Virues-Ortegaetal.2013.pdf

International Journal
of Clinical and Health

www.elsevier.es/ijchp

International Journal of Clinical and Health (2013) 13, 91−100

1697-2600/$ – see front matter © 2012 Asociación Española de Psicología Conductual. Published by Elsevier España, S.L. All rights reserved.

International Journal of
Clinical and Health

Publicación cuatrimestral / Four-monthly publication ISSN 1697-2600

Volumen 13, Número 2
Mayo – 2013

Volume 13, Number 2
May – 2013

Director / Editor:
Juan Carlos Sierra

Directores Asociados / Associate Editors:
Stephen N. Haynes
Michael W. Eysenck

Gualberto Buela-Casal

ORIGINAL ARTICLE

Prediction of treatment outcomes and longitudinal analysis in
children with autism undergoing intensive behavioral intervention

Javier Virues-Ortega*,a, Víctor Rodríguezb, C.T. Yua

aUniversity of Manitoba and St. Amant Research Centre, Canada
bFundación Planeta Imaginario, Spain

Received September 4, 2012; accepted March 18, 2013

*Corresponding author at: University of Manitoba, Department, P518 Duff Roblin Bldg., 190 Dysart Road,
MB R3T Winnipeg, Manitoba, Canada.
E-mail address: [email protected] (J. Virues-Ortega).

Abstract Outcome prediction is an important component of treatment planning and prognosis.
However, reliable predictors of intensive behavioral intervention (IBI) have not been clearly
established. IBI is an evidence-based approach to the systematic teaching of academic, social,
verbal, and daily living skills to individuals with autism spectrum disorder. Incorporating
longitudinal analysis to IBI outcome studies may help to identify outcome predictors of clinical
value. Twenty-four children with autism underwent on average two years of IBI and completed
language, daily living skills, cognitive, and motor assessments (Early Learning Accomplishment
Profile and the Learning Accomplishment Profile-Diagnostic, 3rd edition) every six months. We
used multilevel analysis to identify potential longitudinal predictors including gender, age,
intervention intensity, intervention duration, total intervention time, and pre-intervention
functioning. Results indicated that total intervention time, pre-intervention functioning, and
age caused the greatest increase in goodness-of-fit of the longitudinal multilevel models.
Longitudinal analysis is a promising analytical strategy to identify reliable predictors of the
clinical outcome of IBI.
© 2012 Asociación Española de Psicología Conductual. Published by Elsevier España, S.L.
All rights reserved.

KEYWORDS
Autism;
Predictors;
Applied behavior
analysis;
Quasi-experiment
(interrupted
time-series with
one group)

Resumen La predicción de resultados de tratamiento es un componente importante de la
planificación clínica. No obstante, no se han hallado predictores fiables de los efectos de la in-
tervención conductual intensiva en personas con trastorno del espectro autista. La incorpora-
ción de análisis longitudinales a la investigación sobre resultados de tratamiento en este área
puede contribuir a la identificación de predictores con valor clínico. En el presente estudio se
evaluaron las habilidades verbales, cognitivas y de la vida diaria (Early Learning Accomplish-
ment Profile y Learning Accomplishment Profile-Diagnostic, 3ª ed.) de 24 niños con trastorno del
espectro autista en un programa de intervención conductual intensiva. Las evaluaciones se rea-
lizaron cada seis meses y durante un periodo medio de intervención de dos años. Mediante

PALABRAS CLAVE
Autismo;
predictor
Análisis aplicado
de la conducta;
Cuasi-experimento
(serie temporal
interrumpida con
un grupo)

92 J. Virues-Ortega et al.

Autism spectrum disorder (ASD) is a pervasive developmental
disorder that affects 1 to 2.5% of children (Baio, 2012). A
number of comprehensive psychosocial interventions for
people with ASD have been developed for which preliminary
evidence exists. These include the Early Start Denver model
(ESDM, Dawson et al., 2010), the Treatment and Education
of Autistic and Related Communication Handicapped
Children (TEACCH, Welterlin, Turner-Brown, Harris, Mesibov,
& Delmolino, 2012), and intensive behavioral intervention
based on the UCLA Young Autism Project model and applied
behavior analysis (IBI, Lovaas, 1987). Although there is no
single approach to treatment for all individuals with ASD,
IBI based on applied behavior analysis is among the few
approaches to treatment that have been tested extensively
using clinical trial methodology (Rogers & Vismara, 2008;
Virués-Ortega, 2010; Wetherby & Woods, 2006).

