行政院國家科學委員會專題研究計畫 成果報告
一種對個案實驗研究的統合分析方法:超過基線中數率
計畫類別: 個別型計畫 計畫編號: NSC91-2413-H-004-003- 執行期間: 91 年 08 月 01 日至 92 年 10 月 31 日 執行單位: 國立政治大學教育學系 計畫主持人: 馬信行 計畫參與人員: 高玉靜、陳亮君、蔡秉昆 報告類型: 精簡報告 處理方式: 本計畫可公開查詢中 華 民 國 92 年 10 月 28 日
An alternative method for quantitative synthesis of
single-subject researches: Percentage of data points
exceeding the median of preceding baseline phase (PEM)
Hsen-hsing Ma1
Department of Education, National Chengchi University, Taiwan.
Abstract
The purpose of the present study is twofold: (a) to compare the validation of
percentage of non-overlapping data (PND) approach and percentage of data points
exceeding the median of baseline phase (PEM) approach, the latter having only a
slight difference from the PND approach, and (b) to demonstrate application of the
PEM approach in conducting a quantitative synthesis of single-subject researches
investigating the effectiveness of self-control in the field of applied behavior analysis.
The results show that PEM is a more appropriate method of meta-analysis for
single-subject research and self-control training had significant effect on academic as
well as social behavior. It is hoped that the PEM approach can be accepted for use in
the quantitative synthesis of single-subject research in order that the results of
empirical research of single-subject studies can be more readily consolidated as part
An alternative method for quantitative synthesis of
single-subject researches: Percentage of data points
exceeding the median of preceding baseline phase (PEM)
The purpose of the present study is twofold: (a) to compare the validation of
percentage of non-overlapping data (PND) approach (Mastropieri and Scruggs,
1985-86) and percentage of data points exceeding the median of baseline phase (PEM)
approach, the latter having only a slight difference from the PND approach, and (b) to
demonstrate application of the PEM approach in conducting a quantitative synthesis
of single-subject researches investigating the effectiveness of self-control in the field
of applied behavior analysis. In the present study, single-subject research,
intra-subject design and single-case experimental design are synonymous.
In between group research, many meta-analyses have been conducted to draw
conclusion about the overall effectiveness of interventions. Lipsey & Wilson (1993)
had categorized and listed the effect sizes calculated by researchers in the field of
psychology and education. But for the single-subject experimental researches, such
work is just beginning. Researchers are at present searching for an acceptable
statistical methodology to calculate the effect size of treatment of single-case
Researchers have proposed parametric statistics for this purpose. For example, Center,
Skika, and Casey (1985-86) proposed a piecewise regression model. Kromrey and
Foster-Johnson (1996) suggested formulas for calculating effect size associated with
hanges in level of behavior (mean shift), changes in variance, changes in trend, and
changes in level when the data show trends. Swanson & Sachse-Lee (2000) regarded
effect size as the difference between the mean scores of the baseline (last three
sessions) and treatment phases (last three sessions) divided by the pooled standard
deviation (last three sessions of baseline and treatment). These methodologies are
carried over from conventional between-group research and would not necessarily be
appropriate for single-subject studies. The data in intra-subject research possess a
characteristic that might violate the assumptions of parametric statistics — serial
dependency of data in a phase of single-case experimental designs. Further, in
addition to normality of distribution and homogeneity of variances, a more important
assumption of parametric statistics is the independence of observations. In the case of
successive measurements over time in intra-subject designs, the assumption of
independence of observations is not usually met. (Hersen & Barlow, 1976, p. 272).
Parametric statistics, such as general linear models, are not robust with respect to
violation of the assumption of independence. Owing to serial dependency the
would then inflate the significance of the effect size. The effect size associated with
mean shift obtained by Kromrey & Foster-Johnson (1996,p.80) was –7.92. This
magnitude would probably be treated by Cohen (1977, p.24-27), who considered an
effect size of 0.2 as small, 0.5 as medium, and 0.8 as large, as an outlier.
Ferron & Sentovich (2002) estimated the statistical power of three randomization
tests for multiple-baseline designs: (a) Wampold and Worsham (1986) based their
method on the random assignment of subjects to baselines. However, in practice
subjects are not assigned randomly but usually assigned according to the seriousness
of the problem behavior, the subject with the most serious problem was assigned first
to the treatment, (b) the method presented by Marascuilo & Buck (1988) was based
on the random assignment of the start of the intervention for each of the subjects. On
the contrary, the number of observations in the baseline phase are not customarily
determined by randomization, but by the stability of the observations. The treatment
phase would begin only after the observations in the baseline phase are stable, i.e.,
there is no obvious trend, and (c) Koehler, &Levin (1998) merely combined the
elements from each of the preceding two methods, and they assigned the start of the
intervention and subjects randomly to baselines. Their method was also at odds with
standard practice. If the random assignment was delayed until after the baselines had
randomization would be breached.
Consequently it is not appropriate to apply any of theses three randomizations tests
to the calculation of effect size for intra-subject experimental designs.
