Lrf^P



'LnSfL


Avg. Proportion Opp
Days Spent on Run
.2 jG1-80



2 2-40


.3 -G5-20

AA L lrr rrrrr


30-day Intervals

Figure 13. Group interval -based measures. Each row represents data for one group. Group sizes are in bold next to each group
number.


l~ulL$p~tr










Avg. # Run Initiations


Avg. Proportion Opp
Days Initiating Run
.1-




.1 -


.15




.04-


Avg. # Days on Run


Avg. Proportion Opp
Days Spent on Run


10 -


*_^wm


N,,,,,


30-day Intervals

Figure 13. Continued


e 7n -- # 0%


__YY


1-----------


-1AVA#%"MqA4%rr r rrNA-mFI


,rry


GG-20
I G6-20 I


rl rrr8lmi


Lffirz 11 11M 1 Vri









Avg. # Run Initiations

1 M



1*


Avg. Proportion Opp
Days Initiating Run


Avg. # Days on Run


Avg. Proportion Opp
Days Spent on Run
.4- I--


.1 6


1.jA


30-day Intervals
Figure 13. Continued










Avg. # Run Initiations

1 -




1.5




1.5,


Avg. Proportion Opp
Days Initiating Run


Avg. # Days on Run


Avg. Proportion Opp
Days Spent on Run
.6- G16-5




.4 11-5


.3- G19-5
Gm:


j G2-5


30-day Intervals

Figure 13. Continued


I G8J









Avg. # Run Initiations


Avg. Proportion Opp
Days Initiating Run
.3-




)6-1

.: ^


Avg. # Days on Run


.15-


Avg. Proportion Opp
Days Spent on Run
.3G21-5



.4- G22-5








.3G24-5




.41 1 G25-5


LTt


30-day Intervals
Figure 13. Continued


~121








Avg. Proportion
Avg. # Run Initiations ODD Das Initiatinq
Opp Days Initiatinci


1 ]
1 ...... .











1-


Avg. # Days on Run


.03-


w-----------


Avg. Proportion
ODD Days Spent on
.3G26-5



.6 G27-5


.15- 15

*i----------------iiiiA A ^ ~ i


30-day Intervals
Figure 13. Continued


i ~hh













Avg. # Run Initiations

2


Avg. Proportion Opp
Days Initiating Run


Avg. # Days on Run


Avg. Proportion Opp
Days Spent on Run

1 t G31-5


30-day Intervals

Figure 13. Continued















BIOGRAPHICAL SKETCH

Luanne Witherup graduated from the University of Florida in 2001 with a B. S. in

psychology and a minor in business administration. Following graduation, she became

employed as a Behavior Analyst/Research Assistant for the University of Florida

Behavior Analysis Services Program (BASP). BASP provides services to foster children

and foster families throughout the state of Florida and is sponsored by the Florida

Department of Children and Families. Ms. Witherup began her graduate studies at the

University of Florida in 2002 and is currently pursuing a doctorate degree in psychology

with a specialization in applied behavior analysis. Her primary research interests involve

the development of assessment and treatment methodologies for runaway foster children.