Applied behavior analysis is devoted to the experimental
study of socially significant behavior as a function of
environmental and social variables, and is the branch of
experimental psychology that supports the conceptual
framework of IBI (Luiselli, Russo, Christian, & Wilczynski,
2008). IBI is a comprehensive and evidence-based approach
to the systematic teaching of behavioral, verbal, cognitive,
and social repertoires to individuals diagnosed with ASD
(Howlin, Magiati, & Charman, 2009). Treatment typically
involves over 20 weekly hours of one-to-one teaching
incorporating multiple learning trails and specific programs
for targeted behavioral goals. Teachers program hundreds
of learning trials per day featuring discrimination training,
prompting, generalization, and other reinforcement-based
procedures known to facilitate the acquisition of new skills
in individuals with and without disabilities (Miltenberger,
2011). The IBI curriculum integrates complex sequences of
programs from basic attending or vocalizing skills, up to
complex verbal, social, and problem-solving skills (Lovaas,
2002).

Over 20 independent trials have been conducted which
jointly suggest that IBI has moderate to large effects on
daily living skills, cognitive functioning, language, and
social behavior (Foxx, 2008; Remington et al., 2007; Virués-
Ortega, 2010). The field of IBI has shown a considerable
growth as suggested by the increasing number of service
providers and certified professionals (Shook & Johnston,
2011).

Parents of children undergoing IBI and other evidence-
based interventions frequently want to know whether their
child will be able to attend school without special support,
what areas of behavioral functioning – whether motor,
social or cognitive – are likely to improve as a consequence
of treatment, and what intervention intensity and duration

may be optimal for their child. Until recently, outcome
research had been of little assistance to respond to these
and other questions pertaining to the longitudinal
progression of children undergoing treatment.

While the evidence available strongly suggests that some
individuals benefit significantly from IBI and other
approaches to treatment, participant and intervention
characteristics associated with greater intervention effects
are not well understood. The wider literature of treatment
outcomes in ASD has examined a range of mediating and
moderating factors that could, potentially, be established
as clinically valuable predictors. These include pre-
intervention IQ, treatment duration and intensity, family
characteristics, age at intervention onset, social initiation
skills, and structural dismorphologies of the central nervous
system. The scant literature available on these factors
have been reviewed by Rogers and Vismara (2008) who
concluded that “The current intervention research focus on
main effects models provides little information about who
does well in which treatments and why” (pp. 28-29).

Age, pre-intervention functioning, and intervention
intensity have been examined in the narrower literature of
IBI outcome predictors. Studies that have examined the
role of age at the onset of IBI have shown that the earlier
the intervention, the greater the intervention effect. For
instance, Granpeesheh, Dixon, Tarbox, Kaplan, and Wilke
(2009) found that children below seven years at treatment
onset mastered more behavioral objectives every month
than children who started IBI intervention above that age.

The studies that have examined pre-intervention
functioning as a predictor of treatment outcome have not
always been consistent in their findings. Perry et al. (2008)
examined progress of children with ASD that received IBI
services by comparing standardized assessments at the
beginning and end of the service. Children were classified
as having either higher, intermediate, or lower functioning
at intake based on their Vineland Adaptive Behavior
Composite score. The higher functioning group made
substantial gains (∼20 IQ increments) relative to the other
two groups. By contrast, Ben-Itzchak, Lahat, Burgin, and
Zachor (2008) reported that pre-intervention IQ (normal,
borderline, low) did not predict the IQ gains after a year of
IBI in a group of 81 young children with ASD and
developmental disabilities.

More evidence has been accrued on the effects of
intervention intensity. However, findings remain
inconsistent. Taking IQ as a prototypical outcome (Table 1),
Makrygianni and Reed (2010) in a correlational study did
not find any effects of intensity – similar results were found
by Sheinkopf and Siegel (1998). Virués-Ortega (2010)

análisis multinivel se examinaron posibles predictores longitudinales incluyendo sexo, edad,
intensidad y duración de la intervención, tiempo total de intervención y nivel de funcionamien-
to previo a la intervención. Los resultados indicaron que el tiempo total de intervención, el
funcionamiento previo y la edad causaban los mayores incrementos en bondad de ajuste de los
modelos longitudinales. El análisis longitudinal es una estrategia analítica prometedora en la
identificación de predictores fiables de la efectividad de la intervención conductual intensiva.
© 2012 Asociación Española de Psicología Conductual. Publicado por Elsevier España, S.L.
Todos los derechos reservados.