If all the data points in the treatment phase of a single-case experimental design
exceed the data points of the previous baseline phase, then it will hardly be necessary
to use a statistical tool to judge the effectiveness of a treatment. But, as found by Ma
(1979), there is only about one third of a chance that a treatment phase has
non-overlapping data. Ma computed the percentage of non-overlapping treatment
phases from The Journal of Applied Behavior Analysis (1968-76), Journal of
Behavior Therapy and Experimental Psychiatry (1970-76), Behavior Therapy (1970-76) and Behavior, Research and Therapy (1970-76), and obtained yearly
average of 32.5% of non-overlapping, with a range from 25.6% to 39.7%, and
SD=4.32%.
The small number of data points in the phases of single-subject research would
preclude the application of an ARIMA (autoregressive integrated moving average)
model to the analysis of trend- or level-changes between baseline and treatment
phases. In order to correctly identify an ARIMA model in a time series, one needs at
least 50 observations. A model identified with less than 20 data points would be
less than 20.
Mastropieri and Scruggs (1985-86) took a nonparametric approach to synthesize
the effects of early intervention for socially withdrawn children evaluated with
single-subject methodology, and used PND as the indicator of effect size. This
indicator will have a range between 0% and 100%. The percentage of
non-overlapping data is the percentage of data points in the treatment phase over the
highest point of the distribution in the baseline phase (or below the lowest point of
data points in the baseline phase if the desirable behavior is expected to decrease after
the intervention is introduced). The PND approach was then further applied by
Behavior analysts to synthesize the effect sizes of other variables. (Scruggs,
Mastropieri, Cook, and Escobar, 1986; Scruggs, Mastropieri, Forness, and Kavale,
1988; Mathur, Kavale, Quinn, Forness, and Rutherford Jr.,1998).
The PND approach has the following advantages:
1. As it is a nonparametric approach, it can be free from the constraints of the
assumptions of parametric statistics.
2. It is easy to calculate directly from graphic displays. There is no need to recover the
original value of each data point. For the computation of parametric statistics, the
recovery of data values is necessary, as each data point in a graphic display is
precisely the original values of the data points.
3. It is easy to interpret qualitatively. A PND of 90% and higher indicates highly
effective, 70% to less than 90% represents moderate (or fair) effect, 50% to less
than 70% indicates mild or questionable effect, while below 50% is considered as
an ineffective treatment. This interpretation is based upon previous comparisons of
PND scores by visual analysis (Scruggs, et al. 1986).
4. PND scores have been found to be highly correlated with overall outcome ratings
of treatment effectiveness by experts (with Spearman correlation coefficient rs=0.68,
p<.001 or point-biserial r=0.69, p<.001). (Mastropieri & Scruggs, 1985-86).
White, Rusch, Kazdin, and Hartmann (1989) have raised a further potential
problem regarding the multiple baseline paradigm while calculating the PND. They
contend that when changes in one baseline result in changes in another baseline, such
an effect indicates that the baselines are not independent; therefore the calculated
effect sizes cannot be regarded as independent of the others. This type of no
independence could interfere with the drawing of conclusions about the overall
effectiveness of an intervention.
However this problem does not seem so detrimental, because two important
recommendations for conducting single-case experimental designs are strictly
1. Baseline measurement should be continued until a stable pattern emerges (Hersen
& Barlow, 1976, p.74).
2. In a multiple baseline design, a basic assumption is that the targeted behaviors are
independent from one another. The researcher should be assured that the treatment
in one baseline is effective while the rate of untreated behavior in other baselines
remains relatively constant. A similar requirement is in place when the
multiple-baseline is not across behaviors, but across settings or subjects (Hersen &
Barlow, 1976, p.226).
If there is a failure in the design of the research to follow these two rules, claims
made on the basis of such research would probably be seen as invalid.
However the PND approach has crucial drawback.
1. If some data points in the baseline phase have reached ceiling (or floor, if the
desirable behavior is expected to decrease after the introduction of treatment) level,
then the PND scores will be 0%, although by visual inspection the treatment effect
did exist. In the reality it is not unusual to find data points reaching the ceiling or
floor level in the graphic displays of intra-subject researches (for example, Koegel
& Frea, 1993).
2. It might be expected that in the second baseline phase, the treatment effect noted in
phase but become gradually extinct, and the curve in the second treatment phase
would also rise progressively. There would therefore be an orthogonal slope change
in the second pair of baseline-treatment phases (Scruggs, et al., 1987, p.29). In this
case, the PND scores of the second treatment phase would be greatly
underestimated.
In this regard the PND approach would run the risk of making a Type Ⅱ error, i.e.,
accepting the false null hypothesis. In order to improve these shortcomings, the
present author proposes a PEM (percentage of data points exceeding the median of
the previous baseline) approach.
The null hypothesis of the PEM approach is that if the treatment has no effect, the
data points in the treatment phase will fluctuate up and down around the middle line.
The data points have 50% of chance of being above and 50% of being below the
middle line.
