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An improved effect size for single-case research: nonoverlap of all pairs.

Parker, Richard I., Vannest, Kimberly·2009·Behavior Therapy

DOI 10.1016/j.beth.2008.10.006

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Abstract

Nonoverlap of All Pairs (NAP), an index of data overlap between phases in single-case research, is demonstrated and field tested with 200 published AB contrasts. NAP is a novel application of an established effect size known in various forms as Area Under the Curve (AUC), the Common Language Effect Size (CL), the Probability of Superiority (PS), the Dominance Statistic (DS), Mann-Whitney's U, and Sommers D, among others. NAP was compared with 3 other non-overlap-based indices: PND (percent of nonoverlapping data), PEM (percent of data points exceeding the median), and PAND (percent of all nonoverlapping data), as well as Pearson's R(2). Five questions were addressed about NAP: (a) typical NAP values, (b) its ability to discriminate among typical single-case research results, (c) its power and precision (confidence interval width), (d) its correlation with the established effect size index, R(2), and (e) its relationship with visual judgments. Results were positive, the new index equaling or outperforming the other overlap indices on most criteria.

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BackgroundMethod
An Initial Development and Evaluation of a Culturally Responsive Police Interactions Training for Black Adolescents with Autism Spectrum Disorder
Davenport, M. A., Romero, M. E., Lewis, C. D., Lawson, T., Ferguson, B., Stichter, J., & Kahng, S. (2023) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-021-05181-8 · Cited by 11
“NAP is calculated by determining the frequency of overlap between the baseline and intervention data points (Parker & Vannest, 2009; Brossart et al., 2014).”
BackgroundMethodInfluential
The effect of graph standardization on intervention evaluation of practitioner‐created graphs
Lewis, H. H. J., Radley, K. C., & Dart, E. H. (2021) · Psychology in the Schools · doi:10.1002/pits.22621 · Cited by 11
A proposal for the assessment of replication of effects in single‐case experimental designs
Manolov, R., Tanious, R., & Fernández‐Castilla, B. (2022) · Journal of Applied Behavior Analysis · doi:10.1002/jaba.923 · Cited by 11
“…each A-B comparison could be: (a) empirically based interpretative benchmarks for quantifications of effect (e.g., Harrington & Velicer, 2015; Parker & Vannest, 2009); (b) subjective evaluation of the participants or their significant ones, as part of the assessment of social validity…”
Method
Evidence-Based Applied Behavior Analysis (ABA) Autism Treatments: An Overview of Comprehensive and Focused Meta-Analyses
Ortega, J. V., Pereira, A. P.-B., & Tarifa‐Rodríguez, A. (2022) · Autism and child psychopathology series · doi:10.1007/978-3-030-88538-0_27 · Cited by 13
Brief Report: Telehealth Music-Enhanced Reciprocal Imitation Training in Autism: A Single-Subject Feasibility Study of a Virtual Parent Coaching Intervention
Liu, T., Martinez-Torres, K. A., Mazzone, J., Camarata, S., & Lense, M. D. (2023) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-023-06053-z · Cited by 11
“NAPs in the range of 0 to 0.65 are considered weak effects, 0.66 to 0.92 is a medium effect, and 0.93 to 1.0 is a strong effect (Parker & Vannest, 2009).”
Influential
EVALUATING THE EFFECTS OF ON-TASK IN A BOX AS A CLASS-WIDE INTERVENTION
Battaglia, A. A., Radley, K. C., & Ness, E. J. (2015) · Psychology in the Schools · doi:10.1002/pits.21858 · Cited by 11
“NAP scores were calculated using the Parker and Vannest (2009) procedures.”