Prediction of treatment outcomes and longitudinal analysis in children 93

reported no effects of intensity on IQ in a pooled analysis
of 19 experimental IBI studies. Finally, Reed, Osborne, and
Corness (2007) established a moderate effect of intensity
in a small trial on IBI using the Psychoeducational Profile as
outcome. In summary, treatment intensity has not been
established as a consistent predictor of IBI intervention
effects.

Longitudinal modeling of intervention outcomes may
help to establish intervention predictors more firmly than
traditional pre-post assessments. Longitudinal analyses
are able to fit the mathematical functions followed by
outcome trajectories of individual clients over a period of
time. By doing so longitudinal analysis maximizes the
statistical power of regression models aiming at meaningful
outcome predictors. For instance, if IBI effects were to
follow a non-linear progression, rather than a linear
trajectory, it may be possible to establish the role of a
particular predictor more accurately through longitudinal
multi-level analyses suited to specific non-linear
mathematical functions (Singer & Willett, 2003).
Furthermore, predictors identified based on time-series
spanning the treatment duration, as opposed to pre-post
assessments, may strengthen the clinical utility of the
predictor. For example, pre-intervention functioning could
be a strong predictor of treatment outcomes during the
first year of treatment, but not during the second.

IBI operates through a package of systematic teaching
strategies which are expected to provide the individual
with an increasing set of cognitive and behavioral resources
that will in turn offset, to various extents, the behavioral
excesses and deficits that are characteristic of ASD and
other developmental disabilities. Being a training-based
and goal-directed approach to intervention, IBI may lead to
some degree of behavioral gains for as long as the
intervention is in place. Longitudinal analysis of IBI may
help to identify distinct treatment gain itineraries across
subjects and tie those to specific predictors. For instance,
it may be possible that individuals starting at a higher pre-
intervention level of functioning benefit more from IBI but
reach an asymptote (ceiling) sooner than individuals that
start at a lower level of functioning. The longitudinal
predictors of IBI effects shall be greatly informative, albeit,
they have been rarely explored in the literature. There are
several longitudinal analyses that feature patterns of
change in individuals with ASD (Dietz, Swinkels, Buitelaar,
van Daalen & van Engeland, 2007; Jonsdottir et al., 2007;
Magiati, Moss, Charman, & Howlin, 2011). Nonetheless,
these analyses are constrained by the number of longitudinal

assessments (three or less); the number of treatment
outcomes (e.g., Dietz et al. only reported IQ); and the data
analysis strategy (e.g., no multilevel analyses).

This article describes growth patterns of motor, cognitive,
verbal, daily-living, and social skills in a sample of children
with ASD admitted into a home-based IBI program managed
by trained behavior analysts and delivering 20 to 40 weekly
hours of intervention. We used the children’s performance
in standardized assessments conducted periodically to
longitudinally create curves charting the rates and
asymptotes of various behavioral repertoires. Subsequent
analyses were conducted to test the impact of several
personal and intervention-related predictors on the
longitudinal growth of IBI outcomes. The present analysis
may help to enhance the prognostic information available
to families and clinicians by determining the extent to
which specific client- and treatment-related variables more
closely predict treatment outcome over the duration of the
intervention.

Method

Participants

Twenty-four children diagnosed with ASD (Age: Mean =
50.05 months, SD = 28.3; Gender: 21 boys and 3 girls)
admitted to the IBI program of Fundación Planeta
Imaginario (Barcelona, Spain) participated in the study.
An a priori power analysis indicated that a total sample
size of 15 was required to detect large effects (Cohen
effect size = 1). Therefore, our sample would suffice to
identify moderate to large effect sizes. A priori power
analysis assumptions were based on the pooled effect
size of 20 trials on IBI using IQ reported by Virués-Ortega
(2010) (Pooled effect size = 1.19). Participants were
recruited consecutively and were not excluded based on
their age or pre-intervention functioning at the time of
referral. All participants received a diagnosis of ASD from
an external medical consultant based on the diagnostic
criteria of the Diagnostic and Statistical Manual of Mental
Disorders, 4th edition text revised. Diagnosis was
supported by standardized assessments of autism
including either the Autism Diagnostic Interview-Revised
(ADI-R) or the Autism Diagnostic Observation Schedule-
Generic (ADOS-G) (Le Couteur, Haden, Hammal, &
McConachie, 2008). Further personal characteristics are
presented in Table 2.