The present investigation is to compare the validity of PND with that of PEM. The
validity criterion is the effectiveness judgment of the original author/s of each article
in the meta-analysis. The correlation between the PND scores and the ratings of
effectiveness judgment of the original author/s, and the correlation between PEM
scores and ratings of effectiveness judgment of the original author/s will be compared.
The PEM score has a range of ±1. One can compute one PEM score from each pair
of baseline-treatment phases. The PEM score has the same meaning as the effect size.
One can further calculate the average effect size of each article.
In the presence of ceiling or floor or data points in the baseline, as shown in
Figure 1, the PEM approach is capable of computing the PEM scores and reflect the
effect size while the PND approach can not.
However in the presence of orthogonal slope in the baseline-treatment pair after the
first treatment phase, the PEM could only show an improvement halfway. Scruggs &
Mastropieri (1998) have noted that this problem has rarely been encountered in the
research literature. It is not unreasonable to expect that treatment effect might
maintain into the second baseline, especially when the dependant variable is related to
ability, such as in accuracy of tasks completed. In such cases the researcher usually
employs a multiple-baseline design instead of a reversal design. The present
investigation will count the percentage of baseline-treatment pairs showing
orthogonal slope changes after the first treatment phase.
In order to demonstrate how can the PEM approach be applied in the performance
of a quantitative synthesis of single-subject experimental researches, researches on
self-control treatment were analyzed to provide an example.
of the type A behavior pattern with a multiple baseline design across three subjects, all
self employed women. The independent variable was no work or reading during and
after a meal and the Subjects had to self-record the number of minutes of eating and
relaxing per meal. This treatment resulted in the increase of eating and relaxing time
per meal from 18.3, 23.6, and 25.2 minutes to 47.9, 56.0 and 61.0 in Subject 1, 2, and
3 respectively. These results were maintained at a 12-week follow-up and were
associated with a decrease in the severity of psychosomatic symptoms.
There has been extensive publication of research on assessment of the effect of
self-control on the undesirable behavior to be extinguished or the desirable behavior
to be reinforced. However so far, there is still no study synthesizing the overall
effectiveness of self-control investigated with single-case experimental designs.
Method
Procedures for Locating Studies
The single-subject researches on self-control used in this synthesis were obtained
through a computer-assisted search of the relevant databases, including EBSCOhost,
ERIC, and ProQuest. Descriptors included self-control, self-instruction, self-recording,
self-assessment, self-feedback, self-reinforcement, self-monitoring, and
self-management. Self-instruction, self-recording and self-reinforcement are
journals such as Journal of Applied Behavior Analysis; Behavior Modification;
Behavior Assessment; Behavior Therapy; and Behavior, Research and Therapy was
also conducted. Studies that meet the following criteria were included in this
synthesis:
1. Data of baseline and treatment phases of reversal or multiple-baseline design were
graphically displayed for individual subjects in a time series format enabling the
PND and PEM scores to be computed.
2. The study assessed the efficacy of self-control or one or more of its components.
Procedure for coding the study
Study characteristics.Variables in each of the following areas were coded:
1. Authors’ conclusion of overall effectiveness of treatment (2: effective, 1: partially
effective, or 0: not effective); such terms used by the original authors as slightly
increasing but overlapping with baseline; or increasing but not quite reaching the
norm; were coded as the treatment was partially effective.
2. Categorization of independent variables: Independent variables were divided into
four categories: (a) self-control, including more than two elements such as
self-instruction, self-monitoring, and self-reinforcement, synonymous terms are
aloud the instruction are attributed to this category), (c) monitoring (synonymous
terms are self-evaluation, self-recording, self-assessment, and self-checking), and (d)
self-reinforcement.
3. Categorization of dependent variables: Target behaviors were classified into four
categories: (a) promoting academic behaviors measured as accuracy (or proficiency,
grades, correct responses), (b) increasing academic behaviors measured as task
completed, (c) facilitating social desirable behaviors (on-task, appropriate behaviors,
attending, desirable peer interactions, communication skills, appropriate behaviors
of interveners, such as parents, teachers), and (d) modifying social undesirable
behavior (aggressive behavior, disruptive behaviors, drug abuse, inappropriate
communicative behaviors, off-task, self-stimulations, inappropriate behaviors of
intervener, left too early, absence, coming too late).
4. First pair of baseline-treatment phases or the pair after that. Generalization or
follow-up phase as well as treatment phase without immediate preceding baseline
phase was not included in the analysis.
Computation of treatment outcomes
scores of each pair of baseline-treatment phases. Treatment generalization and
follow-up phases with no immediately preceding baseline phase were excluded from
the calculation of PND and PEM scores as their effect might be contaminated by the
preceding phase.
Reliability. A student of doctoral program in education serving as a part-time
research assistant conducted the variable coding and calculation of PND as well as
PEM scores. The present author checked her work and the percentage of agreement
was counted. Disagreements were resolved by discussion.