BackgroundMethod
Internet delivered transdiagnostic treatment with telephone support for pain patients with emotional comorbidity: a replicated single case study
Wurm, M., Strandberg, E. K., Lorenz, C., Tillfors, M., Buhrman, M., Holländare, F., & Boersma, K. (2017) · Internet Interventions · doi:10.1016/j.invent.2017.10.004 · Cited by 11
“NAP is a nonparametric quantitative approach comparing every measurement in phase A with every measurement in phase B to determine overlap, non-overlap or tie (Parker and Vannest, 2009).”
BackgroundMethodInfluential
Using Video Self-Modeling as a Small Group Reading Fluency Intervention for Elementary School Students
Wu, S., Gadke, D. L., & Stratton, K. K. (2018) · Journal of Applied School Psychology · doi:10.1080/15377903.2018.1443984 · Cited by 11
“According to Parker and Vannest (2009), NAP determines the amount of overlap between baseline and treatment phases or between two intervention conditions within a phase.”
BackgroundMethodInfluential
Acceptance and Commitment Therapy to Promote Value Attainment Among Individuals with overweight: A multiple baseline evaluation
Wallin, E., Parling, T., Weineland, S., & Dahl, J. C. (2018) · Journal of Contextual Behavioral Science · doi:10.1016/j.jcbs.2018.08.007 · Cited by 11
Tek Denekli Deneysel Çalışmalarda Etki Büyüklüğü Hesaplaması: Regresyona Dayalı Olmayan Yöntemlerin İncelenmesi
Şen, N., & Şen, S. (2019) · Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi · doi:10.21031/epod.419625 · Cited by 11
Generalizing the Effects of Group Contingencies Across Instructional Settings for Students With Emotional and Behavioral Disorders
Ramirez, L. H., Hawkins, R. O., Collins, T. A., Ritter, C., & Haydon, T. F. (2019) · School Psychology Review · doi:10.17105/spr-2017-0122.v48-1 · Cited by 11
“NAP is a nonparametric test to evaluate data overlap between baseline/withdrawal and treatment phases and is appropriate for single case research designs (Parker & Vannest, 2009).”
BackgroundMethodInfluential
Translations in Stimulus–Stimulus Pairing: Autoshaping of Learner Vocalizations
da Silva, S. P., & Williams, A. M. (2019) · Perspectives on Behavior Science · doi:10.1007/s40614-019-00228-9 · Cited by 11
“…assessed 13 peer-reviewed, published experiments and found an overall moderate effect (using nonoverlap of all pairs, NAP, effect-size estimations; see Parker & Vannest, 2009) for the use of SSP to increase vocalizations in the eight published studies for which effect sizes could be estimated.”
Method
Assessing Consistency in Single-Case Data Features Using Modified Brinley Plots
Manolov, R., & Tanious, R. (2020) · Behavior Modification · doi:10.1177/0145445520982969 · Cited by 11
“…is called CONEFF and entails computing five effect size measures: a standardized mean difference, difference in ordinary least squares regression slopes, a variance ratio, the Nonoverlap of all pairs (Parker & Vannest, 2009) and the immediate treatment effect (Michiels & Onghena, 2019).”
Method
Comparing the Minimum Celeration Line and the Beat Your Personal Best Goal-Setting Approaches During the Mathematical Practice of Students Diagnosed with Autism
Vostanis, A., Padden, C., McTiernan, A., & Langdon, P. E. (2021) · Journal of Behavioral Education · doi:10.1007/s10864-021-09432-7 · Cited by 11
A precorrection intervention to teach behavioral expectations to young children
Wahman, C. L., & Anderson, E. J. (2021) · Psychology in the Schools · doi:10.1002/pits.22531 · Cited by 11
Using the VA Framework to Teach Algebra to Middle School Students With High-Incidence Disabilities
Bone, E. K., Bouck, E. C., & Smith, J. P. (2021) · Journal of Special Education Technology · doi:10.1177/01626434211019388 · Cited by 11
“Scores between 0.93 to 1 were considered a large effect, 0.66 to .92 a medium effect, and 0 to 0.65 a small effect (Parker et al., 2009).”