Table 1 Effect of treatment intensity on IQ in intensive behavioral intervention outcome studies.

Study Sample Intensity range Analysis Effect
sizea (h/week) size

Makrygianni & Reed (2010) 86 15-30 Correlational (Pearson r) .22
Sheinkopf & Siegel (1998) 11 21-32 Correlational (Pearson r) −.06
Virués-Ortega (2010) 340 12-45 Meta-regression .01

Note. Effects reported as Cohen d effect sizes. a Sample size of the intervention group.
*All effect sizes were non-significant, p > .05.

94 J. Virues-Ortega et al.

Instruments

Fine and gross motor, cognitive, language, self-care and
social skills were assessed by means of the Early Learning
Accomplishment Profile (E-LAP; Glover, Priminger, &
Sanford, 1988; Peisner-Feinberg & Hardin, 2001) and the
Learning Accomplishment Profile-Diagnostic, 3rd edition,
(LAP-D; Hardin, Peisner-Feinberg, & Weeks, 2005). The
E-LAP and LAP-D scores are developmental age values
expressed in months. The score range is 0 to 36 for the
E-LAP and 36 to 72 for the LAP-D. If a participant achieved
the upper limit of the score range of E-LAP, the assessment
would be repeated with the LAP-D, which would then
continue to be used as the means of standardized assessment
every 6-month period until treatment was discontinued. In
order to control for potential ceiling effects in our data, if
a participant reached the LAP-D ceiling, assessment could
be repeated one additional time to inform maintenance
(provided that the individual would continue to receive
services through the program for the next six-month
period).

Both the E-LAP and the LAP-D have a high level of
inter-rater reliability, internal consistency, and
convergent validity with IQ (Fleming, 2000; Hardin et al.,
2005; Long, Blackman, Farrell, Smolkin, & Conaway,
2005; Peisner-Feinberg & Hardin, 2001). The test-retest
reliability of both instruments is reportedly excellent,
ranging between .93 and .99 (Peisner-Feinberg & Hardin,
2001, Hardin et al., 2005). Practice effects were unlikely,
as exposure to materials and tasks during the assessment
was minimal (few trials); and prompting, reinforcement,
and correction strategies were not present during the
assessment. The Spanish version of the E-LAP and the
LAP-D materials were used in the present study. The
LAP-D was validated in a representative sample of
Spanish-speaking children (Hardin et al., 2005). No
Spanish validation of the E-LAP is currently available.

Nonetheless, test scoring is performance-based – there
are no standard scores.

Both instruments have been used frequently as
standardized assessments in intervention studies with
individuals with ASD (e.g., Ganz, Simpson & Corbin-
Newsome, 2008). Moreover, the construct validity of E-LAP
and LAP-D is supported by items screening all diagnostic
areas of ASD (e.g., “initiates on play activities,” “responds
correctly when asked to show a toy,” “inflexible and rigid
in behavior”), items informing non-pathognomonic clinical
features of autism (e.g., motor functioning), and items
covering developmentally relevant skills (e.g., matching
skills). In summary, the E-LAP and LAP-D were considered
adequate for the present analysis due to their likely
resilience to practice effects; excellent stability; excellent
convergent validity with intellectual assessment measures;
and relevance to the clinical, adaptive, and behavioral
features of ASD.

Procedure

Participants were admitted consecutively to an IBI program
within the period May 2006 through January 2011. This
program was an official international replication site of the
UCLA Young Autism Project model and affiliated with the
Lovaas Institute (2011). At the onset of intervention,
participants received an average of 31.87 weekly hours (SD
= 10.11, range 15 -47.30) of home-based systematic
teaching following the UCLA young autism model of service
delivery and curriculum (Lovaas, 2002). Average treatment
duration was 21.87 months (SD = 14.38, range 5.33-58.57).
In keeping with all IBI bonafide programs, in addition to the
hours of formal intervention, incidental teaching and
practice goals were operating during most waking hours
(parents and caregivers acted as active co-therapists).
One-to-one teaching was delivered by trained tutors that
were supervised on a weekly basis by licensed psychologists

Table 2 Characteristics of the study sample.