Calculation of PEM. By computing the PEM scores, one needs only to draw a
horizontal middle line in the baseline phase. This horizontal middle line will hit the
middle point when the number of data points in the baseline phase is odd, and go
between the two middle points if the number of data points is even. This middle line
will stretch out horizontally to the treatment phase. Then the percentage of data points
of treatment phase above the middle line may be calculated. If the desired behavior is
expected to decrease after the treatment is introduced, then the PEM score will be the
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Insert Figure 1 about here
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Figure 1 demonstrates the method of calculating the PEM. First, draw a
horizontal line (median) of the baseline phase and then extend it to the treatment
phase. There are eight points over the median line. Therefore, the PEM is
9/11=81.81%. And the PND =0/11=0%.
Testing the significance of the average effect size. Because the effect size of each
article might be regarded as an independent observation, accordingly, it would be
plausible to employ a t-test to examine whether the overall mean effect size of all
articles used in the meta-analysis deviates from zero. The formula for calculating the
t-value is: t = N SD ES−.5 (1)
Where, ES is the average effect size, SD is the standard deviation of all effect sizes; N
is the number of effect sizes in a meta-analysis for single-case experimental
Results
From the total of 61 articles used for quantitative synthesis in the present study,
16 were sampled for the calculation of coding reliability. Percentage of agreement
between the present author’s coding and that of the research assistant was 83.65% for
the coding of original authors’ judgments, and 95.85% for the PND. But the reliability
of coding was catastrophic for the PEM. Owing to imprecise definitions given by the
present author, the assistant misunderstood the median of baseline phase as the middle
point of time series of baseline phase. The percentage of the agreement for coding for
PEM became complete after explanation. Most of the inconsistency in coding original
authors’ judgments on treatment effects was found in the category of moderate effect,
which was coded as 1, whereas noticeable effect (coded as 2) and little effect or no
improvement (coded as 0) showed little confusion. Altogether 659 pairs of
baseline-treatment phases were analyzed.
As the coding numbers of the judgments of original authors on the treatment effects
were of ordinal scale, the Spearman correlation was used to decide which method, the
PND or PEM, had a higher consonance with original researchers’ judgment on
treatment effect. The matrix of Spearman correlation coefficients between the
number of effect sizes in parentheses.
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Insert Table 1 about here
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Table 1 shows that PEM has a higher correlation with the original authors’
judgment than that of PND with original authors’ judgment, no matter whether it is
calculated with the sample of pairs of baseline-treatment phase or with sample of
articles having only one average value of effect size. This finding indicates that PEM
might be a more suitable indicator for the effect size of treatment in single subject
experimental designs.
PEM scores might not always be distributed normally, however violation of
normality would not cause serious consequence (Lindquist, 1956, p.82). Mean PEM
scores were used to test against 0.5 probability of fluctuating over and below the
median line of the preceding baseline phase to demonstrate whether the averaged
effect size of an independent variable is statistically significant.
The mean of 659 PEMs is .8685 with standard error = 0.009173. To test the
significance of effect size of self control, this mean was compared with 0.5 and a
t-value, t(658)=40.173, p<.001, was obtained. This result indicates that the null
of the preceding baseline phase, is rejected, i.e., the self-control training has positive
significant effect on the behaviors to be modified. The mean of 659 PNDs is .6051
with standard error =0.01537. Comparing this mean with 0 results in t(658)=39.379,
p<.001, which is similar to the result obtained by the PEM approach.
In order to respond to the critics that effect sizes in an article are not independent,
the effect sizes of each article are averaged to form a single average effect size. It was
found that the mean of 61 PEMs is .9029 with standard error = 0.01648. To test the
significance of average effect size (ES) of self control, the averaged effect size was
compared with 0.5, and a t-value, t(60)=24.443, p<.001 was obtained. This result
indicates that the null hypothesis that 50% of data points in the treatment phase would
be distributed above and the other 50% would distributed below the median of
preceding baseline phase is rejected. Therefore self-control training has positive
significant effect on the behaviors to be modified. The mean of 61 PNDs is 0.662 with
standard error =0.03361. A t-test, t(60)=19.823, p<.001, indicates also a significant
effect for self-control.
In noting the change in the orthogonal slope after the first treatment phase, only
two out of 61 articles had clear orthogonal slope changes in the second baseline phase.
Olympia, et al. (1994), and Student 4 in Figure 1 of Koegel & Koegel (1990).
There are 59 ABAB-designs contained in the present study. In order to investigate
whether the orthogonal slope change threats the effect size of the second
baseline-treatment pair, the effect size of the second pair was subtracted from that of
the first baseline-treatment pair. Then a t-test was applied to test whether the average
difference of the first and second pair was significantly different from zero. The result
was obtained that the average difference of the two pairs was –0.0267 for the original
author’s judgment (t (74) = -1.4, p= .159); the average difference was -.074 for PND,
with t (74) = 1.51, p= .135; and the average difference was .077 for PEM, with t
(74)= .255, p= .80. The minus sign of average difference indicates that the effect size of
the second pair is higher than that of the first one. All t-tests were not significant. This
finding manifests the fact that the problem of orthogonal slope change in the
ABAB-designs is not serious.