BackgroundInfluential
Children with handwriting difficulties: developing orthographic knowledge of alphabet-letters to improve capacity to write alphabet symbols
Mathwin, K., Chapparo, C., & Hinitt, J. (2021) · Reading and Writing · doi:10.1007/s11145-021-10207-9 · Cited by 11
Identifying Mechanisms of Change
Riley, A. R., & Gaynor, S. T. (2014) · Behavior Modification · doi:10.1177/0145445514530756 · Cited by 12
Impact of within-case variability on Tau-U indices and the hierarchical linear modeling approach for multiple-baseline design data: A Monte Carlo simulation study
Fingerhut, J., Xu, X., & Moeyaert, M. (2021) · Evidence-Based Communication Assessment and Intervention · doi:10.1080/17489539.2021.1933727 · Cited by 12
“In the past, researchers have used benchmarks to determine if an intervention effect is present (e.g. Parker & Vannest, 2009; Vannest & Ninci, 2015).”
Background
Examining the Generalization of a Combined Independent and Interdependent Group Contingency for Students With Emotional and Behavioral Disorders
Hawkins, R. O., Collins, T. A., Ramirez, L. H., Murphy, J. M., & Ritter, C. (2019) · Behavioral Disorders · doi:10.1177/0198742919888758 · Cited by 10
“Suggested NAP interpretations include 0 to .65 as weak effects, .66 to .92 as medium effects, and .93 to 1.0 as strong effects (Parker & Vannest, 2009).”
BackgroundMethodInfluential
Clues: Using Generative Strategies to Improve the Science Vocabulary of Secondary English Learners With Reading Disabilities
Helman, A. L., Dennis, M. S., & Kern, L. (2020) · Learning Disability Quarterly · doi:10.1177/0731948720929005 · Cited by 10
“The overall TauU for the par ticipants on SU was 1.0, indicating a large effect for the intervention package (Parker & Vannest, 2009).”
BackgroundMethodInfluential
Modified Ride-on Car Intervention for Children With Profound Intellectual and Multiple Disabilities: A Case Series
Sloane, B. M., Case, F., Quinn, E. D., Sanford-Keller, H., & Logan, S. W. (2023) · Pediatric Physical Therapy · doi:10.1097/pep.0000000000001002 · Cited by 10
In-season autoregulation of one weekly strength training session maintains physical and external load match performance in professional male football players
Byrkjedal, P. T., Thunshelle, A., Spencer, M., Luteberget, L. S., Ivarsson, A., Vårvik, F. T., Lindberg, K., & Bjørnsen, T. (2023) · Journal of Sports Sciences · doi:10.1080/02640414.2023.2227536 · Cited by 10
“Effect sizes for NAP values are reported according to Parker and Vannest’s recommendations: 0–.65 = week effects, .66–.92 = moderate effects, .93–1.0 = large or strong effects (Parker & Vannest, 2009).”
MethodInfluential
The effects of rational emotive behavior therapy and motivational interviewing on emotions, automatic thoughts, and perceived performance of elite female volleyball players
Urfa, O., & Aşçı, F. H. (2023) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2023.102497 · Cited by 12
Speech-to-text intervention to support text production for students with intellectual disabilities
Sand, C., Svensson, I., Nilsson, S., Selenius, H., & Fälth, L. (2024) · Disability and Rehabilitation Assistive Technology · doi:10.1080/17483107.2024.2381785 · Cited by 10
“In this study, the NAP assessed the degree of data overlap between the baseline and intervention phases [31].”
A meta-analysis of technology-based interventions for elementary students with reading difficulties
Alqahtani, S. S. (2024) · Humanities and Social Sciences Communications · doi:10.1057/s41599-024-04159-y · Cited by 10
“To interpret the Tau-U scores, 0.93 and above is considered a large effect size, 0.66 to 0.92 is moderate, and 0.66 and below is weak (Parker and Vannest, 2009; Rispoli et al., 2013).”