Pre-test Post-test
(N=24) (N= 24)

Age in months, M±SD 51.91±27.31 69.46±27.26
Gender (male:female) 23:1
Ethnicity (% Caucasian) 100%
Social class,a % high 100%
IQ,b M±SD 74.50±13.98 91.50±16.86
Skills mastered in selected areas,c M±SD
Attending (max. 19) 13.04±4.34 19.16±3.05
Imitation (max. 27) 7.84±8.41 19.92±7.24
Matching (max. 13) 6.02±7.48 13.08±6.08
Basic labeling (max. 13) 12.44±5.33 31.21±19.88
Independent play (max. 15) 3.76±4.76 11.72±6.00
Interaction with peers/adults (max. 25) 2.28±3.82 11.60±9.06

Note. aEstimated by parental education and professional background. bWechsler Preschool and Primary Scale of Intelligence, 3rd ed.;
Bailey Scales of Infant Development, and Merrill-Palmer Scales of Mental Tests. cNumber of skills mastered by area (Lovaas Institute
Midwest, 2010).
M = mean; SD = stardard deviation.

Prediction of treatment outcomes and longitudinal analysis in children 95

with a background in behavior analysis. Parents received
weekly or bi-weekly progress updates, and supervision and
specific routines that required their involvement in order
to ensure the consistency of the interventions across
contexts and caregivers. Intervention was individualized
and comprehensive; and targeted motor, behavioral, daily-
living, verbal, cognitive, and social skills. Goals were
informed by a standardized curriculum composed of over
850 skills organized in 45 broad clinical areas (e.g., reading,
self-control skills). These goals are informed by
developmental sequences of typically developing children
(Luiselli et al., 2008) and include skills that are instrumental
for the acquisition of more complex repertoires (e.g.,
matching skills, imitation). Teaching sessions were delivered
via one-to-one teaching with gradual transition to group
activities and natural contexts. Transition to natural social
contexts was emphasized after mastery in one-to-one
teaching format. Decision-making in terms of hour allocation
and treatment discontinuation weighted a number of
factors including availability of school support, progress
achieved, family priorities, and treatment costs. Typically,
individuals that showed a persistent asymptote in their
learning achievements or that became independent at
school were assigned a reduced number of hours in
preparation of service discontinuation (for details on the

IBI curriculum see Lovaas, 2002). The current program was
in line with the guidelines for responsible conduct published
by the Behavior Analyst Certification Board (2010).

All participants underwent standardized assessments
with the E-LAP or the LAP-D prior to the intervention and
approximately every six months into the program (average
data points per participant 3.8, range 2-6). The selection,
administration, and correction of instruments followed the
guidelines by Jurado and Pueyo (2012).The research
assistants conducting the standardized assessments were
not involved in the administration of treatment and were
not familiar with the hypotheses of the study.

Data analysis

Figure 1 shows the individual growth trajectories of
participants for the eight E-LAP and LAP-D outcomes. Visual
inspection of the data plots over time suggests that
trajectories accelerated away from the start point shortly
after the intervention commenced while progression
decelerated as the individual approached a personal or
scale ceiling. Therefore, individual trajectories did not
follow a linear progression but rather an exponential
negative growth. Exponential negative trajectories are
composed formally of a negatively accelerated curve,

Figure 1 Trajectories of Early Learning Accomplishment Profile and Learning Accomplishment Profile-Diagnostic scores over time.
Fitted exponential negative curves (solid black line) were obtained for individuals above (dotted grey lines) and below (solid grey
lines) the median of pre-intervention functioning at baseline in each domain.

Gross Motor Fine Motor Pre-writing Cognitive

Receptive

80

80

60

60

40

40

20

20

0

0

0 20 40 60 0 20 40 60 0 20 40 60 0 20 40 60

Expressive Self-care Social

Intervention Time (Months)

Sc
al

e
sc

or
es

Sc
al

e
sc

or
es

96 J. Virues-Ortega et al.

ending in an upper asymptote. According to the formal
attributes of the data we selected a multilevel regression
model based on the following exponential negative
function:

Yij = αi – (αi – π0i) e –π TIMEij

Where αi represents the upper asymptote, π0i represents
the lower end of the trajectory, and π1i represents the
slope of the curve. Figure 2 illustrates different exponential
negative patterns of change over time for various parameter
values.