More specific breakdown of the effect of self-control by PEM, PND and original
authors’ judgments are given in Table 2.
Under the condition of unequal size, the heterogeneity of variance would cause
serious consequence (Scheffe, 1961), and it can be seen in Table 2 that the sizes of
subcategories are not equal. Accordingly, score differences by various study
Each subcategory of variable was only tested by means of a single group t-test to
demonstrate whether the mean score of that subcategory was statistically different
from 0.5 for PEM and 0 for PND.
Since there was no obvious discrepancy in the results, regardless of
baseline-treatment pair or article was used as unit of analysis, the N in Table 2
designates the number of baseline-treatment pair as the unit of analysis with the
exception of second line (with article as unit).
Independent Variables. Interventions were divided into four subcategories: (a)
self-control package, (b) self-instruction, (c) self-monitoring, and (d)
self-reinforcement. Interventions in four subcategories all had statistically significant
effect on the behaviors to be modified.
Dependent Variables. Target behaviors were divided into academic behaviors
(measured in performance in accuracy and work completed) and social behaviors
(measured in developing appropriate behaviors and in reducing inappropriate
behaviors). The effect sizes of treatment all reached a significant level (p< .001).
Setting. Intervention settings were classified as home, institution (including clinic and
various therapeutic centers, school), and other places (including company, community,
significant effect in all settings.
Interveners. Breakdown of PEM, PND, and original author’s judgment scores by
researcher, experimenter (including treatment provider, trainer, research assistant,
instructor), staff (including therapist, facilitator, teaching parent, counselor, clinician),
teacher (including swimming coach), and tutor (including peer teacher and home tutor)
revealed that all agents of treatment were creditable and shown to be successful in
implementing self-control treatment programs.
Subject Classifications. Subjects in the present study were classified as attention
deficit hyperactivity disorder, autism, brain injury, chronic alcoholic, emotional
disturbance, learning disability, mental retardation, and normal (including subjects
with normal IQ but having behavior problems, such as disruptive, behavior disorder,
pre-delinquent, socially isolated, and underachieving). With the exception of chronic
alcoholics, all subjects were trained successfully to be self-controlled. The experiment
with chronic alcoholics had only four cases. Contingent electrical shocks had a
temporary suppressing effect, but due to too few sample sizes, the effect was not
statistically significant.
Subject Age and Sex. Table 2 shows that training in self-control has a statistically
significant effect for males as well as females, and for different levels of ages ranging
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Insert Table 2 about here
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Discussion
Examining the results in Table 2, it can be found the PEM, PND and original
authors’ judgment have similar outcomes in the sense of statistical significance. The
display in Table 1 indicates that the PEM scores have a higher correlation with the
original authors’ judgment than PND scores do. Furthermore, PEM is free from the
fatal influence of the data point, which has reached the ceiling (or floor if the behavior
is undesirable and is to be reduced) in the baseline phase. This has been a source for
concern in the use of PND. Researches with results which have data point reaching
ceiling or floor in the baseline phase are found in Kissel, et al. (1983); Koegel, et al.
(1992); Stahmer & Schreibman (1992); Olympia, et al. (1994); Kern, et al. (2001);
Brigham, et al. (1985); Koegel & Frea (1993); Glomb & West (1990); Dunlap &
Dunlap (1989); Burgio, et al.(1983); Gumpel & Davis (2000)l Billings & Wasik
(1985); Burgio, et al. (1980); Wood, et al.(2002); Martin & Manno (1995); Blick &
Test (1987); Carr & Punzo (1993); Swanson (1981); Kern-Dunlap, et al. (1992);
Mckenizie & Rushall (1974); Wilson, et al. (1975). These two observationss lead the
synthesis for single-subject research.
The problem of non-independence of effect sizes mentioned by White, et al.
(1989) did not interfere with the drawing of conclusions about the treatment in the
present study. The first two rows in Table 2 reveal that using baseline-treatment phase
as a unit of analysis, which might have the potential problem of statistical
independence, had same conclusion as using article as a unit. Their means were
significantly different from 0 (in case of PND and original author’s judgment) or 0.5
(in case of PEM) with p< .001.
The present meta-analysis found that self-control training, either in the form of a
self-control package or in the form of single element of self-control, such as self -
instruction, self-monitoring, or self-reinforcement, had statistically significant effect
on all four categories of behaviors: (a) academic behaviors, which were measured in
accuracy, such as performance in spelling words, arithmetic, grade, reading, making
chef salad, emergency responses, science, special study, home works, and steps in
self-instruction, (b) academic behaviors, which were measured in work completed,
e.g., rate of completion in mathematics, verbalization of self-instruction, and printing
tasks, (c) socially desirable variables, e.g., on-task, appropriate conversation,
attending, desirable peer interactions, communicative skills (such as making
with residents, and (d) socially undesirable behaviors to be reduced including
inappropriate social communicative behavior, negative interaction, aggressive
behavior, disruptive behavior, off-task, alcoholic consumption, self-stimulation,
stereotypic behavior, absence, arriving too late, and leaving too early.
