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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

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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.

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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

(4)

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

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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

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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

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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

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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

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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

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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

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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.

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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.

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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

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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

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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

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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

---

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

(18)

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

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number of effect sizes in parentheses.

---

Insert Table 1 about here

---

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

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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.

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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

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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,

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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

---

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

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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

(26)

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.

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References

References marked with an asterisk indicate studies included in the meta-analysis.

Baker, S. B., Swisher, J. D., Nadenichek, P. E., & Popowicz, C. L. (1984). Measured

effects of primary prevention strategies. Personnel and Guidance Journal, April,

459-164.

*Billings, D. C., and Wasik, B. H. (1985). Self-instructional training with

preschoolers: An attempt to replicate. Journal of Applied Behavior Analysis, 18,

61-67.

*Blick, D. W., and Test, D. W. (1987). Effects of self-recording on high-school

students' on task behavior. Learning Disability Quarterly, 10, 203-213.

*Bornstein, P. H., and Quevillon, R. P. (1976). The self-instructional package on

overactive preschool boys. Journal of Applied Behavior Analysis, 9, 179-188.

*Brigham, T. A., Hopper, C., Hill, B., Armas, A. D., and Newsom, P. (1985). A

self-management program for disruptive adolescents in the school: A clinical

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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

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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

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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*

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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

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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

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Figure caption

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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

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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 1R

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Blick 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

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(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

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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

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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

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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

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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

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(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

(55)

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

(56)

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

(57)

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

(58)

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

(59)

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

(60)

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

(61)

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

(62)

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

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