Multilevel models provide two distinct levels of analysis:
level-1 and level-2. The structural parts of the level-1
submodel contain two level-1 parameters and one within-
person variance component (εij). The first parameter, known
as intercept (π0i), represents the initial status of an
individual i in the population. The second parameter, known
as slope (π1i), represents the rate of change for the
individual i in the population by unit of time. Therefore,
level-1 establishes individual change overtime. By contrast,
the parameters at level-2 do not represent individual
variation, but average level of the outcome in the
population. Specifically, the parameters at level-2 represent
the average outcome level in the population corresponding
to the intercept and slope values at level-1. At level-2, the

pattern of change is not examined in terms of time, as is
the case at level-1, but rather, in terms of a predictor. In
summary, there are four parameters at level-2: γ00 is the
population average of level-1 intercept with level-2
predictor value of 0, γ01 is the population average difference
in level-1 intercept for a 1-unit variation in the predictor,
γ10 is the population average of the level-1 slope when the
predictor equals 0, and finally, γ11 is the population average
difference when the predictor equals 1. γ00 and γ10 are
baseline parameters while γ01 and γ11 estimate the association
of the predictor with the initial status and the rate of
change of the longitudinal progression, respectively. The
model also provides a residual variance value for the
intercept (σ02), the slope (σ12), and the covariance among
these two (σ01). For multilevel models incorporating two
predictors we will also report γ12 and γ12, which represents
the population’s average variation in the outcome level for
a one-unit increment in the predictors 1 and 2 (level-1),
respectively (for more details in multilevel analysis refer to
Singer & Willet, 2003). The estimation of the predictor
coefficients at level-2 is presented formally below:

π0i = ϒ00 + ϒ01 (PREDICTORi – PREDICTOR) + ξ0i
π0i = ϒ10 + ϒ11 (PREDICTORi – PREDICTOR) + ξ1i

According to this model, individual growth parameters
(π0i, π1i) across children will be a function of population
average values (γ00, γ10), and population variance components
(ξ0i, ξ1i) represented by residual variances (σ02, σ12) and
covariance (σ01).

We estimated a series of multilevel models using different
sets of predictors in order to select models that would
maximize goodness-of-fit for a given outcome when
compared with an unconditional baseline model (model
with no predictors). This was accomplished in two sequential
multilevel analyses. In the first sets of models we examined
the impact of time-based predictors (intervention duration
in weeks, total hours of intervention – weekly hours of
interventions multiplied by weeks of intervention – and age
in months). We would then select the model incorporating
the single time-based predictor with best goodness-of-fit
for each of the eight outcomes under analysis. Subsequently,
we calculated a new set of two-predictor models
incorporating the predictor previously selected and a
specific personal factor that, when added, resulted in
further increases in goodness-of-fit. The personal factors
examined for each of the eight outcomes were age (if not
selected in the preceding step), gender, and pre-intervention
functioning. Two levels of pre-intervention functioning
were established using the median value at baseline as cut-
off point. The rationale for selecting these predictors is
twofold: a) they are all common individual/treatment
characteristics readily accessible to the clinician, and b)
they have been examined in previous IBI studies although
not in the context of a longitudinal analysis. Longitudinal
predictors that changed overtime (intervention duration,
total intervention duration, age) were re-calculated each
time an individual was assessed.

The Akaike information criterion (AIC) and the Bayesian
information criterion (BIC) were computed as goodness-of-
fit parameters for all one- and two-predictor models. Lower
AIC and BIC values are indicative of better fitting. The best

100

75

50

25

0

E(Y)

Time

0 2 4 6 8 10

α = 100

π1 = .3

π1 = .2

π1 = .1

π0 = 15

Figure 2 Exponential patterns of change based on different
parameter values.

Prediction of treatment outcomes and longitudinal analysis in children 97

fitting two-predictor model was selected for each outcome
and was fully reported. All analyses were conducted with
STATA version 11 (STATA Corporation, College Station, TX)
and its GLAMM program for multi-level analysis. A .05 level
of significance was used …