The results are consistent with the results of meta-analysis with
group-comparison data as samples (Baker, Swisher, Nadenichek, and Popowicz, 1984;
Stage and Quiroz, 1997). Baker, et al. (1984) found that training of self-instruction
could effectively reduce anxiety, and Stage and Quiroz (1997) concluded that
self-management training could diminish disruptive behaviors. Mean of effect size=
0.97, k=30, t=8.30, p< .01.
The sample of self-control articles analyzed in the present study is not final, as
the results of new research appear regularly in journals in the field of applied behavior
analysis. It is hoped that the PEM approach or another newly developed one can be
accepted for use in the quantitative synthesis of single-subject research in order that
the results of empirical research of single-subject studies can be more readily
consolidated as part of the body of knowledge in applied behavior science.
References
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Author note
1. This research was supported by grants from the National Science Council,
Taiwan (NSC91-2413-H-004-003). The assistance of part-time assistants, Miss Gao,
Yu-jing is appreciated. Correspondence concerning this article please address to
Hsen-hsing Ma, Department of Education, National Chengchi University, Wen-Shan
District (116), Chi-nan Road, Section 2, No. 64, Taipei City, Taiwan. Electronic mail
Table 1
Matrix of Spearman correlation coefficients between original authors’ judgment, PND, and PEM Judgment PND PEM Judgment _ 0.50*** 0.53*** (N=647) (N=647) PND 0.47*** _ 0.64*** (k=61) (N=659) PEM 0.61*** 0.70*** _ (k=61) (k=61)
Note. The correlation coefficients of the sample of pairs of baseline- and
treatment-phase are above the diagonal; that of the sample of articles each
having only one average effect size is below the diagonal. In the parentheses,
N is the number of pairs of baseline-treatment phase and k is the number of
articles. *** p< .001
Table 2
Effect size by study characteristics
Variable PEM PND Author's Judgment M SE b N t M SE N T M SE N t Overall effect With baseline-treat ment pair as unit 0.87 0.009 659 40.17*0.61 0.015 659 39.38* 1.67 0.026 647 65.25* With article as unit 0.9 0.016 61 24.44*0.67 0.034 61 19.82* 1.79 0.055 61 32.71* Intervention (independent variable) Self-control package 0.52 0.016 258 19.97*0.51 0.023 258 19.69* 1.57 0.043 251 36.94* Self-instruction 0.88 0.024 91 15.71*0.77 0.035 91 21.60* 1.77 0.065 91 27.40* Self-monitoring 0.4 0.012 301 33.34*0.64 0.021 301 29.54* 1.73 0.037 296 46.77* Self- reinforcement 0.9 0.059 9 7.07* 0.81 0.116 9 6.93* 1.56 0.176 9 8.85* Behavior (dependent variable) Academic behavior (accuracy) 0.89 0.015 221 25.89*0.68 0.026 221 26.22* 1.71 0.038 216 45.10* Academic behavior (work completed) 0.80 0.034 77 8.81* 0.49 0.042 77 11.69* 1.51 0.10 77 15.79*
completed) Social behavior (desirable) 0.88 0.013 266 28.79*0.6 0.024 266 25.30* 1.68 0.041 266 40.95* Social behavior (undesirable behavior reduced) 0.84 0.025 95 13.37*0.54 0.043 95 12.33* 1.72 0.067 88 25.79* Setting Home 0.98 0.009 33 54.88*0.91 0.036 33 25.28* 2 0 33 a Institution 0.91 0.023 147 14.18*0.49 0.032 147 14.99* 1.54 0.065 147 23.67* School 0.88 0.011 416 34.03*0.64 0.019 416 33.21* 1.65 0.032 404 51.43* Other places 0.84 0.031 51 11.15*0.48 0.052 51 9.27* 1.98 0.02 51 101.0* Subject age Below 7 years old 0.91 0.051 15 7.95* 0.54 0.114 15 4.73* 1.6 0.214 15 7.48* 7-12 years old 0.86 0.013 367 28.03*0.59 0.02 367 30.02* 1.56 0.037 362 40.92* 13-15 years old 0.88 0.025 104 15.11*0.62 0.042 104 14.89* 1.87 0.048 97 39.05* 16-18 years old 0.89 0.04 32 9.64* 0.58 0.081 32 7.11* 2 0 32 a Over 18 years old 0.88 0.019 123 19.68*0.64 0.036 123 17.58* 1.74 0.055 123 31.54* Subject Sex Female 0.88 0.016 190 23.09*0.63 0.029 190 22.25* 1.7 0.05 187 34.35* Male 0.88 0.013 323 30.00*0.6 0.022 323 27.35* 1.7 0.037 321 46.01* Subject Classification
Attention deficit hyperactivity disorder 0.93 0.02 16 21.95*0.66 0.087 16 7.63* 1.81 0.1 16 17.99* Autism 0.92 0.023 37 18.46*0.57 0.073 37 7.92* 1.86 0.057 37 32.73* Brain injury 0.96 0.027 16 17.00*0.94 0.035 8 26.83* 2 0 16 a Chronic alcoholics 0.83 0.118 4 2.75 0.56 0.214 4 2.64 1 0 4 a Emotional disturbance 0.89 0.032 66 12.08*0.68 0.051 66 13.36* 1.83 0.06 66 30.83* Learning disability 0.88 0.018 152 20.81*0.59 0.031 152 19.03* 1.54 0.066 147 23.41* Mental retardation 0.83 0.025 128 13.08*0.65 0.034 128 18.84* 1.69 0.063 128 26.59* Normal 0.86 0.015 238 24.25*0.55 0.026 238 21.65* 1.65 0.04 231 41.33* Intervener Researcher 0.83 0.022 12615.02* 0.5 0.037 12613.70* 1.48 0.059 126 24.88* Experimenter 0.91 0.018 127 23.22* 0.73 0.033 12722.38* 1.87 0.041 127 45.67* Staff 0.82 0.027 10011.90* 0.49 0.037 100 13.21* 1.64 0.07 100 23.30* Teacher 0.87 0.015 26425.43* 0.58 0.024 26424.46* 1.63 0.045 252 36.29* Tutor 0.99 0.071 2869.00* 0.97 0.019 2850.42* 2 0 28 a Note. a
because standard error is 0, t value cannot be calculated
b
SE=Standard error * p<.001
Figure caption
75 80 85 90 95 100 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Sessions P er ce nta ge of oc cu re nc e of be ha vior