Influential
Brief intensive EMDR therapy for PTSD in adults with mild intellectual disability or borderline intellectual functioning and behavioural problems: a multiple baseline design study
Versluis, A., de Jongh, A., Mevissen, L., Schuengel, C., Bakkum, L., & Didden, R. (2025) · European Journal of Psychotraumatology · doi:10.1080/20008066.2025.2495642 · Cited by 10
Brothers as Playmates for Their Siblings with Developmental Disabilities: A Multiple-Baseline Design Study
Tsao, L. (2019) · Child & Youth Care Forum · doi:10.1007/s10566-019-09534-4 · Cited by 10
Treatment Burst Data Points and Single Case Design Studies: A Bayesian N-of-1 Analysis for Estimating Treatment Effect Size
Barnard-Brak, L., Richman, D., & Watkins, L. (2020) · Perspectives on Behavior Science · doi:10.1007/s40614-020-00258-8 · Cited by 11
“We chose not to use the exact percent of nonoverlapping data calculation (Scruggs & Mastropieri, 2013) or nonoverlapping of all pairs (NAP); Parker & Vannest, 2009) because these measures do not account for the serial dependency or autocorrelated nature of the data points.”
Method
Assessing generalizability and variability of single-case design effect sizes using two-stage multilevel modeling including moderators
Moeyaert, M., & Yang, P.-P. (2021) · Behaviormetrika · doi:10.1007/s41237-021-00141-z · Cited by 10
Wisdom enhancement and life skills to augment CBT outcomes for depression in later life: a series of N-of-1 trials
Kadri, A., Leddy, A., Gracey, F., & Laidlaw, K. (2022) · Behavioural and Cognitive Psychotherapy · doi:10.1017/s1352465822000224 · Cited by 10
“Tau-U statistic was used for cases with significant baseline trend (Parker and Vannest, 2009; Parker et al., 2011).”
Method
Comparing the percentage of non-overlapping data approach and the hierarchical linear modeling approach for synthesizing single-case studies in autism research
Heyvaert, M., Saenen, L., Maes, B., & Onghena, P. (2015) · Research in Autism · doi:10.1016/j.rasd.2014.12.002 · Cited by 10
“However, PND calculation can be complicated when assessing more compacted SCED graphs with more overlap between baseline and intervention data points (Parker & Vannest, 2009).”
BackgroundMethod
Assigning and combining probabilities in single-case studies.
Manolov, R., & Solanas, A. (2012) · Psychological Methods · doi:10.1037/a0029248 · Cited by 10
Improving oral reading fluency in middle‐school students: A comparison of repeated reading and listening passage preview
Powell, M. B., & Gadke, D. L. (2018) · Psychology in the Schools · doi:10.1002/pits.22184 · Cited by 10
Measuring the Academic Outcomes of iPads for Students with Autism: a Meta-Analysis
Larwin, K. H., & Aspiranti, K. B. (2019) · Review Journal of Autism and Developmental Disorders · doi:10.1007/s40489-019-00165-y · Cited by 10
Otizm Spektrum Bozukluğu Olan Bireylere Matematik Becerilerini Öğretimi: Tek-Denekli Araştırmalarda Betimsel ve Meta Analiz
Aydın, O., & Tekin-İftar, E. (2019) · Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi · doi:10.21565/ozelegitimdergisi.521232 · Cited by 10
Evaluation of the Effectiveness of a Novel Brain-Computer Interface Neuromodulative Intervention to Relieve Neuropathic Pain Following Spinal Cord Injury: Protocol for a Single-Case Experimental Design With Multiple Baselines
Hesam‐Shariati, N., Newton-John, T. R. O., Singh, A. K., Cortes, C., Do, T., Craig, A. R., Middleton, J. W., Jensen, M. P., Trost, Z., Lin, C., et al. (2020) · JMIR Research Protocols · doi:10.2196/20979 · Cited by 10
“Nonoverlap methods do not rely on means or medians, but rather consider the individual values of all data points in pairwise comparisons across phases [62].”