Appendix
Autho r(year ) Indepen dent variable( definitio n) dependent variable Subjec t Ag e Se x Characte ristic Interve ner Setting Author s' judge ments of effecti veness Codi ng of judg emen ts into score s Effec tiven ess(P ND) Effec tiven ess(P EM) Ph ase De sig n Billin gs and Wasik (1985 ) Self-inst ruction Social desirable: daily percentages of attending behavior Brian NA : 4'2 -4' 10 M Normal: behavior problem s (at least 25% off-task behavior ) Teache r School Failed to produc e any major effects 0.0 0.33 0.67 1R Billin gs and Wasik (1985 ) Self-inst ruction Social desirable: daily percentages of attending behavior Elliott NA : 4'2 -4' 11 M Normal: behavior problem s (at least 25% off-task behavior ) Teache r School No effect 0.0 0.25 1.00 2R Billin gs and Wasik (1985 ) Self-inst ruction Social desirable: daily percentages of attending behavior John NA : 4'2 -4' 12 M Normal: behavior problem s (at least 25% off-task behavior ) Teache r School No effect 0.0 0.00 1.00 1RBlick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S1 15 yr 9 mo M LD Teache r School : classro om Increas ed 2 1 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S2 16 yr 4 mo F LD Teache r School : classro om Increas ed 2 1 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S3 15 yr 4 mo F LD Teache r School : classro om Increas ed 2 0.5 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S4 17 yr M LD Teache r School : classro om Increas ed 2 0.5 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S5 17 yr M LD Teache r School : classro om Increas ed 2 1 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S6 16 yr 6 mo M LD Teache r School : classro om Increas ed 2 0 0.5 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S7 15 yr 5 mo M Emotion ally handicap ped Teache r School : classro om Increas ed 2 0.5 0.5 1M Blick and Test Self-mo nitoring: attention Social desirable: academic S8 17 yr 1 M LD Teache r School : classro Increas ed 2 0 1 1M
(1987 ) engagement mo om Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S9 17 yr 1 mo M LD Teache r School : classro om Increas ed 2 0 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S10 16 yr 8 mo M Educable mentally handicap ped Teache r School : classro om Increas ed 2 0 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S11 18 yr 2 mo M Educable mentally handicap ped Teache r School : classro om Increas ed 2 0 1 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement S12 18 yr M LD Teache r School : classro om Increas ed 2 0 0.5 1M Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement Class A S1-S4 LD teacher school: classro om increas ed 2 1 1 1M Blick and Test (1987 ) self-mon itoring: attention social desirable: academic engagement Class B S5-S8 3 with learning disabled and 1 with emotion ally handicap ped Teache r School : classro om Increas ed 2 0.5 1 1M
Blick and Test (1987 ) Self-mo nitoring: attention Social desirable: academic engagement Class C S9-S1 2 2 with learning disabled a and 2 with educable mentally handicap ped Teache r School : classro om Increas ed 2 0 1 1M Borns tein and Quevi llon (1976 ) Self-inst ruction Social desirable: on-task behaviors Scott 4 M Normal: highly disruptiv e and undesira ble classroo m behavior Teache r School Immed iate and dramat ic increas e(10.4 %-82.3 %) 2.0 1.00 1.00 2R Borns tein and Quevi llon (1976 ) Self-inst ruction Social desirable: on-task behaviors Rod 4 M Normal: highly disruptiv e and undesira ble classroo m behavior Teache r School Immed iate and dramat ic increas e(14.6 %-70.8 %) 2.0 1.00 1.00 1R Borns tein and Quevi llon (1976 ) Self-inst ruction Social desirable: on-task behaviors Tim 4 M Normal: highly disruptiv e and undesira ble classroo m behavior Teache r School Immed iate and dramat ic increas e(10%-77.8%) 2.0 1.00 1.00 2R
Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S1 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak,im mature or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School Declin e 2.0 0.00 0.00 2R Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S2 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor Teache r School 0.0 0.17 0.67 1R
classroo m disruptio ns. Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S3 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School . 0.33 0.33 2R Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S4 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak,im mature or impulsiv e, and speaking without permissi on, being Teache r School . 0.17 0.83 1M
out of seat and other minor classroo m disruptio ns. Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S5 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak,im mature or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School Remai ned periodi cally high 0.0 0.00 0.17 1M Brigh am, Hopp er, Hill, Arma s, and News om Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S6 NA : sixt h-, sev ent h-, and eig NA Normal: academi cally weak,im mature or impulsiv e, and speaking Teache r School Immed iately droppe d to zero 2.0 1.00 1.00 1M
(1985 ) hth -gr ade without permissi on, being out of seat and other minor classroo m disruptio ns. Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S7 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak,im mature or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School . 0.00 0.50 1M Brigh am, Hopp er, Hill, Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S8 NA : sixt h-, sev NA Normal: academi cally weak,im mature Teache r School . 0.00 0.50 1M
Arma s, and News om (1985 ) ent h-, and eig hth -gr ade or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S9 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School . 0.00 0.50 1M
Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S10 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School Declin e 2.0 0.00 0.33 1M Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S11 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor Teache r School . 0.00 0.67 1M
classroo m disruptio ns. Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior (detentions) S12 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak, immatur e or impulsiv e, and speaking without permissi on, being out of seat and other minor classroo m disruptio ns. Teache r School . 0.00 0.17 1M Brigh am, Hopp er, Hill, Arma s, and News om (1985 ) Self-cont rol: self-man agement program Social undesirable: disruptive behavior(dete ntions) S13 NA : sixt h-, sev ent h-, and eig hth -gr ade NA Normal: academi cally weak,im mature or impulsiv e, and speaking without permissi on, being Teache r School Declin e 2.0 0.00 0.50 1M
out of seat and other minor classroo m disruptio ns. Brode n, Hall, and Mitts (1971 ) Self-mo nitoring: self-reco rding Social desirable: study behavior (attending to a teacher-assign ed task) Liza 13F Normal Couns elor School : classro om Signifi cant change (30%-78%) 2.0 1.00 1.00 1M Brode n, Hall, and Mitts (1971 ) Self-mo nitoring: self-reco rding Social desirable: study behavior (attending to a teacher-assign ed task) Liza 13F Normal Couns elor School : classro om Increas ed(27 %-80 %) 2.0 0.89 1.00 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on math task Judy 9F MR Experi menter School : classro om High freque ncy 2.0 1.00 1.00 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on math task Angie 11F MR Experi menter School : experi mental room High freque ncy 2.0 0.92 0.92 1M
Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on math task Judy 9F MR Experi menter School : classro om Positiv e effect 2.0 0.31 0.31 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on math task Angie 11F MR Experi menter School : classro om Positiv e effect 2.0 0.88 0.88 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on phonics task Judy 9F MR Experi menter School : classro om No effect 0.0 0.00 0.00 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on phonics task Angie 11F MR Experi menter School : classro om No effect 0.0 0.05 0.05 1M Burgi o, Whit man and Johns Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on printing task Judy 9F MR Experi menter School : experi mental room High freque ncy 2.0 1.00 1.00 1M
on (1980) Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on printing task Angie 11F MR Experi menter School : experi mental room High freque ncy 2.0 0.92 0.92 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on printing task Judy 9F MR Experi menter School : classro om Positiv e effect 2.0 0.63 0.63 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Academic: self-instructio nal verbalization on printing task Angie 11F MR Experi menter School : classro om Positiv e effect 2.0 0.95 0.95 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Judy 9F MR Experi menter School : experi mental room Genera lly low 0.0 0.00 0.84 1M Burgi o, Whit Self-inst ruction: self-instr Social undesirable: off-task Judy 9F MR Experi menter School : experi Genera lly low 0.0 0.00 0.72 1M
man and Johns on (1980) uctional package behavior mental room Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Angie 11F MR Experi menter School : experi mental room Genera lly low 0.0 0.08 0.83 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Angie 11F MR Experi menter School : experi mental room Genera lly low 0.0 0.00 0.83 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Judy 9F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 0.81 1.00 1M Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Judy 9F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 1.00 1.00 1M
Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Judy 9F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 0.90 1.00 1R Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Angie 11F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 0.43 0.96 1R Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Angie 11F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 0.38 0.76 2R Burgi o, Whit man and Johns on (1980) Self-inst ruction: self-instr uctional package Social undesirable: off-task behavior Angie 11F MR Experi menter School : classro om Gradua l but marke d decrea se 2.0 0.30 0.35 1R