Exploring the use of the Cognitive Orientation to daily Occupational Performance approach (CO-OP) with children with executive functions deficits after severe acquired brain injury: A single case experimental design study
Lebrault, H., Chavanne, C., Abada, G., Latinovic, B., Varillon, S., Bertrand, A.-F., Oudjedi, E., Krasny‐Pacini, A., & Chevignard, M. (2021) · Annals of Physical and Rehabilitation Medicine · doi:10.1016/j.rehab.2021.101535 · Cited by 10
Increasing Single‐Word Requests to Multiword Requests in Children with Autism and Related Disabilities
Yosick, R. N., Muskat, L. R., Bowen, C. N., Delfs, C. H., & Shillingsburg, M. A. (2015) · Behavioral Interventions · doi:10.1002/bin.1434 · Cited by 10
“…to quantify results from single-subject research to obtain an effect size (e.g., Ma, 2006; Parker, Hagan-Burke, & Vannest, 2007; Manolov, Solanas, Sierra, & Evans, 2011), and NAP has consistently performed favorably against other nonoverlap indices (Parker & Vannest, 2009; Manolov et al., 2011).”
BackgroundMethodResultInfluential
A Single Case Study of the Impact of Policy Changes on Identification for Gifted Programs
Warne, R. T., & Price, C. J. (2016) · journal for the education of the gifted · doi:10.1177/0162353215624159 · Cited by 10
“It also is preferable to parametric effect sizes, such as R2, because data from an ABA rarely meet the assumptions of parametric statistics (Parker & Vannest, 2009), especially with the small number of data points in our study.”
BackgroundMethodInfluential
On-Task in a Box: An evaluation of a package-ready intervention for increasing levels of on-task behavior and academic performance.
King, B., Radley, K. C., Jenson, W. R., & O’Neill, R. (2016) · School Psychology Quarterly · doi:10.1037/spq0000162 · Cited by 10
Effects of Consultation on Professional Learning Communities
Preast, J. L., & Burns, M. K. (2018) · Journal of Educational and Psychological Consultation · doi:10.1080/10474412.2018.1495084 · Cited by 10
“NAP provides an accurate and efficient measure of effect size for single-case design studies (Parker & Vannest, 2009).”
Method

Authors: Parker, R. I., & Vannest, K.
Affiliations: Texas A&M University (US)
Corresponding author: Parker, Richard I.
ORCID: Vannest, Kimberly
Venue: Behavior Therapy
Publisher: Elsevier BV
Published: 2009-12
Volume: 40
Issue: 4
Pages: 357-367
ISSN: 0005-7894 (ISSN-L)
DOI: 10.1016/j.beth.2008.10.006
OpenAlex: W2028628292
Cited by: 1,126
References: 65
Citations by year: 2026: 61 · 2025: 95 · 2024: 85 · 2023: 97 · 2022: 99 · 2021: 90 · 2020: 87 · 2019: 81 · 2018: 86 · 2017: 84 · 2016: 69 · 2015: 57 · 2014: 49 · 2013: 30 · 2012: 35
FWCI: 12.23
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Behavior Therapy (publishedVersion)
PubMed (publishedVersion)
Topics: Social Sciences › Psychology › Developmental and Educational Psychology › Behavioral and Psychological Studies
Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
Social Sciences › Psychology › Experimental and Cognitive Psychology › Psychology Research and Bibliometrics
Keywords: effect size, single subject research, data overlap, R-squared, visual assessment, confidence interval width, statistical power
MeSH terms: Humans, Models, Psychological, Probability, Psychology, Research Design, Confidence Intervals, Area Under Curve

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An improved effect size for single-case research: nonoverlap of all pairs.

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